Bogoliubov-de Gennes Method and Its Applications
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Beschreibung
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.
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.
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
Autor*in
Jian-Xin Zhu
Themen in »Bogoliubov-de Gennes Method and Its Applications«
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
Stimmen zu »Bogoliubov-de Gennes Method and Its Applications«
“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)
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