# Meissner like effect in holographic superconductors with back reaction

## TL;DR

This paper analytically studies how back reaction influences the Meissner effect in holographic superconductors, revealing that back reaction makes condensation harder and affects the critical magnetic field.

## Contribution

It provides an analytical investigation of back reaction effects on holographic superconductors, including the critical temperature and magnetic field, using the matching method.

## Key findings

- Back reaction increases the ratio of critical magnetic field to temperature squared.
- Condensation becomes more difficult with stronger back reaction.
- Critical magnetic field decreases as back reaction parameter increases.

## Abstract

In this article we employ the matching method to analytically investigate the properties of holographic superconductors in the framework of Maxwell electrodynamics taking into account the effects of back reaction on spacetime. The relationship between the critical temperature ($T_{c}$) and the charge density ($\rho$) has been obtained first. The influence of back reaction on Meissner like effect in this holographic superconductor is then studied. The results for the critical temperature indicate that the condensation gets harder to form when we include the effect of back reaction. The expression for the critical magnetic field ($B_{c}$) above which the superconducting phase vanishes is next obtained. It is observed from our investigation that the ratio of $B_{c}$ and $T_{c}^{2}$ increases with the increase in the back reaction parameter. However, the critical magnetic field $B_c$ decreases with increase in the back reaction parameter.