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

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.