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Holographic fermions in charged Lifshitz theory

We investigate the properties of holographic fermions in charged Lifshitz black holes at finite temperature through the AdS/CFT correspondence. In the charged Lifshitz background with the dynamical exponent $z=2$, we find that the dispersion relation is linear. The scaling behavior of the imaginal part of the Green function relative to $k_{\perp}=k-k_F$ is also discussed. We find, although the system has linear dispersion relation and quadratic quasi-particle width, it does not satisfy Luttinger's theorem. We also find that the variation of the scaling parameters $α$ and $β$ is small as the charge $q$ varies. Furthermore, we also discuss the effect of the dynamical exponent $z$ by considering the cases $z=4$ and $z=6$ and show that $ImG_{ii}$ become smooth when the dynamical exponent $z$ increases.