Ginzburg-Landau Formalism in a Tilted Dirac Cone Metric

Abstract

Recent researches on tilted Dirac cone materials have unveiled an astonishing property, the metric of the spacetime can be altered in these materials by applying a perpendicular electric field. This phenomenon is observed near the Fermi velocity, which is significantly lower than the speed of light. According to this property, we derive the Ginzburg-Landau action from the microscopic Hamiltonian of the BCS theory for the tilted Dirac cone materials. This derivation is performed near the critical point within the framework of curved spacetime. The novelty of the present work lies in deriving a general Ginzburg-Landau action that depends on spacetime curvature, where the curvature is tuned by an external electric field. Furthermore, this finding enables us to apply the Ginzburg-Landau theory at high temperatures by changing the spacetime metric, potentially offering insights into achieving high-temperature superconductivity in these materials.