Analytic fermionic Green's functions from holography

TL;DR

This paper derives exact analytic solutions for fermionic Green's functions in a charged dilatonic black hole background in AdS_5, revealing multiple Fermi surfaces and various non-Fermi liquid behaviors in a strongly coupled system.

Contribution

It provides the first exact analytic solutions of the Dirac equation in this specific holographic black hole background, enabling precise analysis of Fermi surface properties.

Findings

Multiple Fermi surfaces at k_F=q-n-1/2

Fermi liquid, marginal Fermi liquid, and non-Fermi liquid behaviors identified

Exact solutions facilitate detailed holographic fermionic analysis

Abstract

We find exact, analytic solutions of the Dirac equation for a charged, massless fermion in the background of a charged, dilatonic black hole in AdS_5. The black hole descends from type IIB supergravity, where it describes D3-branes with equal angular momenta in two of the three independent planes of rotation orthogonal to the world-volume. The Green's function near the Fermi surface for a strongly coupled fermionic system can be extracted holographically from an exact solution of the Dirac equation at zero frequency but nonzero momentum. There can be several Fermi momenta, and they take the form k_F=q-n-1/2 (in units of the chemical potential), where q is the charge of the spinor, and n is a non-negative integer that labels the Fermi surfaces. Much as for holographic Fermi surfaces based on the Reissner-Nordstrom-AdS_5 solution, the dispersion relation of the excitations near the Fermi surface is determined by the geometry close to the horizon, and one can obtain Fermi liquid, marginal Fermi liquid, and non-Fermi liquid behaviors depending on the value of k_F.