Emergent non-Fermi liquid at the quantum critical point of a topological phase transition in two dimensions

Abstract

We study the effects of Coulomb interaction between 2D Weyl fermions with anisotropic dispersion which displays relativistic dynamics along one direction and Newtonian dynamics along the other. Such a dispersion can be realized in phosphorene under electric field or strain, in TiO${}_2$/VO${}_2$ superlattices, and, more generally, at the quantum critical point between a nodal semimetal and an insulator in systems with a chiral symmetry. Using the one-loop renormalization group approach in combination with the large-$N$ expansion, we find that the system displays interaction-driven non-Fermi liquid behavior in a wide range of intermediate frequencies and marginal Fermi liquid behavior at the smallest frequencies. In the non-Fermi liquid regime, the quasiparticle residue $Z$ at energy $E$ scales as $Z\propto E^a$ with $a>0$, and the parameters of the fermionic dispersion acquire anomalous dimensions. In the marginal Fermi-liquid regime, $Z\propto (|\log E|{)}^{-b}$ with universal $b=3/2$.

15 pages, 5 figures

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• Observation of tunable bandgap and anisotropic Dirac semimetal state in black phosphorus
• Classification of stable three-dimensional Dirac semimetals with nontrivial topology
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• Classification of reflection symmetry protected topological semimetals and nodal superconductors
• Electrically Tunable Quasi-Flat Bands, Conductance and Field Effect Transistor in Phosphorene
• A new magnetic field dependence of Landau levels on a graphene like structure
• Quantum critical point in graphene approached in the limit of infinitely strong Coulomb interaction
• Coulomb interaction, ripples, and the minimal conductivity of graphene
• Pressure-induced Lifshitz transition in black phosphorus
• Interplay of Coulomb and electron-phonon interactions in graphene
• Graphene via large N I: Renormalization
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• Quantum Criticality of Topological Phase Transitions in 3D Interacting Electronic Systems
• Correlated double-Weyl semimetals with Coulomb interactions: possible applications to HgCr2Se4 and SrSi2
• Conductivity of interacting massless Dirac particles in graphene: Collisionless regime
• A semi-Dirac point in the Hofstadter spectrum
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• Correlation effects in double-Weyl semimetals
• A controlled expansion for certain non-Fermi liquid metals

Cited by in corpus (69)

• Observation of an anisotropic Dirac cone reshaping and ferrimagnetic spin polarization in an organic conductor
• Two-Dimensional Dirac Fermions Protected by Space-Time Inversion Symmetry in Black Phosphorus
• Hydrodynamic approach to two-dimensional electron systems
• Supermetal
• Out-of-bounds hydrodynamics in anisotropic Dirac fluids
• Unconventional topological phase transition in two-dimensional systems with space-time inversion symmetry
• Quantum Multicriticality near the Dirac-Semimetal to Band-Insulator Critical Point in Two Dimensions: A Controlled Ascent from One Dimension
• Semi-Dirac Semimetal in Silicene Oxide
• Fermion-induced quantum critical points in three-dimensional Weyl semimetals
• Interplay between topology and disorder in a two-dimensional semi-Dirac material
• New quantum critical points of $j=3/2$ Dirac electrons in antiperovskite topological crystalline insulators
• Dynamical polarization and plasmons in a two-dimensional system with merging Dirac points
• Emergent Anisotropic Non-Fermi Liquid at a Topological Phase Transition in Three Dimensions
• Excitonic pairing and insulating transition in two-dimensional semi-Dirac semimetals
• Coulomb instabilities of 3D higher-order topological insulators
• Effects of the Dirac cone tilt in two-dimensional Dirac semimetal
• Quantum Criticality of Semi-Dirac Fermions in 2+1 Dimensions
• Optical conductivity of black phosphorus with a tunable electronic structure
• Unifying Interacting Nodal Semimetals: A New Route to Strong Coupling
• Semi-Dirac Fermions in a Topological Metal
• Topological quantum critical point in a triple-Weyl semimetal: non-Fermi-liquid behaviors and instabilities
• Correlated triple-Weyl semimetals with Coulomb interactions
• Quantum critical scaling and holographic bound for transport coefficients near Lifshitz points
• Breakdown of Fermi liquid theory in topological multi-Weyl semimetals
• Displacement and annihilation of Dirac gap-nodes in d-wave iron-based superconductors
• Evidence for pressure-induced node-pair annihilation in Cd3As2
• Quantum phase transition and unusual critical behavior in multi-Weyl semimetals
• Quantum criticality preempted by nematicity
• Superconductivity in two-dimensional disordered Dirac semimetals
• Interplay of Coulomb interaction and disorder in a two-dimensional semi-Dirac fermion system
• Coulomb interactions and renormalization of semi-Dirac fermions near a topological Lifshitz transition
• Fermionic criticality of anisotropic nodal point semimetals away from the upper critical dimension: exact $1/N_f$ exponents
• Long-range Coulomb Interaction effects on Topological Phase Transitions between Semi-metals and Insulators
• Quantum Criticalities with Infinite Anisotropy in Topological Phase Transitions between Dirac and Weyl Semi-metals
• Transport properties in non-Fermi liquid phases of nodal-point semimetals
• Coulomb interactions in systems of generalized semi-Dirac fermions
• Nonperturbative Dyson-Schwinger equation approach to strongly interacting Dirac fermion systems
• Effects of random potentials in three-dimensional quantum electrodynamics
• Superconductivity in the nodal-line compound La${}_3$Pt${}_3$Bi${}_4$
• Interaction-driven quantum anomalous Hall insulator in Dirac semimetal
• Cooper instability generated by attractive fermion-fermion interaction in the two-dimensional semi-Dirac semimetals
• Quantum Criticality of Excitonic Insulating Transition in Nodal Line Semimetal ZrSiS
• Topological Quantum Criticality in Superfluids and Superconductors: Surface criticality, Thermal properties, and Lifshitz Majorana fields
• Novel criticality of Dirac fermions from lattice symmetry breaking
• Novel criticality of Dirac fermions in the presence of emergent gauge fields
• Possible instabilities in quadratic and cubic nodal line fermion systems with correlated interactions
• A Passage to Topological Matter: Colloquium
• Unconventional non-Fermi liquid state caused by nematic criticality in cuprates
• Topological Gap Opening without Symmetry Breaking from Dynamical Quantum Correlations
• Nature of Topological Phase Transition of Kitaev Quantum Spin Liquids
• Pressure-induced concomitant topological and metal-insulator quantum phase transitions in Ce${}_3$Pd${}_3$Bi${}_4$
• Probing a Bose Metal via Electrons: Inescapable non-Fermi liquid scattering and pseudogap physics
• Microscopic lattice model for quartic semi-Dirac fermions in two dimensions
• Quantum critical scaling of gapped phases in nodal-line semimetals
• Correlated interaction effects in three-dimensional semi-Dirac semimetal
• Fermion dispersion renormalization in a two-dimensional semi-Dirac semimetal
• Strong-coupling superconductivity near Gross-Neveu quantum criticality in Dirac systems
• Fate of superconductivity in disordered Dirac and semi-Dirac semimetals
• Deep-lying semi-Dirac fermions in hexagonal close-packed cadmium
• Unveiling three types of fermions in a nodal ring topological semimetal through magneto-optical transitions
• Nature of the Topological Transition of the Kitaev Model in [111] Magnetic Field
• Global phase diagram of Coulomb-interacting anisotropic Weyl semimetals with disorder
• Axionic quantum criticality of generalized Weyl semimetals
• Anisotropic marginal Fermi liquid for Coulomb interacting generalized Weyl fermions
• Semi-Dirac spin liquids and frustrated quantum magnetism on the trellis lattice
• Quantum Criticality of Type-I and Critically Tilted Dirac Semimetals
• Renormalization group analysis of weakly interacting van der Waals Fermi system
• Interacting type-II semi-Dirac quasiparticles
• Stability of the Néel quantum critical point in the presence of Dirac fermions