Non-Fermi liquid and topological states with strong spin-orbit coupling

TL;DR

This paper explores how strong spin-orbit coupling in certain materials leads to a novel non-Fermi liquid state with universal properties, and maps out the phase diagram including topological phases.

Contribution

It extends Abrikosov's model using modern renormalization group techniques to identify a stable non-Fermi liquid phase and characterizes its universal exponents and phase diagram.

Findings

Interactions induce a stable non-Fermi liquid phase with universal exponents.

The phase diagram includes topological insulator and Weyl semi-metal phases.

Many phases exhibit a large anomalous Hall effect with sub-linear scaling.

Abstract

We argue that a class of strongly spin-orbit coupled materials, including some pyrochlore iridates and the inverted band gap semiconductor HgTe, may be described by a minimal model consisting of the Luttinger Hamiltonian supplemented by Coulomb interactions, a problem studied by Abrikosov and collaborators. It contains two-fold degenerate conduction and valence bands touching quadratically at the zone center. Using modern renormalization group methods, we update and extend Abrikosov's classic work and show that interactions induce a quantum critical non-Fermi liquid phase, stable provided time-reversal and cubic symmetries are maintained. We determine the universal power-law exponents describing various observables in this "Luttinger Abrikosov Beneslavskii" state, which include conductivity, specific heat,non-linear susceptibility and magnetic Gruneisen number. Furthermore, we determine the phase diagram in the presence of cubic and/or time-reversal symmetry breaking perturbations, which includes topological insulator and Weyl semi-metal phases. Many of these phases possess an extraordinarily large anomalous Hall effect, with the Hall conductivity scaling sub-linearly with magnetization.