# Generalized superconductors from the coupling of a scalar field to the Einstein tensor and their refractive index in massive gravity

## TL;DR

This paper explores how coupling a scalar field to Einstein tensor in massive gravity affects the properties of generalized superconductors, including condensation formation, negative refraction, and dissipation, revealing distinct influences of graviton mass and coupling parameters.

## Contribution

It introduces a novel model of generalized superconductors with scalar-Einstein tensor coupling in massive gravity and analyzes their optical and dissipative properties.

## Key findings

- Larger graviton mass and Einstein tensor coupling hinder condensation formation.
- Certain parameter ranges promote negative refraction with reduced dissipation.
- Graviton mass and coupling parameters have opposite effects on negative refraction range.

## Abstract

We construct the generalized superconductors from the coupling of a scalar field to the Einstein tensor in the massive gravity and investigate their negative refraction in the probe limit. We observe that the larger graviton mass and Einstein tensor coupling parameters both hinder the formation of the condensation, but the larger graviton mass or smaller coupling parameter makes it easier for the emergence of the Cave of Winds. Furthermore, we see that the larger graviton mass but smaller coupling parameter make the range of frequencies or the range of temperatures larger for which a negative Depine-Lakhtakia index occurs, which indicates that the graviton mass and Einstein tensor have completely different effects on the negative refraction. In addition, we find that the larger graviton mass and coupling parameters both can reduce the dissipation and improve the propagation in the holographic setup.