Bogoliubov-de Gennes Method and Its Applications

  • Jian-Xin Zhu

Part of the Lecture Notes in Physics book series (LNP, volume 924)

Table of contents

  1. Front Matter
    Pages i-xi
  2. Bogoliubov-de Gennes Theory: Method

  3. Bogoliubov-de Gennes Theory: Applications

  4. Back Matter
    Pages 187-188

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.


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

Authors and affiliations

  • Jian-Xin Zhu
    • 1
  1. 1.Theoretical Division, MS B262Los Alamos National LaboratoryLos AlamosUSA

Bibliographic information