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1
Slichter, Charles P. "NUCLEAR MAGNETIC RESONANCE AND THE BCS THEORY." International Journal of Modern Physics B 24, no. 20n21 (2010): 3787–813. http://dx.doi.org/10.1142/s0217979210056359.
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The author describes the inspiration for the experiment by Hebel and Slichter to measure the nuclear spin–lattice relaxation time in superconductors, the design considerations for the experiment, the surprising experimental results, their theoretical treatment using the Bardeen–Cooper–Schrieffer theory, and how comparing the nuclear relaxation results with those for ultrasound absorption confirmed the central idea of the BCS theory, the BCS pair wave function.
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Greenberg, O. W. "N-quantum approach to the BCS theory of superconductivity." Canadian Journal of Physics 72, no. 9-10 (1994): 574–77. http://dx.doi.org/10.1139/p94-073.
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A method of general applicability to the solution of second-quantized field theories at finite temperature is illustrated using the BCS (Bardeen–Cooper–Schrieffer) model of superconductivity. Finite-temperature field theory is treated using the thermo field-theory formalism of Umezawa and collaborators. The solution of the field theory uses an expansion in thermal modes analogous to the Haag expansion in asymptotic fields used in the N-quantum approximation at zero temperature. The lowest approximation gives the usual gap equation.
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García, L. A., and M. de Llano. "Entropy and heat capacity in the generalized Bose–Einstein condensation theory of superconductors." International Journal of Modern Physics B 33, no. 26 (2019): 1950311. http://dx.doi.org/10.1142/s0217979219503119.
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The new generalized Bose–Einstein condensation (GBEC) quantum-statistical theory starts from a noninteracting ternary boson-fermion (BF) gas of two-hole Cooper pairs (2hCPs) along with the usual two-electron Cooper pairs (2eCPs) plus unpaired electrons. Here we obtain the entropy and heat capacity and confirm once again that GBEC contains as a special case the Bardeen–Cooper–Schrieffer (BCS) theory. The energy gap is first calculated and compared with that of BCS theory for different values of a new dimensionless coupling parameter n/n[Formula: see text] where n is the total electron number density and n[Formula: see text] that of unpaired electrons at zero absolute temperature. Then, from the entropy, the heat capacity is calculated. Results compare well with elemental-superconductor data suggesting that 2hCPs are indispensable to describe superconductors (SCs).
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Pines, David. "SUPERCONDUCTIVITY: FROM ELECTRON INTERACTION TO NUCLEAR SUPERFLUIDITY." International Journal of Modern Physics B 24, no. 20n21 (2010): 3814–34. http://dx.doi.org/10.1142/s0217979210056360.
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I present an expanded version of a talk given at the Urbana symposium that celebrated the fiftieth anniversary of the publication of the microscopic theory of superconductivity by Bardeen, Cooper, and Schrieffer — BCS. I recall at some length, the work with my Ph.D. mentor, David Bohm, and my postdoctoral mentor, John Bardeen, on electron interaction in metals during the period 1948–55 that helped pave the way for BCS, describe the immediate impact of BCS on a small segment of the Princeton physics community in the early spring of 1957, and discuss the extent to which the Bardeen–Pines–Frohlich effective electron-electron interaction provided a criterion for superconductivity in the periodic system. I describe my lectures on BCS at Niels Bohr's Institute of Theoretical Physics in June 1957 that led to the proposal of nuclear superfluidity, discuss nuclear and cosmic superfluids briefly, and close with a tribute to John Bardeen, whose birth centennial we celebrated in 2008, and who was my mentor, close colleague, and dear friend.
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Wen, Hai-Hu. "Unconventional superconductivity after the BCS paradigm and empirical rules for the exploration of high temperature superconductors." Journal of Physics: Conference Series 2323, no. 1 (2022): 012001. http://dx.doi.org/10.1088/1742-6596/2323/1/012001.
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Abstract Superconducting state is achieved through quantum condensation of Cooper pairs which are new types of charge carriers other than single electrons in normal metals. The theory established by Bardeen-Cooper-Schrieffer (BCS) in 1957 can successfully explain the phenomenon of superconductivity in many single-element and alloy superconductors. Within the BCS scheme, the Cooper pairs are formed by exchanging the virtual vibrations of lattice (phonons) between two electrons with opposite momentum near the Fermi surface. The BCS theory has dominated the field of superconductivity over 64 years. Many superconductors discovered in past four decades, such as the heavy Fermion superconductors, cuprates, iron pnictide/chalcogenide and nickelates seem, however, to strongly violate the BCS picture. The most important issue is that, perhaps the BCS picture based on electron-phonon coupling are the special case for superconductivity, there are a lot of other reasons or routes for the Cooper pairing and superconductivity. In this short overview paper, we will summarize part of these progresses and try to guide readers to some new possible schemes of superconductivity after the BCS paradigm. We also propose several empirical rules for the exploration of high-temperature unconventional superconductors.
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ZHANG, S. S. "PAIRING CORRELATIONS WITH RESONANT CONTINUUM EFFECT IN THE RMF + ACCC + BCS APPROACH." International Journal of Modern Physics E 18, no. 08 (2009): 1761–72. http://dx.doi.org/10.1142/s0218301309013828.
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The relativistic mean field (RMF) + analytic continuation in the coupling constant (ACCC) + Bardeen–Cooper–Schrieffer (BCS) approach is first presented to describe exotic nuclei by taking into account the resonant continuum effect in pairing correlations. Constant pairing strength is used in BCS approximation. Resonance parameters and wave functions are extracted from effective ACCC approach within the framework of the self-consistent RMF theory. The pairing energies, pairing correlation energies, binding energies, two-neutron separation energies, neutron rms radii, and neutron densities for neutron-rich even–even Ni isotopes are explored in the RMF + ACCC + BCS approach with NL3 effective interaction. It shows that the results are in good agreement with those of other theoretical approaches.
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WILCZEK, FRANK. "BCS AS FOUNDATION AND INSPIRATION: THE TRANSMUTATION OF SYMMETRY." Modern Physics Letters A 25, no. 38 (2010): 3169–89. http://dx.doi.org/10.1142/s0217732310034626.
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The BCS theory injected two powerful ideas into the collective consciousness of theoretical physics: pairing and spontaneous symmetry breaking. In the 50 years since the seminal work of Bardeen, Cooper and Schrieffer, those ideas have found important use in areas quite remote from the stem application to metallic superconductivity. This is a brief and eclectic sketch of some highlights, emphasizing relatively recent developments in QCD and in the theory of quantum statistics, and including a few thoughts about future directions. A common theme is the importance of symmetry transmutation, as opposed to the simple breaking of electromagnetic U(1) symmetry in classic metallic superconductors.
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MALIK, G. P. "BCS-BEC CROSSOVER WITHOUT APPEAL TO SCATTERING LENGTH THEORY." International Journal of Modern Physics B 28, no. 08 (2014): 1450054. http://dx.doi.org/10.1142/s0217979214500544.
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BCS-BEC (an acronym formed from Bardeen, Cooper, Schrieffer and Bose–Einstein condensation) crossover physics has customarily been addressed in the framework of the scattering length theory (SLT), which requires regularization/renormalization of equations involving infinities. This paper gives a frame by frame picture, as it were, of the crossover scenario without appealing to SLT. While we believe that the intuitive approach followed here will make the subject accessible to a wider readership, we also show that it sheds light on a feature that has not been under the purview of the customary approach: the role of the hole–hole scatterings vis-à-vis the electron–electron scatterings as one goes from the BCS to the BEC end. More importantly, we show that there are critical values of the concentration (n)and the interaction parameter (λ) at which the condensation of Cooper pairs takes place; this is a finding in contrast with the view that such pairs are automatically condensed.
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Kaplan, Daniel, and Yoseph Imry. "High-temperature superconductivity using a model of hydrogen bonds." Proceedings of the National Academy of Sciences 115, no. 22 (2018): 5709–13. http://dx.doi.org/10.1073/pnas.1803767115.
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Recently, there has been much interest in high-temperature superconductors and more recently in hydrogen-based superconductors. This work offers a simple model that explains the behavior of the superconducting gap based on naive BCS (Bardeen–Cooper–Schrieffer) theory and reproduces most effects seen in experiments, including the isotope effect and Tc enhancement as a function of pressure. We show that this is due to a combination of the factors appearing in the gap equation: the matrix element between the proton states and the level splitting of the proton.
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Kerrouchi, S., N. H. Allal, M. Fellah та M. R. Oudih. "Evaluation of the β+ decay log ft value with inclusion of the neutron–proton pairing and particle number conservation". International Journal of Modern Physics E 24, № 02 (2015): 1550014. http://dx.doi.org/10.1142/s0218301315500147.
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The particle number fluctuation effects, which are inherent to the Bardeen–Cooper–Schrieffer (BCS) theory, on the beta decay log ft values are studied in the isovector case. Expressions of the transition probabilities, of Fermi as well as Gamow–Teller types, which strictly conserve the particle number are established using a projection method. The probabilities are calculated for some transitions of isobars such as N ≃ Z. The obtained results are compared to values obtained before the projection. The nuclear deformation effect on the log ft values is also studied.
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CHENG, ZE. "CONDENSATION STATE OF ULTRA-COLD BOSE ATOMIC GASES WITH NONCONTACT INTERACTION." International Journal of Modern Physics B 27, no. 07 (2013): 1361007. http://dx.doi.org/10.1142/s0217979213610079.
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Within the framework of quantum field theory, we find that uniform Bose atomic gases with noncontact interaction can undergo a Bardeen–Cooper–Schrieffer (BCS) condensation below a critical temperature. In the BCS condensation state, bare atoms with opposite wave vectors are bound into pairs, and unpaired bare atoms are transformed into a new kind of quasi-particle, i.e., the dressed atom. The atom-pair system is a condensate or a superfluid and the dressed-atom system is a normal fluid. At absolute zero temperature the condensate possesses a lowest negative energy. The critical temperature and the effective mass of dressed atoms are derived analytically. The transition from the BCS condensation state to the normal state is a first-order phase transition.
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Pascucci, Filippo, Andrea Perali, and Luca Salasnich. "Reliability of the Ginzburg–Landau Theory in the BCS-BEC Crossover by Including Gaussian Fluctuations for 3D Attractive Fermions." Condensed Matter 6, no. 4 (2021): 49. http://dx.doi.org/10.3390/condmat6040049.
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We calculate the parameters of the Ginzburg–Landau (GL) equation of a three-dimensional attractive Fermi gas around the superfluid critical temperature. We compare different levels of approximation throughout the Bardeen–Cooper–Schrieffer (BCS) to the Bose–Einstein Condensate (BEC) regime. We show that the inclusion of Gaussian fluctuations strongly modifies the values of the Ginzburg–Landau parameters approaching the BEC regime of the crossover. We investigate the reliability of the Ginzburg–Landau theory, with fluctuations, studying the behavior of the coherence length and of the critical rotational frequencies throughout the BCS-BEC crossover. The effect of the Gaussian fluctuations gives qualitative correct trends of the considered physical quantities from the BCS regime up to the unitary limit of the BCS-BEC crossover. Approaching the BEC regime, the Ginzburg–Landau equation with the inclusion of Gaussian fluctuations turns out to be unreliable.
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Brandt, Bastian B., Francesca Cuteri, Gergely Endrődi, and Sebastian Schmalzbauer. "The Dirac Spectrum and the BEC-BCS Crossover in QCD at Nonzero Isospin Asymmetry." Particles 3, no. 1 (2020): 80–86. http://dx.doi.org/10.3390/particles3010007.
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For large isospin asymmetries, perturbation theory predicts the quantum chromodynamic (QCD) ground state to be a superfluid phase of u and d ¯ Cooper pairs. This phase, which is denoted as the Bardeen-Cooper-Schrieffer (BCS) phase, is expected to be smoothly connected to the standard phase with Bose-Einstein condensation (BEC) of charged pions at μ I ≥ m π / 2 by an analytic crossover. A first hint for the existence of the BCS phase, which is likely characterised by the presence of both deconfinement and charged pion condensation, comes from the lattice observation that the deconfinement crossover smoothly penetrates into the BEC phase. To further scrutinize the existence of the BCS phase, in this article we investigate the complex spectrum of the massive Dirac operator in 2+1-flavor QCD at nonzero temperature and isospin chemical potential. The spectral density near the origin is related to the BCS gap via a generalization of the Banks-Casher relation to the case of complex Dirac eigenvalues (derived for the zero-temperature, high-density limits of QCD at nonzero isospin chemical potential).
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SCHMALIAN, JÖRG. "FAILED THEORIES OF SUPERCONDUCTIVITY." Modern Physics Letters B 24, no. 27 (2010): 2679–91. http://dx.doi.org/10.1142/s0217984910025280.
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Almost half a century passed between the discovery of superconductivity by Kamerlingh Onnes and the theoretical explanation of the phenomenon by Bardeen, Cooper and Schrieffer. During the intervening years the brightest minds in theoretical physics tried and failed to develop a microscopic understanding of the effect. A summary of some of those unsuccessful attempts to understand superconductivity not only demonstrates the extraordinary achievement made by formulating the BCS theory, but also illustrates that mistakes are a natural and healthy part of scientific discourse, and that inapplicable, even incorrect theories can turn out to be interesting and inspiring.
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Tanizaki, Yuya, and Tetsuo Hatsuda. "Multi-regulator functional renormalization group for many-fermion systems." International Journal of Modern Physics E 26, no. 01n02 (2017): 1740027. http://dx.doi.org/10.1142/s0218301317400274.
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We propose a method of multi-regulator functional renormalization group (MR-FRG) which is a novel formulation of functional renormalization group with multiple infrared (IR) regulators. It is applied to a two-component fermionic system with an attractive contact interaction to study crossover phenomena between the Bardeen–Cooper–Schrieffer (BCS) phase and the Bose–Einstein condensation (BEC) phase. To control both the fermionic one-particle excitations and the bosonic collective excitations, IR regulators are introduced, one for the fermionic two-point function and another for the four-fermion vertex. It is shown that the Nozières–Schmitt-Rink (NSR) theory, which is successful to capture qualitative features of the BCS–BEC crossover, can be derived from MR–FRG. Some aspects of MR-FRG to go beyond the NSR theory are also discussed.
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Travaglino, Riccardo, and Alessio Zaccone. "Extended analytical BCS theory of superconductivity in thin films." Journal of Applied Physics 133, no. 3 (2023): 033901. http://dx.doi.org/10.1063/5.0132820.
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We present an analytically solvable theory of Bardeen-Cooper-Schrieffer-type superconductivity in good metals which are confined along one of the three spatial directions, such as thin films. Closed-form expressions for the dependence of the superconducting critical temperature [Formula: see text] as a function of the confinement size [Formula: see text] are obtained, in quantitative agreement with experimental data with no adjustable parameters. Upon increasing the confinement, a crossover from a spherical Fermi surface, which contains two growing hollow spheres corresponding to states forbidden by confinement, to a strongly deformed Fermi surface, is predicted. This crossover represents a new topological transition, driven by confinement, between two Fermi surfaces belonging to two different homotopy classes. This topological transition provides a mechanistic explanation of the commonly observed non-monotonic dependence of [Formula: see text] upon film thickness with a maximum which, according to our theory, coincides with the topological transition.
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Yang, Chih-Kai, and Chi-Hsuan Lee. "Pressure-dependent topological superconductivity on the surface of FeTe0.5Se0.5." New Journal of Physics 24, no. 2 (2022): 023001. http://dx.doi.org/10.1088/1367-2630/ac4922.
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Abstract FeTe1−x Se x is a family of iron-based superconductors with its critical temperature (T c) dependent on the composition of Se. A well-known T c is 14.5 K for x = 0.45, which exhibits an s-wave superconducting gap between the topological superconducting surfaces states. Exchange interaction between the electrons has been proposed as the mechanism behind the formation of Cooper pairs for the sample of FeTe0.5Se0.5. In this article we provide further proof that exchange interaction, and hence the associated T c, depends on the applied pressure on FeTe0.5Se0.5. Using density functional calculations for electrons and phonons and the Bardeen–Cooper–Schrieffer (BCS) theory for superconductivity, we found that T c and superconducting gap for FeTe0.5Se0.5 soars under increasing compression, consistent with the results of experiment.
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Hoddeson, Lillian. "John Bardeen and the BCS Theory of Superconductivity." MRS Bulletin 24, no. 1 (1999): 50–55. http://dx.doi.org/10.1557/s0883769400051745.
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Every theory of superconductivity can be disproved! This tongue-in-cheek theorem struck a chord when Felix Bloch announced it in the early 1930s. Virtually every major physicist then working on theory—including Bloch, Niels Bohr, Wolfgang Pauli, Werner Heisenberg, Lev Landau, Leon Brillouin, W. Elsasser, Yakov Frenkel, and Ralph Kronig—had tried and failed to explain the mysterious phenomenon in which below a few degrees kelvin certain metals and alloys lose all their electrical resistance. The frequency with which Bloch's theorem was quoted suggests the frustration of the many physicists who were struggling to explain superconductivity.Neither the tools nor the evidence were yet adequate for solving the problem. These would gradually be created during the 1940s and 1950s, but bringing them to bear on superconductivity and solving the long-standing riddle required a special set of talents and abilities: a deep understanding of quantum mechanics and solid-state physics, confidence in the solubility of the problem, intuition about the phenomenon, a practical approach to problem-solving, patience, teamwork, and above all refusal to give up in the face of repeated failures. When John Bardeen took on the problem of superconductivity in the late 1930s, he held it like a bulldog holds a piece of meat, until he, his student J. Robert Schrieffer, and postdoctoral candidate Leon Cooper solved it in 1957.
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Brändas, Erkki, and Lawrence J. Dunne. "Bardeen–Cooper–Schrieffer (BCS) theory and Yang's concept of off-diagonal long-range order (ODLRO)." Molecular Physics 112, no. 5-6 (2013): 694–99. http://dx.doi.org/10.1080/00268976.2013.853112.
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Matar, Samir F. "Electronic Structure and Chemical Bonding within MgB2 and Related Borides from First Principles." Zeitschrift für Naturforschung B 63, no. 6 (2008): 673–80. http://dx.doi.org/10.1515/znb-2008-0613.
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The electronic structures of actual and hypothetical binary borides AB2 (A = Al, Mg, Li, Be, Ca) and of mixed hypothetical phases A'MgB4 (A' = Al, Li) are obtained and analyzed within the density functional theory using pseudo-potential and all-electron methods (VASP and ASW) in order to address the changes in the electronic structure within the high-temperature superconductor MgB2 by modeling isoelectronic and n/p-doping effects. From the properties of quantum mixing between respective valence states and of chemical bonding we propose an analysis of the high-temperature superconductivity within the two models, the classical one of Bardeen, Cooper and Schrieffer (BCS) and the hole superconductivity model, which is based on experimental and calculated results from the literature.
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Bighin, G., and L. Salasnich. "Renormalization of the superfluid density in the two-dimensional BCS-BEC crossover." International Journal of Modern Physics B 32, no. 17 (2018): 1840022. http://dx.doi.org/10.1142/s0217979218400222.
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We analyze the theoretical derivation of the beyond-mean-field equation of state for two-dimensional gas of dilute, ultracold alkali-metal atoms in the Bardeen–Cooper–Schrieffer (BCS) to Bose–Einstein condensate (BEC) crossover. We show that at zero temperature our theory — considering Gaussian fluctuations on top of the mean-field equation of state — is in very good agreement with experimental data. Subsequently, we investigate the superfluid density at finite temperature and its renormalization due to the proliferation of vortex–antivortex pairs. By doing so, we determine the Berezinskii–Kosterlitz–Thouless (BKT) critical temperature — at which the renormalized superfluid density jumps to zero — as a function of the inter-atomic potential strength. We find that the Nelson–Kosterlitz criterion overestimates the BKT temperature with respect to the renormalization group equations, this effect being particularly relevant in the intermediate regime of the crossover.
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Gabovich, Alexander M., and Vladimir I. Kuznetsov. "What do we mean when using the acronym ‘BCS’? The Bardeen–Cooper–Schrieffer theory of superconductivity." European Journal of Physics 34, no. 2 (2013): 371–82. http://dx.doi.org/10.1088/0143-0807/34/2/371.
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Rahmatinejad, A., R. Razavi, and T. Kakavand. "Studying temperature dependence of pairing gap parameter in a nucleus as a small superconducting system." International Journal of Modern Physics E 25, no. 08 (2016): 1650050. http://dx.doi.org/10.1142/s0218301316500506.
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In this paper, we have taken the effect of small size of nucleus and static fluctuations into account in the Bardeen-Cooper-Schrieffer (BCS) theory of superconductivity calculations of [Formula: see text]Ti nucleus. Thermodynamic quantities of [Formula: see text]Ti have been extracted within the BCS model with the inclusion of the average value of the pairing gap square, extracted by the modified Ginzburg–Landau (MGL) method for small systems. Calculated values of the excitation energy and entropy within the MGL+BCS method improve the extracted results within the usual BCS model and show a smooth behavior around the critical temperature with a very good agreement with the semi-empirical values. The result of using MGL+BCS method for the heat capacity of [Formula: see text]Ti is compared with the corresponding semi-empirical values and the calculated values within the BCS, static path approximation (SPA) and Modified Pairing gap BCS (MPBCS) which is a method that was proposed in our previous publications. Both MGL+BCS and MPBCS avoid the discontinuity of the heat capacity curve, which is observed in the usual BCS method, and lead to an S-shaped curve with a good agreement with the semi-empirical results.
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Sangi Bhanu Prasad, Kandela Ruchitha, Mohammed Faizaan, M.A. Zakim, Mohammed Hannan Mustafa, and Syed Abdul Haseeb. "The Evolution of Superconductivity: Theoretical Foundations and Material Progress." International Research Journal on Advanced Engineering and Management (IRJAEM) 3, no. 05 (2025): 2159–63. https://doi.org/10.47392/irjaem.2025.0341.
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Superconductivity is a quantum mechanical phenomenon observed in certain materials at temperatures below a critical threshold (Tc), characterized by the complete absence of electrical resistance and the expulsion of magnetic fields—a property known as the Meissner effect. This state arises when electrons form Cooper pairs, enabling them to move through the lattice without scattering, as described by the Bardeen–Cooper–Schrieffer (BCS) theory. Since its discovery in 1911, superconductivity has become indispensable across various scientific and technological domains. The advent of high-temperature superconductors (HTS) in the 1980s, which operate at temperatures achievable with liquid nitrogen, has expanded practical applications. These include magnetic resonance imaging (MRI), particle accelerators, maglev trains, and advanced power transmission systems. Recent research into cuprate superconductors has unveiled a quantum critical point that may elucidate the mechanisms behind high-temperature superconductivity. This paper provides an accessible overview of the theoretical foundations of superconductivity and explores its diverse applications, highlighting its transformative impact on modern technology.
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Malozovsky, Y. M., and J. D. Fan. "Cooper Instability for a Given Field in a Quiescent Fermi Gas." International Journal of Modern Physics B 12, no. 06 (1998): 637–52. http://dx.doi.org/10.1142/s0217979298000387.
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The Cooper instability in a Fermi gas is examined using the perturbative diagram approach. A graphical functional derivative technique based on Ward's identity is developed to obtain two-particle interactions and then to calculate the vertex part. The pairing instability for a given interaction, such as a phonon (plasmon, etc.) field, occurs in a quiescent Fermi sea, i.e. without exciting or involving background particles (holes), only if the interaction is attractive, as first proposed by Cooper and adopted in the BCS (Bardeen–Cooper–Schrieffer) theory. The consequence from this technique provides a way to evaluate the effect of the vertex corrections and responses of the Fermi gas in both charge and spin channels incorporating the backward scattering process. The significance of the methodology presented in the present work lies in the fact that it can both reproduce the known results, and, more importantly, be extended to investigate the intermediate or strong coupling case, such as nuclear interactions, where a neglect of vertex corrections may not be a good approximation.
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Raychaudhuri, Pratap, and Surajit Dutta. "Phase fluctuations in conventional superconductors." Journal of Physics: Condensed Matter 34, no. 8 (2021): 083001. http://dx.doi.org/10.1088/1361-648x/ac360b.
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Abstract Within the Bardeen–Cooper–Schrieffer (BCS) theory, superconductivity is entirely governed by the pairing energy scale, which gives rise to the superconducting energy gap, Δ. However, another important energy scale, the superfluid phase stiffness, J, which determines the resilience of the superconductor to phase-fluctuations is normally ignored. The spectacular success of BCS theory owes to the fact that in conventional superconductors J is normally several orders of magnitude larger than Δ and thus an irrelevant energy scale. However, in certain situations such as in the presence of low carrier density, strong disorder, at low-dimensions or in granular superconductors, J can drastically come down and even become smaller than Δ. In such situations, the temperature and magnetic field evolution of superconducting properties is governed by phase fluctuations, which gives rise to novel electronic states where signatures of electronic pairing continue to exist even when the zero resistance state is destroyed. In this article, we will review the recent experimental developments on the study of phase fluctuations in conventional superconductors.
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Tong, Xi, Yi Wang, Chen Zhang, and Yuhang Zhu. "BCS in the sky: signatures of inflationary fermion condensation." Journal of Cosmology and Astroparticle Physics 2024, no. 04 (2024): 022. http://dx.doi.org/10.1088/1475-7516/2024/04/022.
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Abstract We consider a Bardeen-Cooper-Schrieffer (BCS)-like model in the inflationary background. We show that with an axial chemical potential, the attractive quartic fermion self-interaction can lead to a BCS-like condensation. In the rigid-de Sitter (dS) limit of inflation where backreaction from the inflaton and graviton is neglected, we perform the first computation of the non-perturbative effective potential that includes the full spacetime curvature effects in the presence of the chemical potential, subject to the mean-field approximation whose validity has been checked via the Ginzburg criterion. The corresponding BCS phase transition is always first-order, when the varying Hubble is interpreted as an effective Gibbons-Hawking temperature of dS spacetime. In the condensed phase, the theory can be understood from UV and IR sides as fermionic and bosonic, respectively. This leads to distinctive signatures in the primordial non-Gaussianity of curvature perturbations. Namely, the oscillatory cosmological collider signal is smoothly turned off at a finite momentum ratio, since different momentum ratios effectively probe different energy scales. In addition, such BCS phase transitions can also source stochastic gravitational waves, which are feasible for future experiments.
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Zemła, Tomasz P., Klaudia M. Szczȩśniak, Adam Z. Kaczmarek, and Svitlana V. Turchuk. "Characterization of the superconducting phase in tellurium hydride at high pressure." Modern Physics Letters B 33, no. 16 (2019): 1950169. http://dx.doi.org/10.1142/s0217984919501690.
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At present, hydrogen-based compounds constitute one of the most promising classes of materials for applications as phonon-mediated high-temperature superconductors. Herein, the behavior of the superconducting phase in tellurium hydride (HTe) at high pressure (p = 300 GPa) is analyzed in detail, by using the isotropic Migdal–Eliashberg equations. The chosen pressure conditions are considered here as a case study which corresponds to the highest critical temperature value [Formula: see text] in the analyzed material, as determined within recent density functional theory simulations. It is found that the Migdal–Eliashberg formalism, which constitutes a strong-coupling generalization of the Bardeen–Cooper–Schrieffer (BCS) theory, predicts that the critical temperature value ([Formula: see text] K) is higher than previous estimates of the McMillan formula. Further investigations show that the characteristic dimensionless ratios for the thermodynamic critical field, the specific heat for the superconducting state, and the superconducting band gap exceed the limits of the BCS theory. In this context, also the effective electron mass is not equal to the bare electron mass as provided by the BCS theory. On the basis of these findings it is predicted that the strong-coupling and retardation effects play pivotal role in the superconducting phase of HTe at 300 GPa, in agreement with similar theoretical estimates for the sibling hydrogen and hydrogen-based compounds. Hence, it is suggested that the superconducting state in HTe cannot be properly described within the mean-field picture of the BCS theory.
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VOVK, R. V., A. A. ZAVGORODNIY, M. A. OBOLENSKII, I. L. GOULATIS, A. CHRONEOS та V. M. PINTO SIMOES. "INFLUENCE OF HIGH PRESSURE ON THE TEMPERATURE-DEPENDENCE OF THE PSEUDO-GAP IN OXYGEN DEFICIENT YBa2Cu3O7-δ SINGLE CRYSTALS". Modern Physics Letters B 24, № 22 (2010): 2295–301. http://dx.doi.org/10.1142/s0217984910024675.
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The influence of high pressure on the conductivity in the ab-plane of the oxygen deficient YBa 2 Cu 3 O 7-δ single crystals is investigated. It is determined that excess conductivity Δσ(T) in the YBa 2 Cu 3 O 7-δ single crystals in a wide temperature interval (Tc < T < T*, where Tc is the critical temperature and T* is the temperature that the PG regime begins) obeys an exponential temperature-dependence. The description of the excess conductivity with [Formula: see text]) can be interpreted in terms of mean field theory. The temperature-dependence of the pseudo-gap is well described in the framework of the Bardeen–Cooper–Schrieffer (BCS) to the Bose–Einstein condensate (BEC) crossover theory. Increasing the applied pressure leads to the effect of narrowing the temperature range of implementation of the PG regime, thus extending the area of linear ρ(T) dependence in the ab-plane.
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Gandolfi, Stefano, Georgios Palkanoglou, Joseph Carlson, Alexandros Gezerlis, and Kevin E. Schmidt. "The 1S0 Pairing Gap in Neutron Matter." Condensed Matter 7, no. 1 (2022): 19. http://dx.doi.org/10.3390/condmat7010019.
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We report ab initio calculations of the S wave pairing gap in neutron matter calculated using realistic nuclear Hamiltonians that include two- and three-body interactions. We use a trial state, properly optimized to capture the essential pairing correlations, from which we extract ground state properties by means of auxiliary field diffusion Monte Carlo simulations. We extrapolate our results to the thermodynamic limit by studying the finite-size effects in the symmetry-restored projected Bardeen-Cooper-Schrieffer (PBCS) theory and compare our results to other ab initio studies done in the past. Our quantum Monte Carlo results for the pairing gap show a modest suppression with respect to the mean-field BCS values. These results can be connected to cold atom experiments, via the unitarity regime where fermionic superfluidity assumes a unified description, and they are important in the prediction of thermal properties and the cooling of neutron stars.
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Valles, J. M., and R. C. Dynes. "Electron Tunneling in High Tc Superconductors." MRS Bulletin 15, no. 6 (1990): 44–49. http://dx.doi.org/10.1557/s0883769400059509.
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Electron tunneling measurements have proven enormously valuable in studies of conventional superconductors. Very early measurements confirmed, in an especially convincing way, the existence of the superconducting energy gap, and more detailed studies demonstrated the spectral form of the gap and its temperature dependence. These measurements were instrumental in confirming in some detail the predictions of the Bardeen, Cooper, Schrieffer (BCS) theory of superconductivity in simple metals. For example, it was shown very clearly that the ratio of the energy gap (2Δ) and critical temperature Tc was close to the BCS value (2Δ/kTc = 3.5). As the sophistication of the technique improved, deviations from this BCS weak coupling limit became apparent (2Δ/kTc was measured to be >4 in materials like Pb, for example), and subtle structure in the current-voltage characteristics of tunnel junctions unearthed a signature of the electron-phonon interaction—the microscopic mechanism responsible for superconductivity in these traditional materials. Through a quantitative analysis of this structure, people were able to extract a function α2(ω)F(ω), which is the phonon density of states F(ω) modulated by the electron-phonon coupling function α2(ω). This function gave a quantitative description of the electron-phonon interaction and confirmed beyond a doubt that the electron-phonon interaction was responsible for superconductivity.
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ITOYAMA, H., and NOBUHITO MARU. "D-TERM DYNAMICAL SUPERSYMMETRY BREAKING GENERATING SPLIT ${\mathcal N} = 2$ GAUGINO MASSES OF MIXED MAJORANA–DIRAC TYPE." International Journal of Modern Physics A 27, no. 26 (2012): 1250159. http://dx.doi.org/10.1142/s0217751x1250159x.
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Under a few mild assumptions, [Formula: see text] supersymmetry (SUSY) in four dimensions is shown to be spontaneously broken in a metastable vacuum in a self-consistent Hartree–Fock approximation of Bardeen–Cooper–Schrieffer/Nambu–Jona-Lasinio (BCS/NJL) type to the leading order, in the gauge theory specified by the gauge kinetic function and the superpotential of adjoint chiral superfields, in particular, that possess [Formula: see text] extended SUSY spontaneously broken to [Formula: see text] at tree level. We derive an explicit form of the gap equation, showing the existence of a nontrivial solution. The [Formula: see text] gauginos in the observable sector receive mixed Majorana–Dirac masses and are split due to both the nonvanishing 〈D0〉 and 〈F0〉 induced with 〈D0〉. It is argued that proper physical applications and assessment of the range of the validity of our framework are made possible by rendering the approximation into [Formula: see text] expansion.
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Mal, Subhanka, and Bimalendu Deb. "A model study on superfluidity of a unitary Fermi gas of atoms interacting with a finite-ranged potential." Journal of Physics B: Atomic, Molecular and Optical Physics 55, no. 3 (2022): 035301. http://dx.doi.org/10.1088/1361-6455/ac34df.
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Abstract We calculate Bardeen–Cooper–Schrieffer (BCS) state of a unitary Fermi gas of atoms interacting with the finite-ranged Jost-Kohn potential which has been recently shown to account for the resonant interactions (2019 J. Phys. B: At. Mol. Opt. Phys. 52 165004). Using exact scattering solution of the potential, we derive two-body T-matrix element which is employed to construct the BCS Hamiltonian in momentum space. We present results on the energy- and range-dependence of the pairing gap and superfluid density and the range-dependence of the chemical potential for a wide variation of the scattering length including the unitary regime. In the zero range limit our calculated gap at the Fermi energy is found to be nearly equal to that calculated in mean-field theory with contact potential. The mean gap averaged over the full width at half maximum of the gap function in the zero range and unitary limits is found to be 0.42E F which is quite close to the recent result of the quantum Monte-Carlo simulation (2018 Phys. Rev. A 97 013601). The chemical potential in the zero range limit also agrees well with that for the contact potential.
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Swartz, Adrian G., Hisashi Inoue, Tyler A. Merz, et al. "Polaronic behavior in a weak-coupling superconductor." Proceedings of the National Academy of Sciences 115, no. 7 (2018): 1475–80. http://dx.doi.org/10.1073/pnas.1713916115.
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The nature of superconductivity in the dilute semiconductor SrTiO3 has remained an open question for more than 50 y. The extremely low carrier densities (1018–1020 cm−3) at which superconductivity occurs suggest an unconventional origin of superconductivity outside of the adiabatic limit on which the Bardeen–Cooper–Schrieffer (BCS) and Migdal–Eliashberg (ME) theories are based. We take advantage of a newly developed method for engineering band alignments at oxide interfaces and access the electronic structure of Nb-doped SrTiO3, using high-resolution tunneling spectroscopy. We observe strong coupling to the highest-energy longitudinal optic (LO) phonon branch and estimate the doping evolution of the dimensionless electron–phonon interaction strength (𝝀). Upon cooling below the superconducting transition temperature (𝑻𝐜), we observe a single superconducting gap corresponding to the weak-coupling limit of BCS theory, indicating an order of magnitude smaller coupling (𝝀𝐁𝐂𝐒≈0.1). These results suggest that despite the strong normal state interaction with electrons, the highest LO phonon does not provide a dominant contribution to pairing. They further demonstrate that SrTiO3 is an ideal system to probe superconductivity over a wide range of carrier density, adiabatic parameter, and electron–phonon coupling strength.
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Zhao, Guicong, Shenyang Chen, and Xinyue Zhang. "Electronic Structure Study of Pr3Ni2O7 Based on Density Functional Theory." Highlights in Science, Engineering and Technology 132 (March 20, 2025): 64–70. https://doi.org/10.54097/19wm2k02.
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In the study of superconducting materials, nickelates have attracted significant attention due to their crystal structures and electronic properties resembling those of infinite-layer cuprates. The phenomenon of superconductivity was first discovered in 1911 by Dutch physicist Heike Kamerlingh Onnes, who observed that mercury exhibited zero electrical resistance near absolute zero. Subsequently, scientists proposed the BCS theory, formulated by John Bardeen, Leon Cooper, and Robert Schrieffer in 1957, which successfully explained the microscopic mechanisms of superconductivity. In 1986, George Bednorz and Alex Müller discovered the high-temperature superconductor yttrium barium copper oxide (YBCO), which has a superconducting transition temperature as high as 92 K. Recently, the synthesis and study of nickelate materials, such as NdNiO₂ and Nd₀. ₈Sr₀. ₂NiO₂, have shown superconducting transition temperatures ranging from 9 to 15 K, and high-pressure treatment has significantly increased the superconducting temperature. These advancements suggest that nickelates may possess superconducting mechanisms similar to those of cuprates, making them a hot topic of research. We chose Pr₃Ni₂O₇ as our research subject and employed density functional theory to calculate its band structure, finding that the d-orbitals of Ni and O play a crucial role in conductivity, with a substantial number of available electronic states for conduction.
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Miller, John H. "The journey of high-temperature superconductors: From discovery to today." Open Access Government 45, no. 1 (2025): 224–25. https://doi.org/10.56367/oag-045-11330.
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The journey of high-temperature superconductors: From discovery to today John H. Miller, Jr., Professor of Physics at the University of Houston, discusses progress in high-temperature superconductors and its applications. The lab of H. Kamerlingh Onnes, the first group to liquefy helium, discovered superconductivity in 1911. Several metals were found to undergo a phase transition to a new state characterized by the loss of resistance below a critical temperature, or Tc. The Meissner effect, the expulsion of magnetic flux, was discovered in 1933. In 1957, John Bardeen, Leon Cooper, and J. Robert Schrieffer published a microscopic theory, now known as the BCS theory, (1) based on pairing of electrons mediated by phonons. That same year, Abrikosov developed an improved understanding of the magnetic properties of superconductors, distinguishing between type-I (soft) and type-II (hard) superconductors. Most notably, he proposed the formation of flux vortices in a type-II superconductor exposed to a magnetic field. This prevents a magnetic field from driving the entire type-II superconductor into the normal state, enabling it to have a much higher upper critical magnetic field – important for applications such as magnetic resonance imaging (MRI), particle accelerators, and tokamak fusion reactors.
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Al-Khzon, H. A., and M. K. Al-Sugheir. "Thermodynamic properties of spin-imbalance harmonically trapped one-dimensional attractive 6Li atomic gas." International Journal of Modern Physics B 35, no. 04 (2021): 2150059. http://dx.doi.org/10.1142/s0217979221500594.
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The thermodynamic properties of 6Li atomic gas system, with imbalanced spin populations trapped in one-dimension, were systematically investigated using the Static Fluctuation Approximation. The two-body interaction used is an attractive contact potential. The effects of gas parameter [Formula: see text] and spin polarization [Formula: see text], on the thermodynamic properties and effective magnetic field were investigated. We observed a decrease in [Formula: see text] and an enhancement in [Formula: see text] and [Formula: see text] with increasing [Formula: see text]. At strong interaction and at [Formula: see text], the behavior of entropy with [Formula: see text] indicated two different phases. At small spin polarization [Formula: see text], the system could be in Fulde–Ferrell–Larkin Ovchinnikov (FFLO) state, while above [Formula: see text], the system might be in normal state. In addition, we found a clear decrease in both [Formula: see text] and [Formula: see text] and an enhancement in [Formula: see text] with the increase of the interaction strength. Our results are consistent with the reported results obtained by the mean-field Bogoliubov–de Gennes method, the Bardeen–Cooper–Schrieffer (BCS) approximation and Nozieres–Schmitt–Rink (NSR) theory.
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Benner, Michael, and Alfred Rieckers. "Spectral Properties Of Weakly Inhomogeneous Bcs-Models In Different Representations." Zeitschrift für Naturforschung A 60, no. 5 (2005): 343–65. http://dx.doi.org/10.1515/zna-2005-0506.
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For a class of Bardeen-Cooper-Schrieffer (BCS)-models, with complex, weakly momentum dependent interaction coefficients, the representation dependent effective Hamiltonians and their spectra are reconsidered in order to obtain a consistent physical picture by means of operator algebraic methods. The starting point is the limiting dynamics, the existence of which had been proved in a previous work, in terms of a C*-dynamical system acting in a classically extended, electronic Canonical Anticommutation Relations (CAR)-algebra. The C*-algebraic KMS-theory, including the low temperature limit, specifies the order parameters. These appear as classical observables, which commute with all other observables, constituting elements of the center of the algebra. The algebraic spectral theory, in the sense of Arveson, is first applied to the dynamics in general pure energy state representations. The spectra of the finite temperature representations are analyzed, identifying the gap as the lowest of those energy values, which are stable under local perturbations. Further insights are obtained by decomposing the thermal dynamical systems into the pure energy state Heisenberg dynamics, after having first extended them to more comprehensive W*-dynamical systems. The decomposing orthogonal measure is transferred to the infinite product space of quasi-particle occupation numbers and its support is characterized in terms of 0-1-laws leading to an asymptotic ratio of quasi-particles and holes, which depends on the temperature. This ratio is connected with an algebraic invariant of the representation dependent observable algebra. Energy renormalization aspects and pair occupation probabilities are discussed. The latter reveal, beside other things, the difference between macroscopic term occupation and coherent macroscopic term occupation for a condensate.
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Palkanoglou, Georgios, and Alexandros Gezerlis. "Superfluid Neutron Matter with a Twist." Universe 7, no. 2 (2021): 24. http://dx.doi.org/10.3390/universe7020024.
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Superfluid neutron matter is a key ingredient in the composition of neutron stars. The physics of the inner crust are largely dependent on those of its S-wave neutron superfluid, which has made its presence known through pulsar glitches and modifications in neutron star cooling. Moreover, with recent gravitational-wave observations of neutron star mergers, the need for an equation of state for the matter of these compact stars is further accentuated and a model-independent treatment of neutron superfluidity is important. Ab initio techniques developed for finite systems can be guided to perform extrapolations to the thermodynamic limit and attain this model-independent extraction of various quantities of infinite superfluid neutron matter. To inform such an extrapolation scheme, we performed calculations of the neutron 1S0 pairing gap using model-independent odd–even staggering in the context of the particle-conserving, projected Bardeen–Cooper–Schrieffer (BCS) theory under twisted boundary conditions. While the practice of twisted boundary conditions is standard in solid-state physics and has been used repeatedly in the past to reduce finite-size effects, this is the first time that it has been employed in the context of pairing. We find that a twist-averaging approach results in a substantial reduction of the finite-size effects, bringing systems with N⪆50 within a 2% error margin from the infinite system. This can significantly reduce extrapolation-related errors in the extraction of superfluid neutron matter quantities.
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Bezymyannykh, D. G., N. G. Pugach, E. A. Sedov, K. Yu Arutyunov, E. G. Ekomasov, and B. G. Lvov. "QUANTUM SIZE EFFECT IN CLEAN ALUMINUM FILMS." Izvestia Ufimskogo Nauchnogo Tsentra RAN, no. 1 (March 12, 2024): 55–60. http://dx.doi.org/10.31040/2222-8349-2024-0-1-55-60.
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In the modern world, there's a notable trend towards the active miniaturization of electronic devices. With technological advances enabling the manipulation of nanostructures, there's an increasing focus on exploring quantum effects pivotal to such designs. One distinguishing feature of nanostructures is the quantum nature of the electron's energy spectrum. This spectrum becomes discrete in directions where electrons move. Depending on the direction of this confinement, structures can be categorized as nanoplates, quantum wires, or quantum dots. The properties of such structures can significantly differ from those observed in large-scale systems. When discussing superconductivity, particular emphasis is placed on its macroscopic quantum properties.The influence on electronic wave functions is reflected in the characteristics of the superconducting state on broader scales. The Bardeen-Cooper-Schrieffer (BCS) theory is frequently utilized to analyze these nanostructures. The Gor’kov equations method serves as a potent tool for tasks related to the BCS theory. For instance, it can determine the parameters of the superconducting state, critical temperature, and current. Components of these equations, like Green's functions, are associated with various system properties. Research in the early stages of superconductivity studies revealed that the critical temperature (Tc ) – the temperature at which a material transitions to a superconducting state – can differ significantly between thin films and bulk materials. Intriguingly, reducing the film's thickness can both decrease (e.g., in niobium) and increase (e.g., in aluminum) the Tc value. This study delves into the quantum size effect in thin aluminum films, paving the way for materials with higher transition temperatures. Such advancements can simplify and make the maintenance of superconducting systems more cost-effective. In this study, a theoretical relationship between the critical temperature of a thin aluminum film and its thickness was derived. The Green's function method was chosen, which hadn't been previously employed for this computation. This approach offers greater potential compared to other superconductivity theory methods, presenting extensive avenues for theoretical exploration in this domain. The authors are confident that this work will contribute to further research on quantum dimensional effects in low-dimensional superconducting structures.
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Zhang, S. S., S. Y. Zhong, B. Shao, and M. S. Smith. "Self-consistent description of the halo nature of 31Ne with continuum and pairing correlations." Journal of Physics G: Nuclear and Particle Physics 49, no. 2 (2022): 025102. http://dx.doi.org/10.1088/1361-6471/ac430e.
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Abstract Background: A relativistic structure model has previously been used to predict a halo structure for 31Ne (Zhang et al 2014 Phys. Lett. B 730 30), consistent with halo signatures from measured reaction cross sections of Ne isotopes bombarding Carbon targets. However, previous attempts to calculate those cross sections with reaction models were missing contributions from resonances and pairing correlations in their structure input. Purpose: Use a reaction model with our relativistic fully microscopic structure model input to predict these cross sections and momentum distributions and analyze for possible halo signatures. Methods: Structure input for exotic Ne isotopes were obtained via the analytical continuation of the coupling constant (ACCC) method based on the relativistic mean field (RMF) theory with Bardeen–Cooper–Schrieffer (BCS) pairing approximation, the RAB approach. Total reaction cross sections, one-neutron removal cross sections, and momentum distributions of breakup reaction products were calculated with a Glauber model using our relativistic structure input. Results: Our predictions of total reaction and one-neutron removal cross sections of 31Ne on a Carbon target were significantly enhanced compared with those of neighboring Neon isotopes, agreeing with measurements at 240 MeV/nucleon and consistent with a single neutron halo. Furthermore, our calculations of the inclusive longitudinal momentum distribution of the 30Ne and valence neutron residues from the 31Ne breakup reaction indicate a dilute density distribution in coordinate space, another halo signature. Conclusions: We give a full description of the halo nature of 31Ne that includes a self-consistent use of pairing and continuum contributions that makes predictions consistent with reaction cross section measurements. This approach can be utilized to determine the halo structure of other exotic nuclei.
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Sun Shuai, An Rong, Qi Miao, Cao Li-Gang, and Zhang Feng-Shou. "Microscopic study on the low-energy quadrupole states in Ni isotopes." Acta Physica Sinica 74, no. 3 (2025): 0. https://doi.org/10.7498/aps.74.20240991.
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The main goal of this paper is to investigate the properties of the low-energy quadrupole strength in Ni isotopes, especially for the evolution of the pygmy quadrupole states with increasing neutron number. And the effect of shell evolution on the pygmy resonance is also discussed in detail. The Skyrme Hartree-Fock+Bardeen-Cooper-Schrieffer (HF+BCS) theory and the selfconsistent quasiparticle random phase approximation (RPA) method are employed on top of three effective Skyrme interactions named SGII, SLy5 and SKM<sup>*</sup>. In the calculations, a density-dependent zero-range type force are adopted for the pairing correlations. The properties of the first 2<sup>+</sup> state in Ni isotopes are studied firstly. As Fig. (a) shown, a good description on the experimental excited energies of the first 2<sup>+</sup> states are achieved, the SGII and SLy5 can give a good description on the reduced electric transition probabilities for <sup>58-68</sup>Ni. It is found that the energies of the first 2<sup>+</sup> state for <sup>68</sup>Ni and <sup>78</sup>Ni are obviously high than others, which reflects the obvious shell effect. In addition to the first 2<sup>+</sup> states, pygmy quadrupole states between 3 to 5 MeV with relative large electric transition probabilities are evidently found for <sup>70-76</sup>Ni in the isoscalar quadruple strength distribution [see Fig. (b)]. With the increasing of neutron number, the pygmy quadrupole states have decreasing energies but hold gradually increasing strengths, and it is more sensitive to the changes in the shell structure. This is due to the fact that the gradually filling of the neutron level 1<i>g</i><sub>9/2</sub> has an very important impact on the pygmy quadrupole states of <sup>70-76</sup>Ni, and switch from proton-dominated excitations to neutron-dominated ones. Since the pygmy quadrupole states for <sup>70-76</sup>Ni are sensitive to the proton and neutron shell gaps, which can provide information on the shell evolution in neutron-rich nuclei.
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Deuchert, Andreas, Christian Hainzl, and Marcel Oliver Maier. "Microscopic derivation of Ginzburg–Landau theory and the BCS critical temperature shift in general external fields." Calculus of Variations and Partial Differential Equations 62, no. 7 (2023). http://dx.doi.org/10.1007/s00526-023-02539-x.
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AbstractWe consider the Bardeen–Cooper–Schrieffer (BCS) free energy functional with weak and macroscopic external electric and magnetic fields and derive the Ginzburg–Landau functional. We also provide an asymptotic formula for the BCS critical temperature as a function of the external fields. This extends our previous results in Deuchert et al. (Microscopic derivation of Ginzburg-Landau theory and the BCS critical temperature shift in a weak homogeneous magnetic field, PMP 4(1), 1–89 (2023)) for the constant magnetic field to general magnetic fields with a nonzero magnetic flux through the unit cell.
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Chávez, Israel, Marcela Grether, and Manuel de Llano. "Superconductor superfluid density from the Bardeen–Cooper–Schrieffer/Bose crossover theory." SN Applied Sciences 4, no. 7 (2022). http://dx.doi.org/10.1007/s42452-022-05074-0.
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Abstract The superfluid density $$n_{s}(T)$$ n s ( T ) of a superconductor is calculated based on the generalized Bose–Einstein condensation (GBEC) theory that addresses a fully-interacting ternary boson-fermion gas mixture of free electrons as fermions, plus two-electron Cooper pairs (2eCPs) and also, explicitly, two-hole Cooper pairs (2hCPs), both as bosons. Here we consider two special cases (i) 100%–0% (i.e., with no condensed 2hCPs) and (ii) 0%–100% (i.e., with no condensed 2eCPs). Subsumed in GBEC are the Bardeen–Cooper–Schrieffer (BCS) and Bose–Einstein condensation (BEC) theories along with the BCS-BEC crossover theory extended with 2hCPs. We find that in the weak-coupling regime $$n_{s}(0)$$ n s ( 0 ) agrees with data from the Uemura et al. (2004) graph for several elemental SCs by taking in 3D with a quadratic energy-dispersion relation while in 2D with a linear relation are much too far below the data. In the strong-coupling regime the linear behavior of critical temperature $$T_{c}$$ T c vs $$n_{s}(0)$$ n s ( 0 ) obtained here is just as Božović et al. (2016) found. However, in 2D with a linear relation accounting for 0%–100%, $$n_{s}(T)/n_{s}(0)$$ n s ( T ) / n s ( 0 ) compares well with some high-$$T_{c}$$ T c -cuprate SC data between the two coupling regimes.
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Yu, Yue, Harold Y. Hwang, S. Raghu, and Suk Bum Chung. "Theory of superconductivity in doped quantum paraelectrics." npj Quantum Materials 7, no. 1 (2022). http://dx.doi.org/10.1038/s41535-022-00466-2.
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AbstractRecent experiments on Nb-doped SrTiO3 have shown that the superconducting energy gap to the transition temperature ratio maintains the Bardeen–Cooper–Schrieffer (BCS) value throughout its superconducting dome. Motivated by these and related studies, we show that the Cooper pairing mediated by a single soft transverse-optical phonon is the most natural mechanism for such a superconducting dome given experimental constraints, and present the microscopic theory for this pairing mechanism. Furthermore, we show that this mechanism is consistent with the T2 resistivity in the normal state. Lastly, we discuss what physical insights SrTiO3 provides for superconductivity in other quantum paraelectrics such as KTaO3.
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Crépel, Valentin, and Liang Fu. "Spin-triplet superconductivity from excitonic effect in doped insulators." Proceedings of the National Academy of Sciences 119, no. 13 (2022). http://dx.doi.org/10.1073/pnas.2117735119.
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Significance We present a mechanism for unconventional superconductivity in doped band insulators, where short-ranged pairing interaction arises from Coulomb repulsion due to virtual interband or excitonic processes. Remarkably, electron pairing is found upon infinitesimal doping, giving rise to Bose–Einstein condensate (BEC)–Bardeen–Cooper–Schrieffer (BCS) crossover at low density. Our theory explains puzzling behaviors of superconductivity and predicts spin-triplet pairing in electron-doped ZrNCl and WTe 2 .
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Landrò, Elena, Vladimir M. Fomin, and Alessio Zaccone. "Topological Bardeen–Cooper–Schrieffer theory of superconducting quantum rings." European Physical Journal B 98, no. 1 (2025). https://doi.org/10.1140/epjb/s10051-024-00851-9.
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Abstract Quantum rings have emerged as a playground for quantum mechanics and topological physics, with promising technological applications. Experimentally realizable quantum rings, albeit at the scale of a few nanometers, are 3D nanostructures. Surprisingly, no theories exist for the topology of the Fermi sea of quantum rings, and a microscopic theory of superconductivity in nanorings is also missing. In this paper, we remedy this situation by developing a mathematical model for the topology of the Fermi sea and Fermi surface, which features non-trivial hole pockets of electronic states forbidden by quantum confinement, as a function of the geometric parameters of the nanoring. The exactly solvable mathematical model features two topological transitions in the Fermi surface upon shrinking the nanoring size either, first, vertically (along its axis of revolution) and, then, in the plane orthogonal to it, or the other way round. These two topological transitions are reflected in a kink and in a characteristic discontinuity, respectively, in the electronic density of states (DOS) of the quantum ring, which is also computed. Also, closed-form expressions for the Fermi energy as a function of the geometric parameters of the ring are provided. These, along with the DOS, are then used to derive BCS equations for the superconducting critical temperature of nanorings as a function of the geometric parameters of the ring. The $$T_c$$ T c varies non-monotonically with the dominant confinement size and exhibits a prominent maximum, whereas it is a monotonically increasing function of the other, non-dominant, length scale. For the special case of a perfect square toroid (where the two length scales coincide), the $$T_c$$ T c increases monotonically with increasing the confinement size, and in this case, there is just one topological transition. Graphic Abstract
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Sakakibara, Hikaru, Hiroyuki Tajima, and Haozhao Liang. "Finite-range effect in the two-dimensional density-induced BCS-BEC crossover." Progress of Theoretical and Experimental Physics, July 27, 2023. http://dx.doi.org/10.1093/ptep/ptad098.
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Abstract We theoretically investigate the Bardeen-Cooper-Schrieffer (BCS) to Bose-Einstein condensation (BEC) crossover in a two-dimensional Fermi gas with the finite-range interaction by using the Hartree-Fock-Bogoliubov theory. Expanding the scattering phase shift in terms of the scattering length and effective range, we discuss the effect of the finite-range interaction on the pairing and thermodynamic properties. By solving the gap equation and the number equation self-consistently, we numerically calculate the effective-range dependence of the pairing gap, chemical potential, and pair size throughout the BCS-BEC crossover. Our results would be useful for further understanding of low-dimensional many-body problems.
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"John Bardeen, 23 May 1908 - 30 January 1991." Biographical Memoirs of Fellows of the Royal Society 39 (February 1994): 19–34. http://dx.doi.org/10.1098/rsbm.1994.0002.
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John Bardeen was the first person to win two Nobel prizes in the same field. He shared the physics prize for the first time in 1956 with Walter Brattain and William Shockley, for the invention of the transistor, and for the second time in 1972 with Leon Cooper and Robert Schrieffer, for the development of the theory of superconductivity which has been known ever since by their initials, BCS. Of these two major achievements the second is unquestionably the greater intellectual triumph, while the first has proved of far greater social significance for the technological revolution it set in train.
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Su, Yuehua, Hongyun Wu, Kun Cao, and Chao Zhang. "Renormalization formalism for superconducting phase transition with inner-Cooper-pair dynamics." Physica Scripta, July 5, 2023. http://dx.doi.org/10.1088/1402-4896/ace48a.
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Abstract As charge carrier of the macroscopic superconductivity, the Cooper pair is a composite particle of two paired electrons, which has both center-of-mass and inner-pair degrees of freedom. In most cases, these two different degrees of freedom can be well described by the macroscopic Ginzburg-Landau theory and the microscopic Bardeen-Cooper-Schrieffer (BCS) theory, respectively. Near the superconducting phase transition where the Cooper pair is fragile and unstable because of the small binding energy, there are non-trivial couplings between these two different degrees of freedom due to such as finite energy and/or momentum transfer. The non-trivial couplings make the original derivation of the Ginzburg-Landau theory from the BCS theory fail in principle as where these two different degrees of freedom should not be decoupled. In this article, we will present a renormalization formalism for an extended Ginzburg-Landau action for the superconducting phase transition where there is finite energy transfer between the center-of-mass and the inner-pair degrees of freedom of Cooper pairs. This renormalization formalism will provide a theoretical tool to study the unusual dynamical effects of the inner-pair time-retarded physics on the superconducting phase transition.