Abstract
We investigate and classify Fermi surface behavior for a set of fermionic modes in a family of backgrounds holographically dual to $\mathcal{N}=4$ 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 with 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.
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