Probing the Holographic Fermi Arc with scalar field: Numerical and analytical study

Abstract

Fermi arcs are disconnected contour of Fermi surface, which can be observed in the pseudo-gap phase of high temperature superconductors. Aiming to understand this pseudo-gap phenomena, we study a holographic Fermionic system coupled with a massive scalar field in an AdS black hole background. Depending on the boundary condition on the scalar field mode, we discuss two possible scenarios. When the scalar condenses below a critical temperature $T_c$, the Fermi surface undergoes a transition from normal phase to pseudo-gap phase. Hence $T_c$ can be the reminiscent of well-known cross over temperature $T^*$ in cuprate superconductor, below which pseudo-gap appears at constant doping. In the second scenario, the bulk scalar develops a non-normalizable profile at arbitrary temperature for non-zero source at the boundary. Therefore, we can tune the Fermi spectrum by tuning a dual source at the boundary. The dual source for this case can be the reminiscent of hole doping in the real cuprate superconductor. For both the cases we have studied Fermi spectrum and observed anisotropic gap in the spectral function depending on the model parameter and studied the properties of Fermi arcs across different phases.