Topological Invariants of Edge States for Periodic Two-Dimensional Models

  title={Topological Invariants of Edge States for Periodic Two-Dimensional Models},
  author={Julio Avila and Hermann Schulz-Baldes and Carlos Villegas-Blas},
  journal={Mathematical Physics, Analysis and Geometry},
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 ${\mathbb Z}_2$-invariant for the edge states. It is shown… Expand

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