Bogoliubov-de Gennes Method and Its ApplicationsThe 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. |
Other editions - View all
Common terms and phrases
Abrikosov-Gorkov amplitude Andreev reflection approximation BdG equations boundary condition coherence length Cooper pairs d-wave pairing symmetry defined differential conductance discussed disordered dx2 y2-wave pairing effect eigenfunctions eigenvalues electronic structure energy dispersion Fermi energy fermions ferromagnetic field operators Green’s function Hamiltonian high-temperature cuprates ia)n impurity scattering interface LDOS Lett magnetic field magnetic flux Majorana Majorana fermions matrix n1i h n1i hn2 n2i nonmagnetic impurity normal normal-state NS junction obtain orbital pairing interaction particle phase Phys potential scatter properties quantum s-wave superconductor self-consistency shown in Fig single impurity single-particle Hamiltonian solution spatial spin spin-flip scattering spin-orbit coupling square lattice superconducting order parameter superconducting pair potential superconductor junction superfluid superfluid density term theory tight-binding model topological transition temperature tunneling conductance two-dimensional unconventional superconductors vector potential vortex core center wave function wave vector Zeeman zero