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

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 $\mathbf{\text{81}}$, 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 $Im{G}_{11}$ at the maximum, the scaling exponent is not one, which is at odds with that found in the RN black hole.