Theory of a quantum critical phenomenon in a topological insulator: (3+1)-dimensional quantum electrodynamics in solids

Abstract

We study theoretically the quantum critical phenomenon of the phase transition between the trivial insulator and the topological insulator in (3+1) dimensions, which is described by a Dirac fermion coupled to the electromagnetic field. The renormalization group (RG) equations for the running coupling constant α, the speed of light c and electron v are derived. The almost exact analytic solutions to these RG equations are obtained to reveal that (i) c and v approach to the common value with combination c^2v being almost unrenormalized, (ii) the RG flow of αis the same as that of usual QED with c^3 being replaced by c^2v, and (iii) there are two crossover momentum/energy scales separating three regions of different scaling behaviors. The dielectric and magnetic susceptibilities, angle-resolved photoemission spectroscopy (ARPES), and the behavior of the gap are discussed from this viewpoint.

6 pages, 4 figures

References in corpus (7)

• The electronic properties of graphene
• Quantum spin Hall effect in a transition metal oxide Na2IrO3
• Long range magnetic ordering in Na${}_2$IrO${}_3$
• Unexpected mass acquisition of Dirac fermions at the quantum phase transition of a topological insulator
• Possible proximity of the Mott insulating Iridate Na2IrO3 to a topological phase: Phase diagram of the Heisenberg-Kitaev model in a magnetic field
• Disorder effect on 3-dimensional $Z_2$ quantum spin Hall systems
• Interband Effects of Magnetic Field on Hall Effects for Dirac Electrons in Bismuth

Cited by in corpus (18)

• Classification of stable three-dimensional Dirac semimetals with nontrivial topology
• Detection of sub-MeV Dark Matter with Three-Dimensional Dirac Materials
• Quantum Criticality of Topological Phase Transitions in 3D Interacting Electronic Systems
• Interacting Dirac liquid in three-dimensional semimetals
• Quantum Electrodynamics of Non-Hermitian Dirac Fermions
• Yukawa-Lorentz Symmetry in Non-Hermitian Dirac Materials
• Emergent chiral symmetry in a three-dimensional interacting Dirac liquid
• Anomalous Gravitational TTT Vertex, Temperature Inhomogeneity, and Pressure Anisotropy
• Bulk contributions to the Casimir interaction of Dirac materials
• Superconductivity from piezoelectric interactions in Weyl semimetals
• Yukawa-Lorentz symmetry of interacting non-Hermitian birefringent Dirac fermions
• Tilted Dirac superconductor at quantum criticality: Restoration of Lorentz symmetry
• Yukawa-Lorentz Symmetry of Tilted Non-Hermitian Dirac Semimetals at Quantum Criticality
• Re-assessing special aspects of Dirac fermions in presence of Lorentz-symmetry violation
• Conformal anomaly and helicity effects in kinetic theory via scale-dependent coupling
• Renormalization of fermion velocity in finite temperature QED_{3}
• Disordered non-Fermi liquid fixed point for two-dimensional metals at Ising-nematic quantum critical points
• SUSY QED with Lorentz-asymmetric fermionic matter and a glance at the electron's EDM