Non-Fermi-Liquid and Topological States with Strong Spin-Orbit Coupling

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 twofold 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, nonlinear susceptibility, and the magnetic Gruneisen number. Furthermore, we determine the phase diagram in the presence of cubic and/or time-reversal symmetry breaking perturbations, which includes a topological insulator and Weyl semimetal phases. Many of these phases possess an extraordinarily large anomalous Hall effect, with the Hall conductivity scaling sublinearly with magnetization σ(xy)∼M0.51.

Classification of stable three-dimensional Dirac semimetals with nontrivial topology

“…As the in-plane dispersion becomes either quadratic or cubic in the momentum space, which strongly enhances the low energy density of states, it is expected that the interaction and disorder can even bring about new exotic quantum phases. For instance, according to a recent theoretical study, an exotic non-Fermi liquid state can appear in a 3D SM having quadratic energy dispersion in the momentum space 41 . As the interplay between the long-range Coulomb interaction and nontrivial screening because of the enhanced low energy density of states is the fundamental origin leading to the non-Fermi liquid phase, the quadratic Dirac SM and the cubic Dirac SM are also promising systems to observe novel quantum critical states.…”

Out-of-equilibrium dynamics and extended textures of topological defects in spin ice

“…In this compound, the Ir 5d conduction electrons interact with a magnetic 'spinice' texture formed by the localized Pr 3+ moments. The enhanced spin-ice correlations induce anomalous scattering of conduction electrons [24][25][26][27] , and the resultant unusual transport properties have generated considerable theoretical interest [28][29][30][31][32][33] . For instance, the Hall conductivity shows non-monotonic magnetic field dependence, implying that the Hall response is dominated by the topological Hall effect due to the scattering of itinerant electrons from spin triplets with finite spin scalar chirality 25,29 .…”

Spin-orbital entangled molecular jeff states in lacunar spinel compounds

“…Moreover, when incorporated with electron correlations, SOC can give rise to even more fascinating phenomena 7,8 . In the iridium oxide family, where the IrO 6 octahedron is the essential building block, various quantum phases have been predicted or verified according to the electron correlation strength on top of the large SOC of the Ir 5d t 2g orbital: topological band insulator for weak coupling 9,10 , Weyl semi-metal, axion insulator, non-Fermi liquid and TI* phases for intermediate coupling [11][12][13][14][15] , and topological Mott insulator and quantum spin liquid phases for strong coupling 7,16,17 .…”