Order parameter and spectral function in $d$-wave holographic superconductors

TL;DR

This paper studies $d$-wave holographic superconductors with full backreaction, identifying the order parameter and analyzing the spectral function to reveal Fermi arc and gapped behaviors similar to ARPES data.

Contribution

It provides a corrected order parameter for $d$-wave holographic superconductors and explores the spectral function's dependence on various parameters, including the influence of multiple fermion flavors.

Findings

Identified the corrected order parameter via spectral function comparison.

Observed Fermi arc and gapped behavior in spectral functions.

Demonstrated how different condensate combinations produce various spectral functions.

Abstract

We consider the $d$-wave holographic superconductor model with full backreaction on the metric, addressing a missing part in the literature. We have identified the corrected order parameter by comparing the fermionic spectral function with the momentum-dependent order parameter. By numerical investigations of the fermionic spectral function in the presence of a tensor condensate, we find the Fermi arc and the gapped behavior, which closely resemble ARPES data. Moreover, we have examined the influence of the coupling constant, chemical potential, and temperature on the spectral function. We find that $d$-wave fermionic spectral function can be obtained through $p_x$ and $p_y$ condensates combined with two fermion flavors. Similarly, combining $d_{x^2-y^2}$ and $d_{xy}$ orbitals symmetry with two fermion flavors leads to a $g$-wave spectral function.