Effects of massive gravity on $s$-wave holographic superconductor

TL;DR

This paper analytically studies how massive gravity influences $s$-wave holographic superconductors, revealing that increasing massive gravity couplings raises the critical temperature and affects conductivity properties.

Contribution

It provides analytical expressions for critical temperature, condensation operator, and conductivity in massive gravity, highlighting the impact of graviton mass on superconductor behavior.

Findings

Critical temperature increases with massive gravity coupling.

Condensate decreases as graviton mass increases.

Energy band gap is estimated from conductivity analysis.

Abstract

Analytical investigation of the properties of $s$-wave holographic superconductors in the background of a massive gravity theory in the probe limit has been carried out employing the Sturm-Liouville eigenvalue method . We obtain the analytical expression for the relation between the critical temperature and the charge density. We also obtain the expression for the condensation operator and value of the critical exponent. Our findings show that as we increase the massive gravity couplings the critical temperature increases and the condensate decreases. More precisely we observe that the presence of massive graviton increases the critical temperature compared to the superconductors in Einstein gravity at some point if we keep on increasing the coupling constants. We also obtain the frequency dependence of conductivity by solving analytically the wave equation for electromagnetic perturbations. From the real part of the conductivity, we finally estimate the energy band gap.