<p>Recent researches on tilted Dirac cone materials have revealed an remarkable property; the spacetime metric can be altered in these materials by applying a perpendicular electric field. This phenomenon emerges 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 BCS Hamiltonian for tilted Dirac cone materials. The derivation is performed near the superconductivity critical point within the framework of Dirac cone spacetime. The novelty of the present work lies in deriving a generalized Ginzburg–Landau action that explicitly depends on the spacetime metric, where the metric is tuned by an external electric field. This framework also enables the extension of the Ginzburg–Landau theory to higher temperatures, though subject to certain limitations.</p>