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.

arXiv comment6 pages, 4 figures

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• Coulomb interaction effect in tilted Weyl fermion in two dimensions
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• Migdal's theorem and electron-phonon vertex corrections in Dirac materials
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• From Birefringent Electrons to a Marginal or Non-Fermi Liquid of Relativistic Spin-1/2 Fermions: An Emergent Superuniversality
• Fermion-induced quantum critical points in two-dimensional Dirac semimetals
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• Renormalization group analysis of multi-Dirac-node materials
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• Itinerant quantum multi-criticality of two dimensional Dirac fermions
• Chern numbers and chiral anomalies in Weyl butterflies
• Magnetic field induced topological semimetals near a quantum critical point of pyrochlore iridates
• Coulomb-induced instabilities of nodal surfaces
• Direct measurement of a beta function and an indirect check of the Schwinger effect near the boundary in Dirac-Weyl semimetals
• Quantum Electrodynamics of Non-Hermitian Dirac Fermions
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• Long-range Coulomb Interaction effects on Topological Phase Transitions between Semi-metals and Insulators
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• Zitterbewegung in time-reversal Weyl Semimetals
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• Yukawa-Lorentz Symmetry of Tilted Non-Hermitian Dirac Semimetals at Quantum Criticality
• Renormalization of fermion velocity in finite temperature QED_{3}
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• Disordered non-Fermi liquid fixed point for two-dimensional metals at Ising-nematic quantum critical points
• Fate of a multiple-band Fermi liquid that is coupled with critical ${\varphi }^4$ bosons
• Renormalization group analysis of weakly interacting van der Waals Fermi system