Universality classes of topological phase transitions with higher-order band crossing

Abstract

In topological insulators and topological superconductors, the discrete jump of the topological invariant upon tuning a certain system parameter defines a topological phase transition. A unified framework is employed to address the quantum criticality of the topological phase transitions in one to three spatial dimensions, which simultaneously incorporates the symmetry classification, order of band crossing, $m$-fold rotational symmetry, correlation functions, critical exponents, scaling laws, and renormalization group approach. We first classify higher-order Dirac models according to the time-reversal, particle-hole, and chiral symmetries, and determine the even-oddness of the order of band crossing in each symmetry class. The even-oddness further constrains the rotational symmetry $m$ permitted in a symmetry class. Expressing the topological invariant in terms of a momentum space integration over a curvature function, the order of band crossing determines the critical exponent of the curvature function, as well as that of the Wannier state correlation function introduced through the Fourier transform of the curvature function. The conservation of topological invariant further yields a scaling law between critical exponents. In addition, a renormalization group approach based on deforming the curvature function is demonstrated for all dimensions and symmetry classes. Through clarification of how the critical quantities, including the jump of the topological invariant and critical exponents, depend on the nonspatial and the rotational symmetry, our work introduces the notion of universality class into the description of topological phase transitions.

34 pages, 5 figures

References in corpus (15)

• Quantum Spin Hall Effect and Topological Phase Transition in HgTe Quantum Wells
• Topological Insulators with Inversion Symmetry
• Classification of topological insulators and superconductors in three spatial dimensions
• Classification of stable three-dimensional Dirac semimetals with nontrivial topology
• Orbital magnetization in periodic insulators
• Quantum Theory of Orbital Magnetization and its Generalization to Interacting Systems
• An Aharonov-Bohm interferometer for determining Bloch band topology
• Dichroic f-sum rule and the orbital magnetization of crystals
• Interferometric approach to measuring band topology in 2D optical lattices
• Correlation Length, Universality Classes, and Scaling Laws Associated with Topological Phase Transitions
• Correlation effects in double-Weyl semimetals
• Universalities of thermodynamic signatures in topological phases
• Weyl-type topological phase transitions in fractional quantum Hall like systems
• Charge transport in gapless chiral electron systems with arbitrary band dispersion
• Renormalization group approach to a $p$-wave superconducting model

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