# Superconducting States for Semi-Dirac Fermions at Zero and Finite Magnetic Fields

## TL;DR

This paper investigates the unique superconducting properties of anisotropic Dirac fermions with mixed linear and parabolic dispersions, revealing highly anisotropic electromagnetic responses and the potential formation of exotic smectic flux states under magnetic fields.

## Contribution

It introduces the concept of superconductivity in semi-Dirac fermions with uniaxial anisotropy and predicts novel flux domain patterns near quantum criticality.

## Key findings

- Superconducting response is highly anisotropic near the quantum critical point.
- A novel smectic flux state can form under high magnetic fields.
- The study extends understanding of anisotropic Dirac fermion superconductivity.

## Abstract

We address the superconducting singlet state of anisotropic Dirac fermions that disperse linearly in one direction and parabolically in the other. For systems that have uniaxial anisotropy, we show that the electromagnetic response to an external magnetic flux is extremely anisotropic near the quantum critical point of the superconducting order. In the quantum critical regime and above a critical magnetic field, we show that the superconductor may form a novel exotic smectic state, with a stripe pattern of flux domains.