Odd parity superconductivity in Weyl semimetals

TL;DR

This paper investigates odd parity superconductivity in Weyl semimetals, revealing that finite momentum chiral p-wave pairing is favored at finite chemical potential, with different phases competing depending on interaction range and chemical potential.

Contribution

It demonstrates that Weyl semimetals can host odd parity superconductivity with topological properties, identifying conditions favoring chiral p-wave pairing over BCS states.

Findings

Finite momentum chiral p-wave pairing is most favorable at finite chemical potential.

Long-range attraction favors BCS superconductivity across all chemical potentials.

Charge density wave preempts superconductivity at the Weyl node when chemical potential is zero.

Abstract

Unconventional superconducting states of matter are realized in the presence of strong spin orbit coupling. In particular, non degenerate bands can support odd parity superconductivity with rich topological content. Here we study whether this is the case for Weyl semimetals. These are systems whose low energy sector, in the absence of interactions, is described by linearly dispersing chiral fermions in three dimensions. The energy spectrum has nodes at an even number of points in the Brillouin zone. Consequently both intranodal finite momentum pairing and internodal BCS superconductivity are allowed. For local attractive interaction the finite momentum pairing state with chiral p-wave symmetry is found to be most favorable at finite chemical potential. The state is an analog of the superfluid $^{3}$He A phase, with cooper pairs having finite center of mass momentum. For chemical potential at the node the state is preempted by a fully gapped charge density wave. For long range attraction the BCS state wins out for all values of the chemical potential.