Single and double electron emission: combination of projection operator and nonequilibrium Green's function approaches

TL;DR

This paper develops a unified theoretical framework combining projection operator and nonequilibrium Green's function methods to analyze single and double electron emission, providing new insights into correlated electron-pair processes.

Contribution

It introduces a novel combined approach for electron emission analysis and derives explicit forms for the effective Hamiltonian and self-energy in correlated double-electron emission.

Findings

Explicit form of the Feshbach self-energy in many-body systems

Diagrammatic expansion of two-particle current

Analysis of plasmon-assisted two-electron emission

Abstract

This work provides a unified theoretical treatment of the single and correlated double-electron emission from a general electronic system. Using Feshbach projection method, the states of interest are selected by the projection operator; the Feshbach-Schur map determines the effective Hamiltonian and the optical potential for the emitted electrons. On the other hand, the nonequilibrium Green's functions method is demonstrated to be a complementary approach and an explicit correspondence between both methods is established. For a self-contained exposition some results on single electron emission are re-derived using both formalisms. New insights and results are obtained for the correlated electron-pair emission: This includes the effective two-electron Hamiltonian, the explicit form of the Feshbach self-energy in terms of the many-body self-energies, and the diagrammatic expansion of the two-particle current. As an illustration of the diagrammatic technique the process of the two-particle emission assisted by the excitation of plasmons is explicitly worked out.