Interplay of tilt and axion fields in topological superconductors: Anisotropy in the Meissner effect

Abstract

Topological superconductors host gapless surface states that fundamentally alter their electromagnetic response through the axion field term θE·B, arising from the topological magnetoelectric effect. In this work, we investigate the electromagnetic properties of a three-dimensional topological Weyl superconductor by leveraging its theoretical mapping to a four-dimensional topological insulator with s-wave superconducting boundaries. By incorporating the tilt of Weyl cones into this model, we demonstrate that the tilt vector ζ anisotropically modifies the axion field profile near the surface, leading to a tilt-enhanced Meissner effect and anomalous magnetic penetration depths. We show that the magnetic field component perpendicular to the tilt direction exhibits a non-exponential, hypergeometric decay dictated by the interplay between the axion term and ζ, while the parallel component remains largely tilt-insensitive—a hallmark of axion-mediated anisotropy absent in trivial superconductors. Remarkably, all tilt-dependent electromagnetic responses follow a universal scaling law, revealing a fundamental symmetry in the system's behavior. Furthermore, we predict a tilt-dependent planar Hall current at the surface, directly tied to the topological surface states.

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