Long-range Coulomb Interaction effects on Topological Phase Transitions between Semi-metals and Insulators

Abstract

Topological states may be protected by a lattice symmetry in a class of topological semi-metals. In three spatial dimensions, the Berry flux around gapless excitations in momentum space defines a chirality concretely, so a protecting symmetry may be referred to as a chiral symmetry. Prime examples include Dirac semi-metal (DSM) in a distorted spinel, BiZnSiO${}_4$, protected by a mirror symmetry and DSM in Na${}_3$Bi, protected by a rotational symmetry. In these states, topology and a chiral symmetry are intrinsically tied. In this work, we investigate characteristics interplay between a chiral symmetry order parameter and instantaneous long-range Coulomb interaction with the standard renormalization group method. We show that a topological transition associated with a chiral symmetry is stable under the presence of the Coulomb interaction and the electron velocity always becomes faster than one of a chiral symmetry order parameter. Thus, the transition {\it must not} be relativistic, which implies a supersymmetry is intrinsically forbidden by the long-range Coulomb interaction. {Asymptotically exact} universal ratios of physical quantities such as energy gap ratio are obtained, and connections with experiments and recent theoretical proposals are also discussed.

arXiv commentPublished at PRB Rapid Communication (Phys. Rev. B 97, 241101(R) (2018)), Main text: 6 pages, 1 table, 2 figures, Supplementary Meterial: 9 pages, 3 figures

References in corpus (45)

• Topological Insulators
• Topological insulators and superconductors
• Electronic Structure of Pyrochlore Iridates: From Topological Dirac Metal to Mott Insulator
• Weyl and Dirac Semimetals in Three Dimensional Solids
• Classification of topological insulators and superconductors in three spatial dimensions
• Discovery of a Three-dimensional Topological Dirac Semimetal, Na3Bi
• Mott physics and band topology in materials with strong spin-orbit interaction
• Charge Transport in Weyl Semimetals
• Topological and magnetic phases of interacting electrons in the pyrochlore iridates
• Classification of reflection symmetry protected topological semimetals and nodal superconductors
• Dirac and Weyl Superconductors in Three Dimensions
• Emergent Space-time Supersymmetry at the Boundary of a Topological Phase
• Non-Fermi liquid and topological states with strong spin-orbit coupling
• Classification of interacting electronic topological insulators in three dimensions
• Quantum critical scaling in graphene
• Relativistic Mott criticality in graphene
• Recent Developments in Non-Fermi Liquid Theory
• Bulk Dirac points in distorted spinels
• Long-range Coulomb interaction in nodal-ring semimetals
• Topological Mott insulator in three-dimensional systems with quadratic band touching
• Emergent space-time supersymmetry in 3D Weyl and 2D Dirac semimetals
• Emergence of supersymmetry on the surface of three dimensional topological insulators
• A New Type of Quantum Criticality in the Pyrochlore Iridates
• Quantum Criticality of Topological Phase Transitions in 3D Interacting Electronic Systems
• Emergent non-Fermi liquid at the quantum critical point of a topological phase transition in two dimensions
• Correlated double-Weyl semimetals with Coulomb interactions: possible applications to HgCr2Se4 and SrSi2
• Quasi-Local Strange Metal
• Emergence of supersymmetric quantum electrodynamics
• Theory of a quantum critical phenomenon in a topological insulator: (3+1)-dimensional quantum electrodynamics in solids
• Exact critical exponents for the antiferromagnetic quantum critical metal in two dimensions
• Interacting Topological Insulator and Emergent Grand Unified Theory
• Emergent Lorentz symmetry near fermionic quantum critical points in two and three dimensions
• Correlation effects in double-Weyl semimetals
• Optical conductivity of topological surface states with emergent supersymmetry
• Edge quantum criticality and emergent supersymmetry in topological phases
• Intertwining topological order and broken symmetry in a theory of fluctuating spin density waves
• New quantum critical points of $j=3/2$ Dirac electrons in antiperovskite topological crystalline insulators
• Phase diagram of the Quantum Electrodynamics of 2D and 3D Dirac semimetals
• Anisotropic Non-Fermi Liquids
• Emergence of a control parameter for the antiferromagnetic quantum critical metal
• Heart and diamond Fermi arcs in Pd and Pt oxide topological Dirac semimetals
• Renormalization group analysis of multi-Dirac-node materials
• Stability of Multinode Dirac Semimetals against Strong Long-Range Correlations
• Universal Relation among Many-Body Chern Number, Rotation Symmetry, and Filling
• Topological Phase Transitions in Line-nodal Superconductors

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