Holographic Superconductors In Massive Gravity And Their Negative Refraction

As an exotic electromagnetic phenomena,the negative refraction has attracted considerable attention for many years.In recent years,the design and application of negative refractive index materials have become hot research topics.On the other hand,as a powerful mathematical tool,the AdS/CFT correspondence has revealed the profound correspondence between the gravity theory and the field theory,and provided us new insights into the understanding of the strongly coupled system in condensed matter physics.The investigation of the negative refraction in the strongly coupled superconducting systems by using the AdS/CFT correspondence is helpful for the understanding of the core mechanism governing the high-temperature superconductor systems and the application of the superconducting materials.In the probe limit,we used the article use the AdS/CFT correspondence to construct the generalized superconductors from the coupling of a scalar field to the Einstein tensor in the massive gravity and tried to investigate systematically the influence of the doping or impurity on the high temperature superconductors and their optical properties by holography.We found that the critical chemical potential increases with the increase of the graviton mass and Einstein tensor coupling parameters corresponding to the doping or impurity,which indicates that the larger graviton mass and Einstein tensor coupling parameters both hinder the formation of the condensation.However,the larger graviton mass or smaller coupling parameter makes it easier for the emergence of the Cave of Winds.Furthermore,we studied the negative refraction phenomenon of our generalized holographic superconductors and observed the existence of the negative Depine-Lakhtakia index in the superconducting phase at small frequencies.We noted 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 found that the larger graviton mass and coupling parameters both can reduce the dissipation and improve the propagation in the holographic setup.