p-wave superconductivity of triple-point fermions*

This talk will discuss the unconventional superconductivity in three-dimensional inversion- and rotation-symmetric electronic systems whose low energy descriptions are captured by triple-point fermions. We will show that a general contact interaction in such systems may lead to a p-wave superconducting instability that is described by a 2×3 matrix order parameter, unlike the standard 3×3 matrix p-wave order parameter which has been discussed in the context of the superfluid phases in ³He. We will then focus on the Ginzburg-Landau theory for such a p-wave superconducting order and determine the nature of the superconducting ground state. We find that the corresponding  Ginzburg-Landau (GL) theory derived in the weak-coupling limit exhibits an enlarged U (1) × SO(3) × U (1) × SO(3) symmetry, which reduces to the SO(2) × SO(2) in the ordered phase. It will be shown that the Axiplanar phase, which is a large manifold of states characterized by a continuous parameter θ, minimizes the GL free energy exactly. Interestingly, this manifold of ground states can be expressed in terms of two complex vector order parameters that are coupled to two different valleys, which provides a clear physical interpretation for the θ. Finally, we will discuss how the restoration of the lattice removes the extra degeneracy and restricts the superconducting ground state.