Bogoliubov-de Gennes Method and Its Applications

1. Front Matter

   Pages i-xi

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2. Bogoliubov-de Gennes Theory: Method

   1. Front Matter

      Pages 1-1

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   2. Bogliubov-de Gennes Equations for Superconductors in the Continuum Model

      • Jian-Xin Zhu

      Pages 3-36

   3. BdG Equations in Tight-Binding Model

      • Jian-Xin Zhu

      Pages 37-65

3. Bogoliubov-de Gennes Theory: Applications

   1. Front Matter

      Pages 67-67

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   2. Local Electronic Structure Around a Single Impurity in Superconductors

      • Jian-Xin Zhu

      Pages 69-88

   3. Disorder Effects on Electronic and Transport Properties in Superconductors

      • Jian-Xin Zhu

      Pages 89-109

   4. Local Electronic Structure in Superconductors Under a Magnetic Field

      • Jian-Xin Zhu

      Pages 111-139

   5. Transport Across Normal-Metal/Superconductor Junctions

      • Jian-Xin Zhu

      Pages 141-167

   6. Topological and Quantum Size Effects in Superconductors at Reduced Length Scale

      • Jian-Xin Zhu

      Pages 169-185

4. Back Matter

   Pages 187-188

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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.

• 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

“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)

• Theoretical Division, MS B262, Los Alamos National Laboratory, Los Alamos, USA

  Jian-Xin Zhu

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.

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