Disorder-driven destruction of a non-Fermi liquid semimetal via renormalization group

Abstract

We investigate the interplay of Coulomb interactions and short-range-correlated disorder in three dimensional systems where absent disorder the non-interacting band structure hosts a quadratic band crossing. Though the clean Coulomb problem is believed to host a 'non-Fermi liquid' phase, disorder and Coulomb interactions have the same scaling dimension in a renormalization group (RG) sense, and thus should be treated on an equal footing. We therefore implement a controlled $\epsilon$-expansion and apply it at leading order to derive RG flow equations valid when disorder and interactions are both weak. We find that the non-Fermi liquid fixed point is unstable to disorder, and demonstrate that the problem inevitably flows to strong coupling, outside the regime of applicability of the perturbative RG. An examination of the flow to strong coupling suggests that disorder is asymptotically more important than interactions, so that the low energy behavior of the system can be described by a non-interacting sigma model in the appropriate symmetry class (which depends on whether exact particle-hole symmetry is imposed on the problem). We close with a discussion of general principles unveiled by our analysis that dictate the interplay of disorder and Coulomb interactions in gapless semiconductors, and of connections to many-body localized systems with long-range interactions.

15 pages, 4 figures

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Cited by in corpus (57)

• Weyl and Dirac Semimetals in Three Dimensional Solids
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• Fate of superconductivity in three-dimensional disordered Luttinger semimetals
• Circular dichroism as a probe for topology in three-dimensional semimetals
• Effect of interactions on the quantization of the chiral photocurrent for double-Weyl semimetals
• Floquet scattering of quadratic band-touching semimetals through a time-periodic potential well
• Tunneling of multi-Weyl semimetals through a potential barrier under the influence of magnetic fields
• Magneto-optical conductivity in the type-I and type-II phases of Weyl/multi-Weyl semimetals
• Interplay between short-range correlated disorder and Coulomb interaction in nodal-line semimetals
• Effects of the Dirac cone tilt in two-dimensional Dirac semimetal
• Robust Marginal Fermi Liquid In Birefringent Semimetals
• Magnus Hall effect in three-dimensional topological semimetals
• Transport in the non-Fermi liquid phase of isotropic Luttinger semimetals
• Transmission and conductance across junctions of isotropic and anisotropic three-dimensional semimetals
• Thermoelectric response in nodal-point semimetals
• Thermoelectric and thermal properties of the weakly disordered non-Fermi liquid phase of Luttinger semimetals
• Electric and thermoelectric response for Weyl and multi-Weyl semimetals in planar Hall configurations including the effects of strain
• Magneto-transport signatures in periodically-driven Weyl and multi-Weyl semimetals
• Non-Fermi liquid at the FFLO quantum critical point
• Signatures of two- and three-dimensional semimetals from circular dichroism
• Critical Fermi surfaces in generic dimensions arising from transverse gauge field interactions
• Floquet transmission in Weyl/multi-Weyl and nodal-line semimetals through a time-periodic potential well
• Role of four-fermion interaction and impurity in the states of two-dimensional semi-Dirac materials
• Stability of two-dimensional asymmetric materials with a quadratic band crossing point under four-fermion interaction and impurity scattering
• Tunneling in Fermi Systems with Quadratic Band Crossing Points
• Raman response and shear viscosity in the non-Fermi liquid phase of Luttinger semimetals
• Robust quantum transport at particle-hole symmetry
• Quantum phase transition and unusual critical behavior in multi-Weyl semimetals
• Electric, thermal, and thermoelectric magnetoconductivity for Weyl/multi-Weyl semimetals in planar Hall set-ups induced by the combined effects of topology and strain
• Search for plasmons in isotropic Luttinger semimetals
• Direction-dependent conductivity in planar Hall set-ups with tilted Weyl/multi-Weyl semimetals
• Zero sound and plasmon modes for non-Fermi liquids
• Transport properties in non-Fermi liquid phases of nodal-point semimetals
• Linear response in planar Hall and thermal Hall setups for Rarita-Schwinger-Weyl semimetals
• Using Disorder to Identify Bogoliubov Fermi-Surface States
• Reflections of topological properties in the planar-Hall response for semimetals carrying pseudospin-1 quantum numbers
• Fermion-fermion interaction driven instability and criticality of quadratic band crossing systems with the breaking of time-reversal symmetry
• Anatomy of plasmons in generic Luttinger semimetals
• Cooper instability generated by attractive fermion-fermion interaction in the two-dimensional semi-Dirac semimetals
• Interplay between tilt, disorder, and Coulomb interaction in type-I Dirac fermions
• Quantum criticality of fermion velocities and critical temperature nearby a putative quantum phase transition in the $d$-wave superconductors
• Stable non-Fermi liquid fixed point at the onset of incommensurate $2k_F$ charge density wave order
• Generic deformation channels for critical Fermi surfaces in the collisionless regime
• Quenched disorder at antiferromagnetic quantum critical points in $2d$ metals
• Induction of non-Fermi liquids by critical cavity photons at the onset of superradiance
• Linear response of tilted anisotropic two-dimensional Dirac cones
• Fermion-fermion interaction driven phase transitions in rhombohedral trilayer graphene
• Anisotropic conductivity for the type-I and type-II phases of Weyl/multi-Weyl semimetals in planar Hall set-ups
• Tunable zero-energy Dirac and Luttinger nodes in a two-dimensional topological superconductor
• Critical behavior around the fixed points driven by fermion-fermion interactions and disorders in the nodal-line superconductors
• Global phase diagram of Coulomb-interacting anisotropic Weyl semimetals with disorder
• Delta-function-potential junctions with quasiparticles occupying tilted bands with quadratic-in-momentum dispersion
• Transmission through rectangular potentials in semimetals featuring quadratic dispersion
• Disordered non-Fermi liquid fixed point for two-dimensional metals at Ising-nematic quantum critical points
• Impurities in 3D quadratic band-touching Luttinger semimetals : Friedel and RKKY oscillations
• Critical fates induced by the interaction competition in three-dimensional tilted Dirac semimetals