Electron–hole coherent states for the Bogoliubov–de Gennes equation

Abstract

We construct a new set of generalized coherent states, the electron–hole coherent states, for a (quasi-)spin particle on the infinite line. The definition is inspired by applications to the Bogoliubov–de Gennes equations where the quasi-spin refers to electron- and hole-like components of electronic excitations in a superconductor. Electron–hole coherent states generally entangle the space and the quasi-spin degrees of freedom. We show that the electron–hole coherent states allow a resolution of unity to be obtained and form minimum uncertainty states for position and velocity where the velocity operator is defined using the Bogoliubov–de Gennes Hamiltonian. The usefulness and the limitations of electron–hole coherent states and the phase space representations built from them are discussed in terms of basic applications to the Bogoliubov–de Gennes equation such as Andreev reflection.