Mapping topological order in coordinate space

By Raffaello Bianco, Raffaele Resta. 2011

259 citations recorded by the source corpus.

The organization of the electrons in the ground state is classified by means of topological invariants, defined as global properties of the wave function. Here we address the Chern number of a two-dimensional insulator and we show that the corresponding topological order can be mapped by means of a ``topological marker,'' defined in $\mathbf{r}$ space, and which may vary in different regions of the same sample. Notably, this applies equally well to periodic and open boundary conditions. Simulations over a model Hamiltonian validate our theory.

Subfields: Algebra and Number Theory, Atomic and Molecular Physics, and Optics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/f1b79349c75794657e26e94ff7172a9cd6cf34fd

Citations in the corpus

• Topological bands for ultracold atoms (2018, unknown): “For non-interacting systems without translational invariance, a local Chern marker 8 can be defined (Bianco and Resta, 2011).”