Effective field theories of topological crystalline insulators and topological crystals

Abstract

We present a general approach to obtain effective field theories for topological crystalline insulators whose low-energy theories are described by massive Dirac fermions. We show that these phases are characterized by the responses to spatially dependent mass parameters with interfaces. These mass interfaces implement the dimensional reduction procedure such that the state of interest is smoothly deformed into a topological crystal, which serves as a representative state of a phase in the general classification. Effective field theories are obtained by integrating out the massive Dirac fermions, and various quantized topological terms are uncovered. Our approach can be generalized to other crystalline symmetry protected topological phases and provides a general strategy to derive effective field theories for such crystalline topological phases.

20 pages, 10 figures, 1 table. Published version with minor changes

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Cited by in corpus (8)

• "Quantum Geometric Nesting" and Solvable Model Flat-Band Systems
• Interacting Topological Quantum Chemistry in 2D: Many-body Real Space Invariants
• Crystalline Responses for Rotation-Invariant Higher-Order Topological Insulators
• Higher Berry Phase of Fermions and Index Theorem
• Effective action approach to the filling anomaly in crystalline topological matter
• Topological invariants beyond symmetry indicators: Boundary diagnostics for twofold rotationally symmetric superconductors
• Topological Field Theories of Three-Dimensional Rotation Symmetric Insulators: Coupling Curvature and Electromagnetism
• Intrinsic (Axion) Statistical Topological Insulator