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Bogoliubov-de Gennes Method and Its Applications 1st ed. 2016 [Pehme köide]

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  • Formaat: Paperback / softback, 188 pages, kõrgus x laius: 235x155 mm, kaal: 454 g, 33 Illustrations, color; 17 Illustrations, black and white; XI, 188 p. 50 illus., 33 illus. in color., 1 Paperback / softback
  • Sari: Lecture Notes in Physics 924
  • Ilmumisaeg: 22-Jun-2016
  • Kirjastus: Springer International Publishing AG
  • ISBN-10: 3319313126
  • ISBN-13: 9783319313122
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Bogoliubov-de Gennes Method and Its Applications 1st ed. 2016Suurem pilt
  • Formaat: Paperback / softback, 188 pages, kõrgus x laius: 235x155 mm, kaal: 454 g, 33 Illustrations, color; 17 Illustrations, black and white; XI, 188 p. 50 illus., 33 illus. in color., 1 Paperback / softback
  • Sari: Lecture Notes in Physics 924
  • Ilmumisaeg: 22-Jun-2016
  • Kirjastus: Springer International Publishing AG
  • ISBN-10: 3319313126
  • ISBN-13: 9783319313122
Teised raamatud teemal:
Püsilink: https://www.kriso.ee/db/9783319313122.html
Märksõnad:
The purpose of this book is to provide an elementary yet systematic description of the Bogoliubov-de Gennes (BdG) equations, their unique symmetry properties and their relation to Greens function theory. Specifically, it introduces readers to the supercell technique for the solutions of the BdG equations, as well as other related techniques for more rapidly solving the equations in practical applications.

The BdG equations are derived from a microscopic model Hamiltonian with an effective pairing interaction and fully capture the local electronic structure through self-consistent solutions via exact diagonalization. This approach has been successfully generalized to study many aspects of conventional and unconventional superconductors with inhomogeneities including defects, disorder or the presence of a magnetic field and becomes an even more attractive choice when the first-principles information of a typical superconductor is incorporated via the construction of a low-energy tight-binding model. Further, the lattice BdG approach is essential when theoretical results for local electronic states around such defects are compared with the scanning tunneling microscopy measurements.

Altogether, these lectures provide a timely primer for graduate students and non-specialist researchers, while also offering a useful reference guide for experts in the field.

Arvustused

The lecture notes discuss the Bogoliubov-de-Gennes (BdG) method and its applications in superconductivity. The book will be useful for gradient students and all those interested in moderate problems of superconductivity. (Ivan A. Parinov, zbMATH 1361.82007, 2017)

Part I Bogoliubov-de Gennes Theory: Method
1 Bogliubov-de Gennes Equations for Superconductors in the Continuum Model
3(34)
1.1 Introduction
3(1)
1.2 Quantum Many-Body Hamiltonian
4(5)
1.3 Second Quantization
9(4)
1.4 Basic Properties of Superconductors
13(1)
1.5 Derivation of the BdG Equations in the Continuum Model
14(8)
1.5.1 Derivation
15(6)
1.5.2 Local Density of States
21(1)
1.5.3 Gauge In variance
22(1)
1.6 Structure of a General Gap Matrix
22(3)
1.7 Solution to the BdG Equations in Homogeneous Systems
25(6)
1.8 Relation to the Abrikosov-Gor'kov Equations
31(6)
References
35(2)
2 BdG Equations in Tight-Binding Model
37(32)
2.1 Derivation of BdG Equations in a Tight-Bind Model
37(19)
2.1.1 Local Density of States and Bond Current in the Lattice Model
44(1)
2.1.2 Optical Conductivity and Superfluid Density in the Lattice Model
45(11)
2.2 Solution to the BdG Equations in the Lattice Model for a Uniform Superconductor
56(4)
2.3 Abrikosov-Gorkov Equations in the Lattice Model
60(9)
References
64(5)
Part II Bogoliubov-de Gennes Theory: Applications
3 Local Electronic Structure Around a Single Impurity in Superconductors
69(20)
3.1 Introduction
69(1)
3.2 Yu-Shiba-Rusinov Impurity States in an s-Wave Superconductor
69(8)
3.3 Majorana Fermion in an s-Wave Superconductor with a Chain of Localized Spins
77(5)
3.4 Impurity Resonance State in a d-Wave Superconductor
82(7)
References
87(2)
4 Disorder Effects on Electronic and Transport Properties in Superconductors
89(22)
4.1 Anderson Theorem for Disordered s-Wave Superconductor
89(5)
4.2 Suppression of Superconductivity in a Disordered d-Wave Superconductor
94(6)
4.3 Quasiparticle Localization in a Disordered d-Wave Superconductor
100(11)
References
109(2)
5 Local Electronic Structure in Superconductors Under a Magnetic Field
111(30)
5.1 Effect of the Magnetic Field
111(3)
5.2 Vortex Core State in an s-Wave Superconductor
114(10)
5.2.1 Single Isolated Vortex
114(9)
5.2.2 High Field Limit
123(1)
5.3 Vortex Core States in a d-Wave Superconductor
124(10)
5.3.1 Single Isolated Vortex
125(2)
5.3.2 Quasiparticle States in a Mixed-State of d-Wave Superconductors
127(7)
5.4 Fulde-Ferrell-Larkin-Ovchinikov State due to a Zeeman Magnetic Field
134(7)
References
138(3)
6 Transport Across Normal-Metal/Superconductor Junctions
141(28)
6.1 Blonder-Tinkham-Klapwijk Scattering Formalism
141(5)
6.2 Tunneling Conductance Through a Normal-Metal/Superconductor Junction
146(9)
6.3 Suppression of Andreev Reflection in a Ferromagnet/s-Wave Superconductor Junction
155(3)
6.4 Transport Properties Through a Topological-Insulator/Superconductor Junction
158(11)
References
166(3)
7 Topological and Quantum Size Effects in Superconductors at Reduced Length Scale
169(18)
7.1 Persistent Current in a Mesoscopic s-Wave Superconducting Ring
169(7)
7.2 Persistent Current in Multiply Connected Mesoscopic d-Wave Superconducting Geometries
176(5)
7.2.1 Cylindrical Geometry
176(2)
7.2.2 Square Loop Geometry
178(3)
7.3 Quantum Size Effects in Nanoscale Superconductors
181(6)
References
184(3)
Additional Reading 187
Dr Jian-Xin Zhu obtained his PhD from the University of Hong Kong in 1997. He is presently a staff member of the Theoretical Division,  Los Alamos National Laboratory, and also a Partner Science Leader in the thrust of Theory and Simulation of Nanoscale Phenomena of the Center for Integrated Nanotechnologies (CINT), a U.S. DOE BES user facility. Dr Zhu, who was awarded the LANL Postdoctoral Distinguished Performance Award in 2003, is an internationally known expert on the theory of superconductivity and on electronic structure in strongly correlated systems, with a particular focus on the theoretical analysis of scanning tunneling microscopy and photoemission spectroscopy measurements.