Orbital Magnetism and Related Phenomena in Topological Metals
Final Report Abstract
In this project we have expressed the MCN in terms of the HWFs and studied the different Wannier band structures which can arise in presence of the reflection symmetry. Interestingly, energy eigenstates and eigenvalues of bipartite lattices have analogous features to those discussed by us, because their Hamiltonian anticommutes with the chiral symmetry operator. A practical aspect of our work is the fact that the absolute value of the MCN can be obtained without constructing the mirror operator explicitly when there are either flat bands in the Wannier band structure and the pairs do not touch, or when there is an isolated single pair with Dirac nodes (the studied models are respective examples for these situations). This may be beneficiary for a large-scale search for reflection-symmetric TIs, since the currently used algorithms rely on an explicit construction of the mirror operator for each lattice and the chosen basis of the wave functions. In a following work we already managed to generalize our results to the case of 3D crystals with reflection symmetries. In some of them, two nonequivalent parallel mirror planes coexist and such insulators are classified by a pair of MCNs. We derived expressions for these MCNs in terms of HWFs localized perpendicular to the mirror planes, in analogy to the 2D case. The Wannier band structure generically features flat bands at the two mirror planes, as well as pairs of bands mirror symmetric with respect to one of the mirror planes. We confirmed our results by model calculations similar to those we present for the 2D case. Finally, we were able to relate the values of the MCNs to the quantized ME coupling. To the best of our knowledge, this relation was shown previously only by counting the edge states, but not by considering the bulk electronic structure only. We also plan to study the behavior of the Wannier bands and the interplay between flat bands and touching pairs of bands during topological phase transitions.
Publications
- Geometric and nongeometric contributions to the surface anomalous Hall conductivity, Physical Review B 98, 115108 (2018)
T. Rauch, T. Olsen, D. Vanderbilt, and I. Souza
(See online at https://doi.org/10.1103/PhysRevB.98.115108)
