Overview
- Provides a timely primer on a method increasingly used for various applications, such as investigation of the electronic structure in the vicinity of impurities
- Authored by an active researcher in the field
- Covers the most important applications of the Bologliubov-de Gennes method at a level accessible to graduate students and nonspecialists
- Includes supplementary material: sn.pub/extras
Part of the book series: Lecture Notes in Physics (LNP, volume 924)
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Table of contents (7 chapters)
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Bogoliubov-de Gennes Theory: Method
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Bogoliubov-de Gennes Theory: Applications
Keywords
- Andreev Reflection Process
- Blonder-Tinkham-Klapwijk Theory
- Distribution of Nonmagnetic Impurities
- Green’s Function Method
- High-Tc Cuprates
- Kondo Coherence Order Parameter
- Kondo Hole System
- Majorana Fermions
- Mesoscopic Superconductivity
- Multi-Orbital SuperConductors
- S-wave Superconductors
- Topological Kondo Insulator
- Topological Superconductor
- Transport Across Superconductor Junctions
- Vortices in Superconductors
- d-wave Superconductors
About this book
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 Green’s 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.
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Authors and Affiliations
About the author
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.
Bibliographic Information
Book Title: Bogoliubov-de Gennes Method and Its Applications
Authors: Jian-Xin Zhu
Series Title: Lecture Notes in Physics
DOI: https://doi.org/10.1007/978-3-319-31314-6
Publisher: Springer Cham
eBook Packages: Physics and Astronomy, Physics and Astronomy (R0)
Copyright Information: Springer International Publishing Switzerland 2016
Softcover ISBN: 978-3-319-31312-2Published: 22 June 2016
eBook ISBN: 978-3-319-31314-6Published: 21 June 2016
Series ISSN: 0075-8450
Series E-ISSN: 1616-6361
Edition Number: 1
Number of Pages: XI, 188
Number of Illustrations: 17 b/w illustrations, 33 illustrations in colour
Topics: Strongly Correlated Systems, Superconductivity, Numerical and Computational Physics, Simulation, Mathematical Applications in the Physical Sciences, Nanoscale Science and Technology, Mathematical Methods in Physics