Estudo de supercondutores em espaços curvos: a abordagem de Atanasov para o acoplamento da teoria de Ginzburg-Landau e a teoria da relatividade geral

Abstract

In a recent article, Victor Atanasov [Physica B, 517(2017)] proposed a coupling between the superconducting order parameter and the geometry of spacetime, in an extended Ginzburg-Landau Theory (GLT). In this verson, the curvature plays an effective role of a chemical potential. It is found that the coherence length and the Ginzburg-Landau parameter of the superconductor are affected by gravity in such a way as to change a superconductor from Type-I to Type-II and vice-versa. Moreover, for a sufficiently negative curvature of space-time the superconductivity is destroyed. In our work, in the framework of Atanasov’s extended GLT, we study the effects of a gravitational field in a vortex dynamics of a Type-II superconductor near the transition temperature. The work consists of investigating whether the perturbation caused by gravitational fields is enough to modify the superconducting state. We minimize the energy of the superconducting Condensate proposed in TGL plus the term proposed by Atanasov, starting from the Abelian-Higgs field theory model, non-minimally coupled to gravity proposed by Y. Verbin [Phys. Rev. D, 59(1999)]. We study a problem of a static gravitational field. The chosen case was that of a superconductor near a black hole. We describe a GLT equations and Atanasov’s extended GLT necessary for obtaining the coupled Einstein-Higgs field equations, that were subsequently written dimensionless form to obtain a numerical solution.