p-wave superconductivity in Luttinger semimetals

Abstract

We consider the three-dimensional spin-orbit-coupled Luttinger semimetal of "spin" $3/2$ particles in presence of weak attractive interaction in the $l=1$ (p-wave) channel, and determine the low-temperature phase diagram for both particle- and hole-dopings. The phase diagram depends crucially on the sign of the chemical potential, with two different states (with total angular momentum $j=0$ and $j=3$) competing on the hole-doped side, and three (one $j=1$ and two different $j=2$) states on the particle-doped side. The ground state condensates of Cooper pairs with the total angular momentum $j=1,2,3$ are selected by the quartic, and even sextic terms in the Ginzburg-Landau free energy. Interestingly, we find that all the p-wave ground states that appear in the phase diagram, while displaying different patterns of reduction of the rotational symmetry, preserve the time reversal symmetry. The resulting quasiparticle spectrum is either fully gapped or with point nodes, with nodal lines being absent.

19 pages, four figures

References in corpus (4)

• Topological Mott insulator in three-dimensional systems with quadratic band touching
• Superconductivity in three-dimensional spin-orbit coupled semimetals
• Phase diagram of electronic systems with quadratic Fermi nodes in $2<d<4$: $2+\epsilon$ expansion, $4-\epsilon$ expansion, and functional renormalization group
• Anisotropy induces non-Fermi-liquid behavior and nematic magnetic order in three-dimensional Luttinger semimetals