The topological invariants of rotationally symmetric crystals
arXiv:2107.03222 · doi:10.1103/PhysRevB.104.L201110
Abstract
Recent formal classifications of crystalline topological insulators predict that the combination of time-reversal and rotational symmetry gives rise to topological invariants beyond the ones known for other lattice symmetries. Although the classification proves their existence, it does not indicate a way of calculating the values of those invariants. Here, we show that a specific set of concentric Wilson loops and line invariants yields the values of all topological invariants in two-dimensional systems with pure rotation symmetry in class AII. Examples of this analysis are given for specific models with two-fold and three-fold rotational symmetry. We find new invariants that relate to the presence of higher-order topology and corner charges.
arXiv comment12 pages, 9 figures
References in corpus (27)
- Quantum Spin Hall Effect in Graphene
- Topological Order and the Quantum Spin Hall Effect
- Higher-Order Topological Insulators
- Time Reversal Polarization and a Z_2 Adiabatic Spin Pump
- An equivalent expression of Z2 Topological Invariant for band insulators using Non-Abelian Berry's connection
- Topological quantization of the spin Hall effect in two-dimensional paramagnetic semiconductors
- Symmetry-based Indicators of Band Topology in the 230 Space Groups
- Dirac Semimetals in Two Dimensions
- The space group classification of topological band insulators
- Topological classification of crystalline insulators through band structure combinatorics
- Fragile Topology and Wannier Obstructions
- Structure and Topology of Band Structures in the 1651 Magnetic Space Groups
- Wilson loop approach to fragile topology of split elementary band representations and topological crystalline insulators with time reversal symmetry
- Twisted equivariant matter
- Disconnected Elementary Band Representations, Fragile Topology, and Wilson Loops as Topological Indices: An Example on the Triangular Lattice
- Spinless Topological Insulators without Time-Reversal Symmetry
- Topological correspondence between magnetic space group representations
- Fragile Topology Protected by Inversion Symmetry: Diagnosis, Bulk-Boundary Correspondence, and Wilson Loop
- Distant-Neighbor Hopping in Graphene and Haldane Models
- Topological Mirror Insulators in One Dimension
- Bulk-corner correspondence of time-reversal symmetric insulators: deduplicating real-space invariants
- Many-body generalization of the Z2 topological invariant for the quantum spin Hall effect
- Subdimensional topologies, indicators and higher order phases
- Tenfold Topology of Crystals: Unified classification of crystalline topological insulators and superconductors
- Classification of crystalline insulators without symmetry indicators: atomic and fragile topological phases in twofold rotation symmetric systems
- Quenching in Chern insulators with satellite Dirac points: The fate of edge states
- Topology in time-reversal symmetric crystals