Journal
PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA
Volume 116, Issue 10, Pages 4135-4140Publisher
NATL ACAD SCIENCES
DOI: 10.1073/pnas.1816904116
Keywords
time-dependent density functional theory; Berry curvature; quantum spin Hall effect; topological insulator
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Funding
- European Research Council [ERC-2015-AdG-694097]
- Grupos Consolidados Universidad del Pais Vasco/Euskal Herriko Unibertsitatea (UPV/EHU) [IT578-13]
- Alexander von Humboldt Foundation
- National Research Foundation of Korea (NRF) through the Basic Research Laboratory [NRF-2017R1A4A1015323]
- Basic Science Research Program [NRF-2016R1D1A1B03931542]
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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.
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