Unraveling materials Berry curvature and Chern numbers from real-time evolution of Bloch states

Proceedings Of The National Academy Of Sciences Of The United States Of America 116 (10), 4135 - 4140 (2019)

Unraveling materials Berry curvature and Chern numbers from real-time evolution of Bloch states

Dongbin Shin, Shunsuke A. Sato, Hannes Hübener, Umberto De Giovannini, Jeongwoo Kim, Noejung Park,, Angel Rubio

Materials can be classified by the topological character of their electronic structure and, in this perspective, global attributes immune to local deformations have been discussed in terms of Berry curvature and Chern numbers. Except for instructional simple models, linear response theories have been ubiquitously used in calculations of topological properties of real materials. Here we propose a completely different and versatile approach to obtain the topological characteristics of materials by calculating physical observables from the real-time evolving Bloch states: The cellaveraged current density reveals the anomalous velocities that lead to the conductivity quantum. Results for prototypical cases are shown, including a spin-frozen valley Hall and a quantum anomalous Hall insulator. The advantage of this method is best illustrated by the example of a quantum spin Hall insulator: The quantized spin Hall conductivity is straightforwardly obtained irrespective of the non-Abelian nature in its Berry curvature. Moreover, the method can be extended to the description of real observables in nonequilibrium states of topological materials.

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We acknowledge financial support from the European Research Council (ERC-2015-AdG-694097) and Grupos Consolidados Universidad del Pa´ıs Vasco/Euskal Herriko Unibertsitatea (UPV/EHU) (IT578-13). The Flatiron Institute is a division of the Simons Foundation. S.A.S.gratefully acknowledges the support from the Alexander von Humboldt Foundation. D.S. and N.P. acknowledge the support from the National Research Foundation of Korea (NRF) through the Basic Research Laboratory (NRF-2017R1A4A1015323) and the Basic Science Research Program (NRF-2016R1D1A1B03931542).

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