Topological invariants of edge states for periodic two-dimensional models

Abstract

Transfer matrix methods and intersection theory are used to calculate the bands of edge states for a wide class of periodic two-dimensional tight-binding models including a sublattice and spin degree of freedom. This allows to define topological invariants by considering the associated Bott-Maslov indices which can be easily calculated numerically. For time-reversal symmetric systems in the symplectic universality class this leads to a Z_2-invariant for the edge states. It is shown that the edge state invariants are related to Chern numbers of the bulk systems and also to (spin) edge currents, in the spirit of the theory of topological insulators.

typos corrected, to appear in Math. Phys., Anal. Geom

References in corpus (2)

• Quantum Spin Hall Effect and Topologically Invariant Chern Numbers
• Robustness of the Spin-Chern number

Cited by in corpus (47)

• Wannier Center Sheets in Topological Insulators
• Bulk-boundary correspondence for non-Hermitian Hamiltonians via Green functions
• Controlled topological phases and bulk-edge correspondence
• A generalization of Bloch's theorem for arbitrary boundary conditions: Theory
• The $K$-theoretic bulk-edge correspondence for topological insulators
• Anomalous bulk-edge correspondence in continuous media
• Of Bulk and Boundaries: Generalized Transfer Matrices for Tight-Binding Models
• Photonic Dirac monopoles and skyrmions: spin-1 quantization
• PAI-graphene: a new topological semimetallic two-dimensional carbon allotrope with highly tunable anisotropic Dirac cones
• Quantum gyro-electric effect: Photon spin-1 quantization in continuum topological bosonic phases
• Index pairings in presence of symmetries with applications to topological insulators
• A noncommutative framework for topological insulators
• Topological invariants and corner states for Hamiltonians on a three-dimensional lattice
• Differential topology of semimetals
• The Colored Hofstadter Butterfly for the Honeycomb Lattice
• Topology in shallow-water waves: a violation of bulk-edge correspondence
• Notes on topological insulators
• Spectral flows associated to flux tubes
• A Unified Perspective of Complex Band Structure: Interpretations, Formulations, and Applications
• Topological edge states on time-periodically strained armchair graphene nanoribbons
• Microlocal analysis of the bulk-edge correspondence
• Exponentially growing bulk Green functions as signature of nontrivial non-Hermitian winding number in one dimension
• Wannier functions and Z_2 invariants in time-reversal symmetric topological insulators
• T-duality simplifies bulk-boundary correspondence
• Persistence of spin edge currents in disordered quantum spin Hall systems
• Topological edge states in two-gap unitary systems: A transfer matrix approach
• Characterization of edge states in perturbed honeycomb structures
• T-duality simplifies bulk-boundary correspondence: some higher dimensional cases
• Fu-Kane-Mele monopoles in semimetals
• Spin Hall insulators beyond the Helical Luttinger model
• Topology in shallow-water waves: A spectral flow perspective
• Spin Conductance and Spin Conductivity in Topological Insulators: Analysis of Kubo-like terms
• Quantization of interface currents
• Sensitivity of quantum walks to boundary of two-dimensional lattices: approaches from the CGMV method and topological phases
• Bulk-edge correspondence and the cobordism invariance of the index
• Edge states in ordinary differential equations for dislocations
• Two-Dimensional Time-Reversal-Invariant Topological Insulators via Fredholm Theory
• Approximate symmetries and conservation laws in topological insulators and associated $\mathbb{Z}$-invariants
• Topological states in the Hofstadter model on a honeycomb lattice
• Edge states in 2D lattices with hopping anisotropy and Chebyshev polynomials
• T-duality and the bulk-boundary correspondence
• From orbital magnetism to bulk-edge correspondence
• Dimensional reduction and scattering formulation for even topological invariants
• Classifying bulk-edge anomalies in the Dirac Hamiltonian
• Boundary conditions and violations of bulk-edge correspondence in a hydrodynamic model
• Mean--field stability for the junction of quasi 1D systems with Coulomb interactions
• Spin transport and lack of quantisation for time-reversal symmetric insulators on the honeycomb structure