Time reversal symmetry breaking and $d$-wave superconductivity of triple-point fermions

TL;DR

This paper explores complex tensor ($d$-wave) superconductivity in 3D semimetals with triple-point fermions, revealing time reversal symmetry breaking and distinct magnetic phases with unique quasiparticle spectra.

Contribution

It introduces a mean-field $d$-wave superconducting state in triple-point fermions, analyzing its phase diagram and quasiparticle properties, highlighting novel symmetry-breaking phenomena.

Findings

Time reversal symmetry is broken in the $d$-wave superconducting state.

The phase diagram includes cyclic and ferromagnetic states distinguished by magnetization.

Mini Bogoliubov-Fermi surfaces are present in the quasiparticle spectrum.

Abstract

We study the possibility of complex tensor ($d$-wave) superconducting order in three-dimensional semimetals with chiral spin-1/2 triple-point fermions, which have an effective orbital angular momentum of $L=1$ arising from a crossing of three bands. Retaining the first three lowest order terms in momentum and assuming rotational symmetry we show that the resulting mean-field $d$-wave ground state breaks time reversal symmetry, and depends crucially on the coefficients of the two quadratic terms in the Hamiltonian. The phase diagram at a finite chemical potential displays both the "cyclic" and the "ferromagnetic" states, distinguished by the average value of the magnetization; in the former state it is minimal (zero), whereas in the latter it is maximal (two). In both states we find mini Bogoliubov-Fermi surfaces in the quasiparticle spectrum, conforming to recent general arguments.