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

Shin, D.; Sato, S.; Hübener, H.; de Giovannini, U.; Kim, J.; Park, N.; Rubio, A.

doi:10.1073/pnas.1816904116

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

MPS-Authors

/persons/resource/persons222317

Sato, S.
Theory Group, Theory Department, Max Planck Institute for the Structure and Dynamics of Matter, Max Planck Society;
Center for Free Electron Laser Science;

/persons/resource/persons221951

Hübener, H.
Theory Group, Theory Department, Max Planck Institute for the Structure and Dynamics of Matter, Max Planck Society;
Center for Free Electron Laser Science;

/persons/resource/persons221949

de Giovannini, U.
Theory Group, Theory Department, Max Planck Institute for the Structure and Dynamics of Matter, Max Planck Society;
Center for Free Electron Laser Science;

/persons/resource/persons222947

Park, N.
Theory Group, Theory Department, Max Planck Institute for the Structure and Dynamics of Matter, Max Planck Society;
Center for Free Electron Laser Science;

/persons/resource/persons22028

Rubio, A.
Theory Group, Theory Department, Max Planck Institute for the Structure and Dynamics of Matter, Max Planck Society;
Center for Free Electron Laser Science;
Center for Computational Quantum Physics (CCQ), The Flatiron Institute;
Nano-Bio Spectroscopy Group, Departamento de Fisica de Materiales, Universidad del País Vasco UPV/EHU;

External Resource

https://arxiv.org/abs/1809.07439
(Preprint)

https://dx.doi.org/10.1073/pnas.1816904116
(Publisher version)

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4135.full.pdf
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pnas.1816904116.sapp.pdf
(Supplementary material), 2MB

Citation

Shin, D., Sato, S., Hübener, H., de Giovannini, U., Kim, J., Park, N., et al. (2019). 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. doi:10.1073/pnas.1816904116.

Cite as: https://hdl.handle.net/21.11116/0000-0002-7446-D

Abstract

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 cell-averaged 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.