The Spin of Holographic Electrons at Nonzero Density and Temperature

TL;DR

This paper investigates how the spin of probe fermions influences the Green's function in a strongly coupled field theory at finite temperature and density, revealing spin-orbit coupling effects and a Rashba-like dispersion relation via holography.

Contribution

It introduces the study of fermion spin effects on Green's functions in holographic models with charged black holes, highlighting spin-orbit coupling and dispersion relation modifications.

Findings

Identification of spin-orbit coupling effects on Green's functions.

Discovery of a Rashba-like dispersion relation due to fermion spin.

Analysis of spin influence on fermionic quasinormal modes.

Abstract

We study the Green's function of a gauge invariant fermionic operator in a strongly coupled field theory at nonzero temperature and density using a dual gravity description. The gravity model contains a charged black hole in four dimensional anti-de Sitter space and probe charged fermions. In particular, we consider the effects of the spin of these probe fermions on the properties of the Green's function. There exists a spin-orbit coupling between the spin of an electron and the electric field of a Reissner-Nordstrom black hole. On the field theory side, this coupling leads to a Rashba like dispersion relation. We also study the effects of spin on the damping term in the dispersion relation by considering how the spin affects the placement of the fermionic quasinormal modes in the complex frequency plane in a WKB limit. An appendix contains some exact solutions of the Dirac equation in terms of Heun polynomials.