Some properties of the holographic fermions in an extremal charged dilatonic black hole

TL;DR

This paper investigates fermionic Green's functions in an extremal charged dilatonic black hole, revealing Fermi-liquid-like behavior with linear dispersion, contrasting with non-Fermi liquid properties in Reissner-Nordström black holes.

Contribution

It provides new insights into fermionic properties in dilatonic black holes, highlighting differences from RN black holes and exploring their Fermi-liquid characteristics.

Findings

Dispersion relation is linear, indicating Fermi-liquid behavior.

Contrasts with non-Fermi liquid behavior in RN black holes.

Different scaling behavior of the imaginary part of Green's function.

Abstract

We study the properties of the Green's functions of the fermions in the extremal charged dilatonic black hole proposed by Gubser and Rocha [Phys. Rev. D \textbf{81}, 046001 (2010)]. We find that many properties seem to be in agreement with that of Fermi liquid. Especially, the dispersion relation is linear. It is very different from that found in the extremal Reissner-Nordstr$\ddot{o}$m (RN) black hole for massless fermion, which is obviously non-Fermi liquid due to a nonlinear dispersion relation. However, for another scaling behavior of the height of $ImG_{11}$ at the maximum, the scaling exponent is not one, which is at odds with that found in the RN black hole.