Effective field theory, chiral anomaly and vortex zero modes for odd parity topological superconducting state of three dimensional Dirac materials

TL;DR

This paper develops an effective field theory for odd parity topological superconducting states in three-dimensional Dirac materials, revealing chiral anomalies and vortex zero modes with potential experimental implications.

Contribution

It derives a novel effective field theory incorporating anomalies and zero modes for 3D Dirac superconductors with odd parity, connecting topological features to physical phenomena.

Findings

Existence of fermion zero modes in vortex phases.

Effective theory includes mixed electromagnetic and chiral anomalies.

Potential experimental signatures in topological superconductors.

Abstract

The low energy quasiparticle dispersion of various narrow gap and gapless semiconductors are respectively described by three dimensional massive and massless Dirac fermions. The three dimensional Dirac spinor structure admits a time-reversal invariant, odd parity and Lorentz pseudoscalar topological superconducting state. Here we derive the effective field theory of this topological paired state for massless Dirac fermions in the presence of a fluctuating Zeeman term, which appears as a chiral gauge field. The effective theory consists of a mixed electromagnetic and chiral anomaly term in the bulk, and a combination of pure and mixed anomalies for the surface. In this paper we demonstrate the existence of fermion zero modes in the dilute vortex phase under generic conditions. Guided by the existence of the zero modes and its intimate connection with the anomaly, we propose an effective topological field theory in the presence of Dirac mass. We briefly discuss the experimental consequences of the effective field theory and the zero modes for the low temperature unconventional superconducting states of $\mathrm{Cu}_x\mathrm{Bi}_2\mathrm{Se}_3$ and $\mathrm{Sn}_{1-x}\mathrm{In}_x\mathrm{Te}$.