Is a color superconductor topological?

TL;DR

This paper investigates the topological properties of color superconductors in 3D Dirac fermions, revealing how fermion mass and pairing symmetry influence the existence of gapless surface and vortex-bound states.

Contribution

It provides a detailed analysis of topological phases in color superconductors, highlighting the effects of fermion mass and pairing parity on localized fermion states.

Findings

Vortex lines support gapless chiral fermions with opposite propagation directions.

Fermion mass opens a gap for localized fermions in parity-even pairing.

Topological phase transition occurs at a critical fermion mass value.

Abstract

A fully gapped state of matter, whether insulator or superconductor, can be asked if it is topologically trivial or nontrivial. Here we investigate topological properties of superconducting Dirac fermions in 3D having a color superconductor as an application. In the chiral limit, when the pairing gap is parity even, the right-handed and left-handed sectors of the free space Hamiltonian have nontrivial topological charges with opposite signs. Accordingly, a vortex line in the superconductor supports localized gapless right-handed and left-handed fermions with the dispersion relations E=+/-vp_z (v is a parameter dependent velocity) and thus propagating in opposite directions along the vortex line. However, the presence of the fermion mass immediately opens up a mass gap for such localized fermions and the dispersion relations become E=+/-v(m^2+p_z^2)^(1/2). When the pairing gap is parity odd, the situation is qualitatively different. The right-handed and left-handed sectors of the free space Hamiltonian in the chiral limit have nontrivial topological charges with the same sign and therefore the presence of the small fermion mass does not open up a mass gap for the fermions localized around the vortex line. When the fermion mass is increased further, there is a topological phase transition at m=(\mu^2+\Delta^2)^(1/2) and the localized gapless fermions disappear. We also elucidate the existence of gapless surface fermions localized at a boundary when two phases with different topological charges are connected. A part of our results is relevant to the color superconductivity of quarks.