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Journal articles on the topic 'Self-Consistent Born approximation'

Author: Grafiati

Published: 4 June 2021

Last updated: 25 May 2024

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1

Jin, Jinshuang, Jun Li, Yu Liu, Xin-Qi Li, and YiJing Yan. "Improved master equation approach to quantum transport: From Born to self-consistent Born approximation." Journal of Chemical Physics 140, no. 24 (2014): 244111. http://dx.doi.org/10.1063/1.4884390.

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2

Seke, J., A. V. Soldatov, and N. N. Bogolubov. "Novel Technique for Quantum-Mechanical Eigenstate and Eigenvalue Calculations based on Seke's Self-Consistent Projection-Operator Method." Modern Physics Letters B 11, no. 06 (1997): 245–58. http://dx.doi.org/10.1142/s0217984997000311.

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Seke's self-consistent projection-operator method has been developed for deriving non-Markovian equations of motion for probability amplitudes of a relevant set of state vectors. This method, in a Born-like approximation, leads automatically to an Hamiltonian restricted to a subspace and thus enables the construction of effective Hamiltonians. In the present paper, in order to explain the efficiency of Seke's method in particular applications, its algebraic operator structure is analyzed and a new successive approximation technique for the calculation of eigenstates and eigenvalues of an arbit

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3

Fukuzawa, Toshiyuki, Mikito Koshino, and Tsuneya Ando. "Weak-Field Hall Effect in Graphene Calculated within Self-Consistent Born Approximation." Journal of the Physical Society of Japan 78, no. 9 (2009): 094714. http://dx.doi.org/10.1143/jpsj.78.094714.

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4

Mašek, J. "Electronic states in disordered systems with statistical correlations: Self-consistent born approximation." Zeitschrift für Physik B Condensed Matter 64, no. 2 (1986): 145–50. http://dx.doi.org/10.1007/bf01303695.

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5

Ando, Tsuneya. "Bilayer Graphene with Long-Range Scatterers Studied in a Self-Consistent Born Approximation." Journal of the Physical Society of Japan 80, no. 1 (2011): 014707. http://dx.doi.org/10.1143/jpsj.80.014707.

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6

Hershfield, Selman. "Equivalence of the multilead approach to dephasing and the self-consistent Born approximation." Physical Review B 43, no. 14 (1991): 11586–94. http://dx.doi.org/10.1103/physrevb.43.11586.

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7

Yang, Jun, Wei-Guo Yin, and Chang-De Gong. "Study of Spin Polarons in Extended t–J Model by Self-Consistent Born Approximation." Modern Physics Letters B 12, no. 06n07 (1998): 205–13. http://dx.doi.org/10.1142/s0217984998000275.

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By introducing the second and third neighbors t′ and t″ terms to the pure t–J Hamiltonian, we could obtain the quasiparticle dispersion data which are consistent with the experimental results for Sr 2 CuO 2 Cl 2. The correlation of hole motion with ferromagnetic correlations is automatically included in our approach, thus leading to a experimentally observed asymmetry of the quasiparticle between k and k + (π, π).

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8

Zhang, Hou-Dao, and YiJing Yan. "Onsets of hierarchy truncation and self–consistent Born approximation with quantum mechanics prescriptions invariance." Journal of Chemical Physics 143, no. 21 (2015): 214112. http://dx.doi.org/10.1063/1.4936831.

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9

Yin, Wei-Guo, Hao Biao, and Chang-De Gong. "Dynamics of a single hole in a quantum antiferromagnet: self-consistent Born approximation study." Physics Letters A 220, no. 4-5 (1996): 281–86. http://dx.doi.org/10.1016/0375-9601(96)00542-7.

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10

Liu, Yu, JinShuang Jin, Jun Li, XinQi Li, and YiJing Yan. "Number-resolved master equation approach to quantum transport under the self-consistent Born approximation." Science China Physics, Mechanics and Astronomy 56, no. 10 (2013): 1866–73. http://dx.doi.org/10.1007/s11433-013-5238-7.

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11

Vasileska, Dragica, Terry Eldridge, Paolo Bordone, and David K. Ferry. "Quantum Transport Simulation of the DOS function, Self-Consistent Fields and Mobility in MOS Inversion Layers." VLSI Design 6, no. 1-4 (1998): 21–25. http://dx.doi.org/10.1155/1998/46360.

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We describe a simulation of the self-consistent fields and mobility in (100) Si-inversion layers for arbitrary inversion charge densities and temperatures. A nonequilibrium Green's functions formalism is employed for the state broadening and conductivity. The subband structure of the inversion layer electrons is calculated self-consistently by simultaneously solving the Schrödinger, Poisson and Dyson equations. The self-energy contributions from the various scattering mechanisms are calculated within the self-consistent Born approximation. Screening is treated within RPA. Simulation results su

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12

Wang, Bin-Bin, Wei Wang, Shun-Li Yu, and Jian-Xin Li. "Dynamics of a single hole in the Heisenberg–Kitaev model: a self-consistent Born approximation study." Journal of Physics: Condensed Matter 30, no. 38 (2018): 385602. http://dx.doi.org/10.1088/1361-648x/aada9c.

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13

Ghaderzadeh, A., S. H. Ebrahimnazhad Rahbari, and A. Phirouznia. "Aharonov-Casher effect and quantum transport in graphene based nano rings: A self-consistent Born approximation." Journal of Magnetism and Magnetic Materials 449 (March 2018): 485–92. http://dx.doi.org/10.1016/j.jmmm.2017.09.085.

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14

Rösch, Oliver, and Olle Gunnarsson. "Electron–phonon interaction in undoped cuprates: Sum rules, vertex corrections and the self-consistent Born approximation." Physica C: Superconductivity 460-462 (September 2007): 1123–24. http://dx.doi.org/10.1016/j.physc.2007.03.235.

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15

Sturm, K. "Dynamic Structure Factor: An Introduction." Zeitschrift für Naturforschung A 48, no. 1-2 (1993): 233–42. http://dx.doi.org/10.1515/zna-1993-1-244.

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Abstract The doubly differential cross-section for weak inelastic scattering of waves or particles by manybody systems is derived in Born approximation and expressed in terms of the dynamic structure factor according to van Hove. The application of this very general scheme to scattering of neutrons, x-rays and high-energy electrons is discussed briefly. The dynamic structure factor, which is the space and time Fourier transform of the density-density correlation function, is a property of the many-body system independent of the external probe and carries information on the excitation spectrum

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16

BARENTZEN, HEINZ, and VIKTOR OUDOVENKO. "A SELF-CONSISTENT ANALYTIC THEORY OF THE SPIN BIPOLARON IN THE t–J MODEL." International Journal of Modern Physics B 14, no. 08 (2000): 809–35. http://dx.doi.org/10.1142/s0217979200000674.

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The spin bipolaron in the t–J model, i.e., two holes interacting with an antiferromagnetic spin background, is treated by an extension of the self-consistent Born approximation (SCBA), which has proved to be very accurate in the single-hole (spin polaron) problem. One of the main ingredients of our approach is the exact form of the bipolaron eigenstates in terms of a complete set of two-hole basis vectors. This enables us to eliminate the hole operators and to obtain the eigenvalue problem solely in terms of the boson (magnon) operators. The eigenvalue equation is then solved by a procedure si

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17

Afzalian, Aryan. "Computationally efficient self-consistent born approximation treatments of phonon scattering for coupled-mode space non-equilibrium Green’s function." Journal of Applied Physics 110, no. 9 (2011): 094517. http://dx.doi.org/10.1063/1.3658809.

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18

Starykh, Oleg A., Oziel F. de Alcantara Bonfim, and George F. Reiter. "Self-consistent Born approximation for the hole motion in the three-band model: A comparison with photoemission experiments." Physical Review B 52, no. 17 (1995): 12534–37. http://dx.doi.org/10.1103/physrevb.52.12534.

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19

Mabong, S., G. Maynard, and K. Katsonis. "Parametric potential for modelling of highly charged heavy ions." Laser and Particle Beams 14, no. 4 (1996): 575–86. http://dx.doi.org/10.1017/s0263034600010296.

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Parametric electron-ion potential for fast estimation of atomic data required for “on-line” calculations in inertial confinement fusion (ICF) driven by heavy ions is presented. Comparisons of our results (outer- and inner-shell ionization energies, oscillator strengths, and logarithmic mean excitation energies) with experimental and self-consistent-field (SCF) calculation values are made. Using the wave functions generated by the previously mentioned potential, generalized oscillator strengths and integrated inelastic collision cross sections are computed within the frame of Born approximation

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20

Basu, P. K. "Effect of interface roughness on excitonic linewidth in a quantum well: Golden-rule and self-consistent-Born-approximation calculations." Physical Review B 44, no. 16 (1991): 8798–801. http://dx.doi.org/10.1103/physrevb.44.8798.

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21

MISHCHENKO, ALEXEY, and AXEL KÖNIES. "A many-particle approach to the gyro-kinetic theory." Journal of Plasma Physics 73, no. 5 (2007): 757–72. http://dx.doi.org/10.1017/s0022377806006258.

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AbstractA systematic first-principles approach to the many-particle formulation of the gyro-kinetic theory is suggested. The gyro-kinetic many-particle Hamiltonian is derived using the Lie transform technique. The generalized gyro-kinetic equation is obtained following the Born–Bogoliubov–Green–Kirkwood–Yvon approach. The microscopic expression for the self-consistent potential and the polarization density is obtained. It is shown that new terms appear in the gyro-kinetic polarization that can not be derived in the conventional approach. An expression for the collision term is obtained in the

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22

Ma, Manman, Shuangliang Zhao, and Zhenli Xu. "Investigation of Dielectric Decrement and Correlation Effects on Electric Double-Layer Capacitance by Self-Consistent Field Model." Communications in Computational Physics 20, no. 2 (2016): 441–58. http://dx.doi.org/10.4208/cicp.260715.210316a.

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AbstractThe differential capacitance of electric double-layer capacitors is studied by developing a generalized model of the self-consistent Gaussian field theory. This model includes many-body effects of particles near the interface such as ionic sizes, the order of water alignment and electrostatic correlations, and thus can present more accurate predictions of the electric double-layer structure and hence the capacitance than traditional continuum theories. Analytical simplification of the model and efficient numerical method are introduced, in particular, the approximation of the self-Gree

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23

Liu, Yu, Jin-Shuang Jin, Jun Li, Xin-Qi Li, and Yi-Jing Yan. "Nonequilibrium Shot Noise Spectrum Through a Quantum Dot in the Kondo Regime: A Master Equation Approach under Self-Consistent Born Approximation." Communications in Theoretical Physics 60, no. 4 (2013): 503–9. http://dx.doi.org/10.1088/0253-6102/60/4/20.

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24

Seibold, Götz, Sergio Caprara, Marco Grilli, and Roberto Raimondi. "On the Evaluation of the Spin Galvanic Effect in Lattice Models with Rashba Spin-Orbit Coupling." Condensed Matter 3, no. 3 (2018): 22. http://dx.doi.org/10.3390/condmat3030022.

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The spin galvanic effect (SGE) describes the conversion of a non-equilibrium spin polarization into a charge current and has recently attracted renewed interest due to the large conversion efficiency observed in oxide interfaces. An important factor in the SGE theory is disorder which ensures the stationarity of the conversion. Through this paper, we propose a procedure for the evaluation of the SGE on disordered lattices which can also be readily implemented for multiband systems. We demonstrate the performance of the method for a single-band Rashba model and compare our results with those ob

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25

Iztihad, Hossain Md, Touhid Khan, Abu Sufian, Md Nur Kutubul Alam, Md Nurunnabi Mollah, and Md Rafiqul Islam. "Ballistic Performance Study of Nanowire FET: Effect of Channel Materials and Phonon Scattering." International Journal of Nanoscience 15, no. 03 (2016): 1640003. http://dx.doi.org/10.1142/s0219581x16400032.

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The ballistic performance of Si and Ge nanowire (NW) is compared in this study. Current–voltage characteristic is obtained by self-consistently solving the nonequilibrium Green’s function (NEGF) transport equation with Poisson’s equation. The result is obtained at [Formula: see text] channel orientation. Simulation result shows Ge NW gives higher ON-state current than Si NW, when OFF-state current is made equal by gate metal work function engineering. However, at subthreshold region, performance of NW FET for both material is almost identical. The intravalley and intervalley electron–phonon sc

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26

Hafiz, Md Samzid Bin, Quazi Deen Mohd Khosru, Momotaz Begum, and Bimal Chandra Das. "First-principles quantum treatment of electron–phonon interactions in thin-film nanodevices." AIP Advances 12, no. 11 (2022): 115015. http://dx.doi.org/10.1063/5.0124158.

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Electron–phonon interactions play a crucial role in nano-electronic device performance. As the accurate calculation of these interactions requires huge computational resources, reduction of this burden without losing accuracy poses an important challenge. Here, we investigate the electron–phonon interactions of nano-devices using two first-principles-based methods in numerically efficient manners. The first method is the Lowest Order Approximation (LOA) version of the computationally burdensome self-consistent Born approximation method. The LOA method incorporates the effect of each phonon mod

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27

Korolkov, Denis, Peter Busch, Lutz Willner, et al. "Analysis of randomly oriented structures by grazing-incidence small-angle neutron scattering." Journal of Applied Crystallography 45, no. 2 (2012): 245–54. http://dx.doi.org/10.1107/s0021889812002324.

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A formalism is presented which allows the quantitative evaluation of data from grazing-incidence small-angle neutron and X-ray scattering – GISANS and GISAXS – in the framework of the distorted wave Born approximation. While several aspects have been reported previously, this formalism combines solutions for scattering intensities in both reflection and transmission hemispheres, taking into account instrumental resolution effects. This formalism is applied to the case of GISANS from self-organized diblock copolymers, ordered in perpendicular lamellar structures on an Si wafer in randomly orien

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28

Yarmohammadi, Mohsen, Houshang Araghi Kazzaz, and Mohammad Saeed Feali. "Orbital magneto-electronic heat capacity of hydrogenated graphene in the presence of dilute charged impurity." International Journal of Modern Physics B 31, no. 08 (2017): 1750053. http://dx.doi.org/10.1142/s0217979217500539.

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In this paper, the effect of dilute charged impurity and external magnetic field on orbital-resolved density of states (DOS) and electronic heat capacity (EHC) of a monolayer hydrogenated graphene which is called chair-like graphane is investigated within the Harrison model and Green’s function technique. The self-consistent Born approximation has been implemented to describe the effect of scattering between electrons and dilute charged impurities. Our results show that the graphane is a semiconductor and its band gap decreases with impurity and magnetic field. EHC reaches almost linearly to S

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29

LIU, S. Y., N. J. M. HORING, and X. L. LEI. "THE SPIN-HALL EFFECT IN p-TYPE BULK SEMICONDUCTORS." International Journal of High Speed Electronics and Systems 18, no. 01 (2008): 137–45. http://dx.doi.org/10.1142/s0129156408005217.

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The spin Hall effect provides a new possible way to effectively inject spins into paramagnetic semiconductors. Here, we investigate the spin-Hall effect in a p-type Luttinger semiconductor employing a two-band kinetic equation analysis. The long-range disorder effect on spin-Hall current (SHC) is considered within the self-consistent Born approximation. We find that in addition to the intrinsic SHC proposed previously, there is a nonvanishing SHC that originates from long-range electron-impurity scattering, but which is independent of impurity density in the diffusive regime. This SHC has an o

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30

Martinez, Antonio, and John Barker. "Quantum Transport in a Silicon Nanowire FET Transistor: Hot Electrons and Local Power Dissipation." Materials 13, no. 15 (2020): 3326. http://dx.doi.org/10.3390/ma13153326.

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A review and perspective is presented of the classical, semi-classical and fully quantum routes to the simulation of electro-thermal phenomena in ultra-scaled silicon nanowire field-effect transistors. It is shown that the physics of ultra-scaled devices requires at least a coupled electron quantum transport semi-classical heat equation model outlined here. The importance of the local density of states (LDOS) is discussed from classical to fully quantum versions. It is shown that the minimal quantum approach requires self-consistency with the Poisson equation and that the electronic LDOS must

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31

Král, Karel, and Miroslav Menšík. "Quantum dots with indirect band gap: power-law photoluminescence decay." World Journal of Engineering 11, no. 5 (2014): 507–12. http://dx.doi.org/10.1260/1708-5284.11.5.507.

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In this work the experimental effect of a slow decay of the photoluminescence is studied theoretically in the case of quantum dots with an indirect energy band gap. The slow decay of the photoluminescence is considered as decay in time of the luminescence intensity, following the excitation of the quantum dot sample electronic system by a short optical pulse. In the presented theoretical treatment the process is studied as a single dot property. The inter-valley deformation potential interaction of the excited conduction band electrons with lattice vibrations is considered in the self-consiste

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32

KRÁL, K., Z. KHÁS, P. ZDENĚK, M. ČERŇANSKÝ, and C. Y. LIN. "ELECTRON-ENERGY RELAXATION IN POLAR SEMICONDUCTOR DOUBLE QUANTUM DOTS." International Journal of Modern Physics B 15, no. 27 (2001): 3503–12. http://dx.doi.org/10.1142/s0217979201007403.

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The zero-dimensional semiconductor nanostructures belong to the candidates for the realization of the quantum bits. They are expected to be scalable for the purpose of tuning their physical properties. In these structures the quantum bit could be realized in the form of a single quantum dot with two electronic energy levels, with only one electron in the dot. As the basic states of the quantum bit, realized in this way, the two orbital states of the electron in the dot could be used. It appears however that usually the relaxation of the energy of the electron from the excited energy level is o

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33

Lee, Youseung, Demetrio Logoteta, Nicolas Cavassilas, Michel Lannoo, Mathieu Luisier, and Marc Bescond. "Quantum Treatment of Inelastic Interactions for the Modeling of Nanowire Field-Effect Transistors." Materials 13, no. 1 (2019): 60. http://dx.doi.org/10.3390/ma13010060.

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During the last decades, the Nonequilibrium Green’s function (NEGF) formalism has been proposed to develop nano-scaled device-simulation tools since it is especially convenient to deal with open device systems on a quantum-mechanical base and allows the treatment of inelastic scattering. In particular, it is able to account for inelastic effects on the electronic and thermal current, originating from the interactions of electron–phonon and phonon–phonon, respectively. However, the treatment of inelastic mechanisms within the NEGF framework usually relies on a numerically expensive scheme, impl

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34

Prasanti, Marla, Anjali Jha, and Ch Ravi Shankar Kumar. "Electronic Properties of Aldehyde Complexes Using DFT for Electrooptical Activity." Materials Science Forum 1048 (January 4, 2022): 212–20. http://dx.doi.org/10.4028/www.scientific.net/msf.1048.212.

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Characterization of materials infer for physical and chemical properties that depend on its molecular structure. Structure of molecule has its dependence on respective electrons of molecule under consideration occupying their positions that correspond to changes in density of electrons. Many theories of its kind were developed to study density of electrons with roots from wavefunction method and electron density method. Wavefunction method has its dependence with linear combination of atomic orbitals, Born approximation, variational principle ,potential energy surfaces for development of Hucke

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35

Basak, Anirban, Pratik Brahma, and Bhaskaran Muralidharan. "Momentum relaxation effects in 2D-Xene field effect device structures." Journal of Physics D: Applied Physics 55, no. 7 (2021): 075302. http://dx.doi.org/10.1088/1361-6463/ac3354.

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Abstract We analyze the electric field driven topological field effect transition on 2D-xene materials with the addition of momentum relaxation effects, in order to account for dephasing processes. The topological field effect transition between the quantum spin Hall phase and the quantum valley Hall phase is analyzed in detail using the Keldysh non-equilibrium Green’s function technique with the inclusion of momentum and phase relaxation, within the self-consistent Born approximation. Details of the transition with applied electric field are elucidated for the ON–OFF characteristics with emph

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36

Hassaneen, Khaled S. A. "Self-Consistent Green Function Method in Nuclear Matter." Physics Research International 2013 (July 16, 2013): 1–6. http://dx.doi.org/10.1155/2013/415605.

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Symmetric nuclear matter is studied within the Brueckner-Hartree-Fock (BHF) approach and is extending to the self-consistent Green’s function (SCGF) approach. Both approximations are based on realistic nucleon-nucleon interaction; that is, CD-Bonn potential is chosen. The single-particle energy and the equation of state (EOS) are studied. The Fermi energy at the saturation point fulfills the Hugenholtz-Van Hove theorem. In comparison to the BHF approach, the binding energy is reduced and the EOS is stiffer. Both the SCGF and BHF approaches do not reproduce the correct saturation point. A simpl

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37

Korda, David, and Michal Švanda. "Combined helioseismic inversions for 3D vector flows and sound-speed perturbations." Astronomy & Astrophysics 622 (February 2019): A163. http://dx.doi.org/10.1051/0004-6361/201833000.

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Context. Time–distance helioseismology is the method of the study of the propagation of waves through the solar interior via the travel times of those waves. The travel times of wave packets contain information about the conditions in the interior integrated along the propagation path of the wave. The travel times are sensitive to perturbations of a variety of quantities. The usual task is to invert for the vector of plasma flows or the sound–speed perturbations separately. The separate inversions may be polluted by systematic bias, for instance, originating in the leakage of vector flows into

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38

Scarlatella, Orazio, and Marco Schirò. "Self-consistent dynamical maps for open quantum systems." SciPost Physics 16, no. 1 (2024). http://dx.doi.org/10.21468/scipostphys.16.1.026.

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In several cases, open quantum systems can be successfully described using master equations relying on Born-Markov approximations, but going beyond these approaches has become often necessary. In this work, we introduce the NCA and NCA-Markov dynamical maps for open quantum systems, which go beyond these master equations replacing the Born approximation with a self-consistent approximation, known as non-crossing approximation (NCA). These maps are formally similar to master equations, but allow to capture non-perturbative effects of the environment at a moderate extra numerical cost. To demons

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39

Sinner, A., and K. Ziegler. "Corrections to the self-consistent Born approximation for Weyl fermions." Physical Review B 96, no. 16 (2017). http://dx.doi.org/10.1103/physrevb.96.165140.

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40

Koshino, Mikito, and Tsuneya Ando. "Transport in bilayer graphene: Calculations within a self-consistent Born approximation." Physical Review B 73, no. 24 (2006). http://dx.doi.org/10.1103/physrevb.73.245403.

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41

Klier, J., I. V. Gornyi, and A. D. Mirlin. "From weak to strong disorder in Weyl semimetals: Self-consistent Born approximation." Physical Review B 100, no. 12 (2019). http://dx.doi.org/10.1103/physrevb.100.125160.

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42

Gunnarsson, O., and O. Rösch. "Electron-phonon coupling in the self-consistent Born approximation of thet−Jmodel." Physical Review B 73, no. 17 (2006). http://dx.doi.org/10.1103/physrevb.73.174521.

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43

Lee, William, Nicola Jean, and Stefano Sanvito. "Exploring the limits of the self-consistent Born approximation for inelastic electronic transport." Physical Review B 79, no. 8 (2009). http://dx.doi.org/10.1103/physrevb.79.085120.

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44

Dash, L. K., H. Ness, and R. W. Godby. "Nonequilibrium inelastic electronic transport: Polarization effects and vertex corrections to the self-consistent Born approximation." Physical Review B 84, no. 8 (2011). http://dx.doi.org/10.1103/physrevb.84.085433.

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45

McEniry, Eunan J., Thomas Frederiksen, Tchavdar N. Todorov, Daniel Dundas, and Andrew P. Horsfield. "Inelastic quantum transport in nanostructures: The self-consistent Born approximation and correlated electron-ion dynamics." Physical Review B 78, no. 3 (2008). http://dx.doi.org/10.1103/physrevb.78.035446.

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46

de Juan, F., E. H. Hwang, and M. A. H. Vozmediano. "Spectral and optical properties of doped graphene with charged impurities in the self-consistent Born approximation." Physical Review B 82, no. 24 (2010). http://dx.doi.org/10.1103/physrevb.82.245418.

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47

Nakai, Ryota, and Kentaro Nomura. "Disorder effects on thermal transport on the surface of topological superconductors by the self-consistent Born approximation." Physical Review B 89, no. 6 (2014). http://dx.doi.org/10.1103/physrevb.89.064503.

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48

Arii, Katsuyuki, Mikito Koshino, and Tsuneya Ando. "Dynamical spin Hall conductivity in a disordered two-dimensional system calculated in a self-consistent Born approximation." Physical Review B 76, no. 4 (2007). http://dx.doi.org/10.1103/physrevb.76.045311.

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49

Honeychurch, Thomas D., and Daniel S. Kosov. "Quantum transport in driven systems with vibrations: Floquet nonequilibrium Green's functions and the self-consistent Born approximation." Physical Review B 107, no. 3 (2023). http://dx.doi.org/10.1103/physrevb.107.035410.

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50

Ryndyk, D. A., M. Hartung, and G. Cuniberti. "Nonequilibrium molecular vibrons: An approach based on the nonequilibrium Green function technique and the self-consistent Born approximation." Physical Review B 73, no. 4 (2006). http://dx.doi.org/10.1103/physrevb.73.045420.

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