Fermi surfaces in N=4 Super-Yang-Mills theory

TL;DR

This paper classifies Fermi surface behaviors in a holographic model of N=4 Super-Yang-Mills theory at zero temperature, revealing various non-Fermi liquid states and their properties under different limits.

Contribution

It provides a detailed numerical and analytical study of fermionic modes and Fermi surfaces in a holographic setting, including limits with vanishing entropy and phase transitions.

Findings

Identification of multiple Fermi surface singularities associated with non-Fermi liquids

Demonstration of a Fermi surface approaching a marginal Fermi liquid analytically

Discovery of insulating and superconducting phases with distinct conductivity gaps

Abstract

We investigate and classify Fermi surface behavior for a set of fermionic modes in a family of backgrounds holographically dual to N=4 Super-Yang-Mills theory at zero temperature with two distinct chemical potentials. We numerically solve fluctuation equations for every spin-1/2 field in five-dimensional maximally supersymmetric gauged supergravity not mixing with gravitini. Different modes manifest two, one or zero Fermi surface singularities, all associated to non-Fermi liquids, and we calculate dispersion relations and widths of excitations. We study two limits where the zero-temperature entropy vanishes. In one limit, a Fermi surface approaches a marginal Fermi liquid, which we demonstrate analytically, and conductivity calculations show a hard gap with the current dual to the active gauge field superconducting, while the other is insulating. In the other limit, conductivities reveal a soft gap with the roles of the gauge fields reversed.