Crystal symmetry protected gapless vortex line phases in superconducting Dirac semimetals

Vortex lines in superconducting Dirac semimetals realize crystal symmetry protected gapless vortex line phases in which gapless excitations propagate inside a vortex line, in the presence of appropriate crystal symmetry, spin-orbit coupling, and multiband structures. In this talk we present a general scheme to classify possible gapless vortex line phases in s-wave superconducting states of Dirac semimetals with rotation (or screw) symmetry and inversion symmetry, assuming that the rotation (screw) axis is parallel to the vortex line. The rotation (screw) symmetry protected gapless modes are stable as long as they have different rotation

(screw) eigenvalues. The underlying mechanism for the formation of gapless vortex bound states depends on irreducible representations of rotation (screw) symmetry subject to a vortex field and is classified into three types: (i) accidental band crossing of two vortex bound-state modes under rotation symmetry; (ii) accidental and

(iii) enforced band crossing of four vortex bound-state modes under screw symmetry. Using a tight-binding model of screw symmetry protected Dirac semimetal with an s-wave pair potential, we demonstrate a gapless vortex line phase of type (ii).