$d+id$ Holographic Superconductors

TL;DR

This paper develops a holographic $d+id$ superconductor model using a charged spin two field in AdS spacetime, analyzing fermion spectral functions, fermi arcs, and Hall conductivity, revealing novel properties of time-reversal symmetry breaking superconductors.

Contribution

It introduces a holographic $d+id$ superconductor model with a charged spin two field and explores its fermionic and transport properties, including spontaneous Hall conductivity.

Findings

Existence of fermi arcs in the spectral function.

Spectral function becomes isotropic at equal $d$ and $id$ condensate strength.

Non-zero Hall conductivity without external magnetic field.

Abstract

A holographic model of $d+id$ superconductors based on the action proposed by Benini, Herzog, and Yarom [arXiv:1006.0731] is studied. This model has a charged spin two field in an AdS black hole spacetime. Working in the probe limit, the normalizable solution of the spin two field in the bulk gives rise to a $d+id$ superconducting order parameter at the boundary of the AdS. We calculate the fermion spectral function in this\ superconducting background and confirm the existence of fermi arcs for non-vanishing Majorana couplings. By changing the relative strength $\gamma $ of the $d$ and $id$ condensations, the position and the size of the fermi arcs are changed. When $\gamma =1$, the spectrum becomes isotropic and the spectral function is s-wave like. By changing the fermion mass, the fermi momentum is changed. We also calculate the conductivity for these holographic $d+id$ superconductors where time reversal symmetry has been broken spontaneously. A non-vanishing Hall conductivity is obtained even without an external magnetic field.