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The geometry of quantum states is well-established as a basis for understanding the response of electronic systems to static electromagnetic fields, as exemplified by the theory of the quantum and anomalous Hall effects.
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Anomalous Hall effect
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Circular photogalvanic effect on topological insulator surfaces: Berry-curvature-dependent response
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Maximally localized Wannier functions: Theory and applications
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Measuring the quantum geometry of Bloch bands with current noise
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The Euler number of Bloch states manifold and the quantum phases in gapped fermionic systems
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Quantum nonlinear Hall effect induced by Berry curvature dipole in time-reversal invariant materials
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Semiclassical wave packet dynamics in nonuniform electric fields
Lapa, M. F. & Hughes, T. L · 2019
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Nonreciprocal directional dichroism induced by the quantum metric dipole
Gao, Y. & Xiao, D · 2019
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Bulk photovoltaic effects in the presence of a static electric field
Fregoso, B. M · 2019
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Bounds on the superconducting transition temperature: Applications to twisted bilayer graphene and cold atoms
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Experimental measurement of the quantum metric tensor and related topological phase transition with a superconducting qubit
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Superfluidity in topologically nontrivial flat bands
Peotta, S. & Törmä, P · 2015
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Geometrical effects in orbital magnetic susceptibility
Gao, Y., Yang, S. A. & Niu, Q · 2015
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Germanene: the germanium analogue of graphene
Acun, A. et al · 2015
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Topological nature of nonlinear optical effects in solids
Morimoto, T. & Nagaosa, N · 2016
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Concept of quantum geometry in optoelectronic processes in solids: Application to solar cells
Nagaosa, N. & Morimoto, T · 2017
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de Juan, F., Grushin, A. G., Morimoto, T. & Moore, J. E · 2017
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Stiefel-Whitney classes and topological phases in band theory
Ahn, J., Park, S., Kim, D., Kim, Y. & Yang, B.-J · 2019
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J. Ahn, S. Park, D. Kim, Y. Kim, and B.-J. Yang, Stiefel-Whitney classes and topological phases in band theory, Chin. Phys. B 28
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Topology-bounded superfluid weight in twisted bilayer graphene
Xie, F., Song, Z., Lian, B. & Bernevig, B. A · 2020
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Electric polarization in inhomogeneous crystals
Zhao, Y., Gao, Y. & Xiao, D · 2020
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Intrinsic anomalous Hall conductivity in non-uniform electric field
Kozii, V., Avdoshkin, A., Zhong, S. & Moore, J. E · 2020
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Quantum distance and anomalous Landau levels of flat bands
Rhim, J.-W., Kim, K. & Yang, B.-J · 2020
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Low-frequency divergence and quantum geometry of the bulk photovoltaic effect in topological semimetals
Ahn, J., Guo, G.-Y. & Nagaosa, N · 2020
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Difference frequency generation in topological semimetals
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Consequences of time-reversal-symmetry breaking in the light-matter interaction: Berry curvature, quantum metric, and diabatic motion
Holder, T., Kaplan, D. & Yan, B · 2020
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Nonlinear optics (Academic press, 2020)
Boyd, R. W · 2020
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Euler characteristic number of the energy band and the reason for its non-integer values
Ma, Y.-Q · 2020
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Chiral photocurrent in parity-violating magnet and enhanced response in topological antiferromagnet
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