Extended Bloch theorem for topological lattice models with open boundaries
| Autor: | Emil J. Bergholtz, Guido van Miert, Flore K. Kunst |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2018 |
| Předmět: |
Physics
Condensed Matter - Mesoscale and Nanoscale Physics FOS: Physical sciences 02 engineering and technology Codimension 021001 nanoscience & nanotechnology 01 natural sciences Theoretical physics symbols.namesake Fourier transform Topological insulator Lattice (order) Mesoscale and Nanoscale Physics (cond-mat.mes-hall) 0103 physical sciences symbols Boundary value problem 010306 general physics 0210 nano-technology Mirror symmetry Eigenvalues and eigenvectors Bloch wave |
| Popis: | While the Bloch spectrum of translationally invariant noninteracting lattice models is trivially obtained by a Fourier transformation, diagonalizing the same problem in the presence of open boundary conditions is typically only possible numerically or in idealized limits. Here we present exact analytic solutions for the boundary states in a number of lattice models of current interest, including nodal-line semimetals on a hyperhoneycomb lattice, spin-orbit coupled graphene, and three-dimensional topological insulators on a diamond lattice, for which no previous exact finite-size solutions are available in the literature. Furthermore, we identify spectral mirror symmetry as the key criterium for analytically obtaining the entire (bulk and boundary) spectrum as well as the concomitant eigenstates, and exemplify this for Chern and ${\mathcal{Z}}_{2}$ insulators with open boundaries of codimension one. In the case of the two-dimensional Lieb lattice, we extend this further and show how to analytically obtain the entire spectrum in the presence of open boundaries in both directions, where it has a clear interpretation in terms of bulk, edge, and corner states. |
| Databáze: | OpenAIRE |
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