Academic literature on the topic 'Unkonventionelle Supraleitung'

In this thesis, an extended periodic Anderson model with an additional local Coulomb repulsion U f c between localized f electrons and conduction electrons is investigated by use of the projector-based renormalization method (PRM). First, it is shown that the model in one dimension shows a valence transition, which becomes sharper, when the energy of the f level approaches the Fermi level. The transition becomes also enhanced, when the hybridization V between the localized and conduction electrons decreases, for the case that the total number of electrons is fixed. In the two-dimensional case, one finds a similar valence transition behavior. However, in the valence transition regime also a superconducting phase may occur. To investigate this phase, we start from an Hamiltonian which includes small gauge symmetry breaking fields. We derive renormalization equations, from which the superconducting pairing functions are self-consistently determined. Our analytical and numerical results show that d- wave superconductivity becomes dominant in the valence transition regime. This confirms the suggestion by Miyake that valence fluctuations may lead to superconductivity in the Ce based heavy-fermion systems under high pressure
In dieser Arbeit wird mit Hilfe der projektiven Renormierungsmethode (PRM) ein erweitertes periodische Anderson Modell untersucht, das zusätzlich eine Coulomb-Abstoßung zwischen den lokalisierten f-Elektronen und den Leitungselektronen enthält. In einer Dimension zeigt das Modell einen Valenzübergang, wenn sich die Energie des f-Niveaus der Fermienergie nähert. Der Übergang wird ebenfalls schärfer, wenn bei festgehaltener Gesamtelektronenzahl die Hybridisierung V zwischen den lokalisierten und den Leitungselekronen abnimmt. In zwei Dimensionen findet man ein ähnliches Valenzübergangsverhalten. Allerdings kann zusätzlich eine supraleitende Phase im Valenzübergangsgebiet auftreten. Um die supraleitende Phase zu untersuchen, betrachten wir einen Hamiltonoperator mit kleinen zusätzlichen Feldern, die die Eichsymmetrie brechen. Wir leiten Renormierungsgleichungen her, aus denen sich die supraleitenden Paarfunktionen selbstkonsistent bestimmen lassen. Unsere analytischen und numerischen Resultate zeigen, dass im Valenzübergangsgebiet d-Wellen-Supraleitung dominiert. Dies bestätigt eine Vermutung von Miyake, dass Valenzfluktuationen in Ce-basierten Schwerfermionensystemen bei hohen Drücken zur Supraleitung führen können

CeCu_2Si_2 was the first heavy-fermion compound showing signatures of bulk superconductivity (T_c = 0.5 K). Further observations have put in evidence the correlations between superconductivity, magnetic order, Kondo physics, and quantum critical phenomena. In spite of the interest generated, a systematic study of such correlations was hampered by strong sample dependences. Fortunately, the inherent complexity associated to the stoichiometric composition has been recently understood. The availability of single-crystals with well-defined properties has thus reignited the interest in CeCu_2Si_2 as a window to novel phenomena, such as unconventional superconductivity. The present work summarizes the results of my doctoral research. It exemplifies the importance not only of high-quality materials, but also of suitable experimental techniques. A first step in this project involved the design of angle-dependent techniques in the milli-kelvin range, namely: electrical resistivity and thermal conductivity. It comprised the development of a rotational stage, the construction of sample holders, and the implementation of controlling and measuring components. In the second part of the project, electrical- and thermal-transport measurements on CeCu_2Si_2 were performed. Power-law behavior below T_c in the thermal conductivity suggests the presence of lines of nodes in the gap function. Also, the non-vanishing extrapolated residual terms (k_00/T ) support the presence of a residual density of states. The nodes are broadened by potential scattering, which appears to be significant in CeCu_2Si_2. The scattering hinders the determination of the symmetry of the order parameter and might be responsible for the observed isotropic angle dependence of the thermal conductivity. In contrast, angle-dependent measurements of the upper critical field exhibit a four-folded behavior, which also points towards the presence of nodes. By comparing with a weak-coupling model including the effects of Pauli limiting and anisotropic Fermi velocity, the results point towards a d_xy-wave symmetry of the order parameter. Such results represent the first angle-dependent measurements supporting a d-wave symmetry in CeCu_2Si_2.

In this thesis, the electronic properties in superconducting LiFeAs single crystal are investigated using low temperature scanning tunneling microscopy and spectroscopy (STM/S) at various temperatures. For this purpose, the differential conductance (dI/dV) measured by STS which is directly proportional to the local density of states (LDOS) of the sample to the sub-atomic precision, is used together with the topography information. The dI/dV spectra within the ±1 V energy range reveal a characteristic feature at around -350 mV to -400 mV in stoichiometric LiFeAs. This feature seems to be a universal property among all the Fe-based high temperature superconductors, because it is also found in Fe0.965Se1.035 and NaFe0.975Co0.025As single crystals at the energy of -210 mV and -200 mV, respectively. The temperature dependent spectroscopy data averaged over a spatially fixed clean area of 2 nm × 2 nm are successfully executed between 5 K and 20 K. The two distinct superconducting phases with critical temperatures Tc = 16 K and 18 K are observed. In addition, the distance between the dip position outside the superconducting gap and the superconducting coherence peak in the spectra remains temperature independent which confirms that it is not connected to an antiferromagnetic (AFM) spin resonance. The temperature dependent spectra have been measured between 5 K and 61 K within the energy range of ±100 mV as well. The hump structure at 42 mV tends to disappear around 60 K from unknown origin. The temperature dependent quasiparticle interference (QPI) has been studied within the temperature range between 6.7 K and 25 K and analyzed by the Fourier transformation of the measured spectroscopic maps. The dispersion plots in momentum space as a function of temperature show an enhancement of QPI intensity (±5.5 mV) within the superconducting gap at the Fermi level at 6.7 K near q ~ 0. This is interpreted on the basis of Andreev bound state. In both polarities outside of this, a depletion of QPI intensity is noticed between 5.5 mV and around 9 mV. At positive energies, the QPI intensity becomes very rich above 9 mV. The size of the enhanced QPI intensity near the Fermi level, and the edge of the rich QPI intensity beyond 9 mV are found to behave like superconducting order parameter with rising of temperature. Furthermore, an energy mode peaked at around 14 mV appears in the integrated QPI intensity below superconducting Tc (6.7 K). This is consistent with the observed peak at 1st derivative of the dI/dV spectra. In both of these cases, such 14 mV peak is suppressed at normal state (25 K). This mode is therefore directly related to superconductivity in LiFeAs. The off-stoichiometric LiFeAs single crystal with superconducting Tc of 6.5 K has a 10 mV rigid band shift of the Fermi level towards electron doping. The absence of the rich QPI intensity between 9 mV and 17 mV is found compared to the stoichiometric LiFeAs, and hence the 14 mV mode is absent here. This brings us to conclude once more time that such 14 mV energy mode is relevant for superconductivity in LiFeAs.

Despite its history of more than one hundred years, the phenomenon of superconductivity has not lost any of its allure. During that time the concept and perception of the superconducting state - both from an experimental and theoretical point of view - has evolved in way that has triggered increasing interest. What was initially believed to simply be the disappearance of electrical resistivity, turned out to be a universal and inevitable result of quantum statistics, characterized by many more aspects apart from its zero resistivity. The insights of BCS-theory eventually helped to uncover its deep connection to particle physics and consequently led to the formulation of the Anderson-Higgs-mechanism. The very core of this theory is the concept of gauge symmetry (breaking). Within the framework of condensed-matter theory, gauge invariance is only one of several symmetry groups which are crucial for the description and classification of superconducting states. \\ In this thesis, we employ time-reversal, inversion, point group and spin symmetries to investigate and derive possible Hamiltonians featuring spin-orbit interaction in two and three spatial dimensions. In particular, this thesis aims at a generalization of existing numerical concepts to open up the path to spin-orbit coupled (non)centrosymmetric superconductors in multi-orbital models. This is done in a two-fold way: On the one hand, we formulate - based on the Kohn-Luttinger effect - the perturbative renormalization group in the weak-coupling limit. On the other hand, we define the spinful flow equations of the effective action in the framework of functional renormalization, which is valid for finite interaction strength as well. Both perturbative and functional renormalization groups produce a low-energy effective (spinful) theory that eventually gives rise to a particular superconducting state, which is investigated on the level of the irreducible two-particle vertex. The symbiotic relationship between both perturbative and functional renormalization can be traced back to the fact that, while the perturbative renormalization at infinitesimal coupling is only capable of dealing with the Cooper instability, the functional renormalization can investigate a plethora of instabilities both in the particle-particle and particle-hole channels. \\ Time-reversal and inversion are the two key symmetries, which are being used to discriminate between two scenarios. If both time-reversal and inversion symmetry are present, the Fermi surface will be two-fold degenerate and characterized by a pseudospin degree of freedom. In contrast, if inversion symmetry is broken, the Fermi surface will be spin-split and labeled by helicity. In both cases, we construct the symmetry allowed states in the particle-particle as well as the particle-hole channel. The methods presented are formally unified and implemented in a modern object-oriented reusable and extendable C++ code. This methodological implementation is employed to one member of both families of pseudospin and helicity characterized systems. For the pseudospin case, we choose the intriguing matter of strontium ruthenate, which has been heavily investigated for already twenty-four years, but still keeps puzzling researchers. Finally, as the helicity based application, we consider the oxide heterostructure LaAlO$_{3}$/SrTiO$_{3}$, which became famous for its highly mobile two- dimensional electron gas and is suspected to host topological superconductivity
Trotz seiner über hundertjährigen Geschichte seit seiner Entdeckung hat das Phänomen der Supraleitung nichts von seiner ursprünglichen Faszination eingebüßt. Vielmehr hat sich in der Zwischenzeit der Begriff und das Verständnis des supraleitenden Zustandes in einer Weise weiterentwickelt, die das Interesse daran eher hat zunehmen lassen. Was anfänglich ausschließlich für ein Verschwinden des elektrischen Widerstands gehalten wurde, ist tatsächlich ein universelles und unvermeidliches Resultat der Quantenstatistik und besitzt viel mehr bemerkenswerte Eigenschaften als nur den widerstandslosen elektrischen Transport. Die Erkenntnisse der BCS-Theorie haben schließlich dazu geführt die tiefe Verbindung zur Teilchenphysik zu offenbaren und trugen entscheidend zur Formulierung des Anderson-Higgs-Mechanismus bei. Der wichtigste Baustein dieser Theorie ist das Konzept der (Brechung der) Eichsymmetrie. Im Rahmen der Festkörperphysik ist die Eichsymmetrie nur eine von mehreren Symmetrien, die eine essentielle Rolle für die Beschreibung und Einordnung von Phänomenen der Supraleitung spielen. \\ In dieser Arbeit wenden wir Zeitumkehr-, (räumliche) Inversions-, Punktgruppen- und Spin-Symmetrien an, um mögliche Hamilton-Operatoren in zwei und drei räumlichen Dimensionen, welche Spin-Bahn-Kopplung enthalten, herzuleiten und zu untersuchen. Diese Arbeit zielt auf eine Verallgemeinerung von existierenden numerischen Konzepten ab und erschließt den Weg die supraleitenden Eigenschaften von Modellen mit starker Spin-Bahn-Kopplung und mit oder ohne Inversionszentrum zu untersuchen. Dies geschieht mit Hilfe zweier methodischer Ansätze. Erstens formulieren wir aufbauend auf dem Kohn-Luttinger Effekt die störungstheoretische Renormierungsgruppe im Limes schwacher Kopplung. Zweitens verwenden wir die spinaufgelösten Flussgleichungen der effektiven Wirkung im Rahmen der funktionalen Renormierungsgruppe, die auch für endliche Wechselwirkungsstärke gültig sind. Die symbiotische Ergänzung der perturbativen und funktionalen Renormierungsgruppen ist darauf zurückzuführen, dass es mit der perturbativen Methode zwar möglich ist die Cooper Instabilität bei infinitesimaler Wechselwirkung numerisch exakt zu berechnen, aber nur die funktionale Renormierungsgruppe auch Teilchen-Loch Kondensate zugänglich macht. \\ Zeitumkehr- und Inversionssymmetrie sind die beiden Schlüsselsymmetrien, die verwendet werden, um zwei Szenarien zu unterscheiden. Falls sowohl Zeitumkehr- als auch Inversionssymmetrie gültig sind, sind die Fermiflächen zweifach entartet und durch einen Pseudospin-Freiheitsgrad charakterisiert. Im Gegensatz dazu führt der Verlust der Inversionssymmetrie zur Spinaufspaltung der Fermiflächen, die dann durch die sogenannte Helizität gekennzeichnet sind. In beiden Fällen leiten wir alle symmetrie-erlaubten Zustände her, welche die entsprechenden Teilchen-Teilchen und Teilchen-Loch Kondensate beschreiben. Die vorstellten und verallgemeinerten Methoden sind im Rahmen dieser Arbeit formal miteinander verbunden und in einem modernen objektorientierten C++ Quellcode implementiert worden. \\ Als erste vorläufige Anwendungen für diese methodische Implementierung betrachten wir zwei Systeme, die jeweils einer der beiden Familien zugeordnet werden können. Zum einen berechnen wir in der Pseudospin-Formulierung der perturbativen und funktionalen Renormierungsgruppen die Instabilitäten eines Dreiorbital-Modells für Strontiumruthenat, das seit seiner erstmaligen Synthese trotz intensiver Forschung immer noch Rätsel aufgibt. Zum anderen betrachten wir das zweidimensionale Elektronengas, das sich an der Schnittstelle zwischen LaAlO$_{3}$ und SrTiO$_{3}$ bildet und welches durch seine hohe Ladungsträgermobilität bekannt geworden ist

CeCu_2Si_2 was the first heavy-fermion compound showing signatures of bulk superconductivity (T_c = 0.5 K). Further observations have put in evidence the correlations between superconductivity, magnetic order, Kondo physics, and quantum critical phenomena. In spite of the interest generated, a systematic study of such correlations was hampered by strong sample dependences. Fortunately, the inherent complexity associated to the stoichiometric composition has been recently understood. The availability of single-crystals with well-defined properties has thus reignited the interest in CeCu_2Si_2 as a window to novel phenomena, such as unconventional superconductivity. The present work summarizes the results of my doctoral research. It exemplifies the importance not only of high-quality materials, but also of suitable experimental techniques. A first step in this project involved the design of angle-dependent techniques in the milli-kelvin range, namely: electrical resistivity and thermal conductivity. It comprised the development of a rotational stage, the construction of sample holders, and the implementation of controlling and measuring components. In the second part of the project, electrical- and thermal-transport measurements on CeCu_2Si_2 were performed. Power-law behavior below T_c in the thermal conductivity suggests the presence of lines of nodes in the gap function. Also, the non-vanishing extrapolated residual terms (k_00/T ) support the presence of a residual density of states. The nodes are broadened by potential scattering, which appears to be significant in CeCu_2Si_2. The scattering hinders the determination of the symmetry of the order parameter and might be responsible for the observed isotropic angle dependence of the thermal conductivity. In contrast, angle-dependent measurements of the upper critical field exhibit a four-folded behavior, which also points towards the presence of nodes. By comparing with a weak-coupling model including the effects of Pauli limiting and anisotropic Fermi velocity, the results point towards a d_xy-wave symmetry of the order parameter. Such results represent the first angle-dependent measurements supporting a d-wave symmetry in CeCu_2Si_2.