Bogoliubov-de Gennes Method and Its Applications

von Jian-Xin Zhu
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Jian-Xin Zhu Bogoliubov-de Gennes Method and Its Applications
Jian-Xin Zhu - Bogoliubov-de Gennes Method and Its Applications

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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.


Jian-Xin Zhu

Weitere Informationen

Anmerkung Illustrationen:
XI, 188 p. 50 illus., 33 illus. in color.
Part I Bogoliubov-de Gennes Theory: Method.- Bogliubov-de Gennes Equations for Superconductors in the continuum model.- BdG Equations in Tight-Binding Model.- Part II Bogoliubov-de Gennes Theory: Applications.- Local Electronic Structure around a Single Impurity in Superconductors.- Disorder Effects on Electronic and Transport Properties in Superconductors.- Local Electronic Structure in Superconductors under a Magnetic Field.- Transport across Normal-Metal/Superconductor Junctions.- Topological and Quantum Size Effects in Superconductors at Reduced Length Scale.- References.- Additional Reading. 
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:

Springer International Publishing
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.

"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)

1st ed. 2016


22. Juni 2016
0.232 x 0.154 x 0.014 m; 0.3 kg
€ 36,99
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