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• W2913144890 endingPage "073003" @default.
• W2913144890 startingPage "073003" @default.
• W2913144890 abstract "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." @default.
• W2913144890 created "2019-02-21" @default.
• W2913144890 creator A5017541508 @default.
• W2913144890 creator A5022813763 @default.
• W2913144890 date "2019-07-01" @default.
• W2913144890 modified "2023-09-30" @default.
• W2913144890 title "Universality classes of topological phase transitions with higher-order band crossing" @default.
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• W2913144890 doi "https://doi.org/10.1088/1367-2630/ab2a2d" @default.
• W2913144890 hasPublicationYear "2019" @default.
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