Anisotropy induces non-Fermi-liquid behavior and nematic magnetic order in three-dimensional Luttinger semimetals

TL;DR

This paper explores how spatial anisotropy in three-dimensional Luttinger semimetals influences their quantum phases, revealing non-Fermi-liquid behavior and nematic magnetic order through perturbative renormalization group analysis.

Contribution

It demonstrates that anisotropy leads to new fixed points, inducing non-Fermi-liquid states and nematic magnetic orders in 3D Luttinger semimetals, with implications for real materials.

Findings

Anisotropy causes a non-Fermi-liquid ground state.

New fixed points describe quantum phase transitions to nematic magnetic phases.

Anisotropy influences magnetic ordering in pyrochlore lattice materials.

Abstract

We illuminate the intriguing role played by spatial anisotropy in three-dimensional Luttinger semimetals featuring quadratic band touching and long-range Coulomb interactions. We observe the anisotropy to be subject to an exceptionally slow renormalization group (RG) evolution so that it can be considered approximately constant when computing the impact of quantum fluctuations on the remaining couplings of the system. Using perturbative RG we then study the competition of all local short-range interactions that are generated from the long-range interactions for fixed anisotropy. Two main effects come to light for sufficiently strong anisotropy. First, the three-dimensional system features an Abrikosov non-Fermi liquid ground state. Second, there appear qualitatively new fixed points which describe quantum phase transitions into phases with nemagnetic orders - higher-rank tensor orders that break time-reversal symmetry, and thus have both nematic and magnetic character. In real materials these phases may be realized through sufficiently strong microscopic short-range interactions. On the pyrochlore lattice, the anisotropy-induced fixed points determine the onset of all-in-all-out or spin ice ordering of local magnetic moments of the electrons.