Unified description of collective modes in superconductors and semiconductors with an exciton condensed phase

Abstract

It is shown that the Bethe-Salpeter approach, the Bardeen, Cooper, and Schrieffer (BCS) based vertex method, and a generalized random-phase approximation (GRPA) to the manyelectron problem in the presence of a condensed quantum phase yield the same theoretical excitation spectrum vðQÞ to collective modes. This spectrum reveals a secondary peak in optical absorption in semiconductors that can be understood as signaling the existence of an excitonic Bose-Einstein condensate (BEC). The analysis shows as well that there is an additional, non-trivial linearly-dispersive '' moving'' Cooperpair solution for superconductors in both weak and strong coupling.

Excitonic collective modes in Weyl semimetals

“…This approach is equivalent to summation over ladder diagrams (e.g., compare Refs. 15,16), the Bethe-Salpeter equation 17,18 and equations-of-motion approaches 19 . It has been shown to work well even in the strong coupling limit where it provides good agreement with the appropriate spin wave expansion 16,20 .…”