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

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 employed in calculations of topological properties of real materials. Here we propose a completely different and versatile approach to get 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 whose integration leads 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 non-equilibrium states of topological materials.

arXiv commentWe intend to reorganize the contents and author's affiliation substantially. Later, we will consider a new submission

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Cited by in corpus (16)

• Strong-field physics in three-dimensional topological insulators
• Prediction of ferroelectricity-driven Berry curvature enabling charge- and spin-controllable photocurrent in tin telluride monolayers
• Nonlinear phononics in 2D SnTe: a ferroelectric material with phonon dynamical amplification of electric polarization
• Direct probing of phonon mode specific electron-phonon scatterings in two-dimensional semiconductor transition metal dichalcogenides: Symmetry and Berry phase
• Light-induced topological magnons in two-dimensional van der Waals magnets
• Tracing out the Berry curvature dipole and multipoles in second harmonic Hall responses of time-reversal symmetric insulators
• Optoelectronic manifestation of orbital angular momentum driven by chiral hopping in helical Se chains
• Theory for all-optical responses in topological materials: the velocity gauge picture
• A Snapshot of Time-Dependent Density-Functional Theory
• Geometric Origin of Intrinsic Spin Hall Effect in an Inhomogeneous Electric Field
• First-Principles Demonstration of Non-adiabatic Thouless Pumping of Electrons in A Molecular System
• Superlattice induced electron percolation within a single Landau level
• Photo-induced modification and relaxation dynamics of Weyl-semimetals
• Ultrafast Optical Control of Multi-Valley States in 2D SnS
• Time- and angle-resolved photoelectron spectroscopy of strong-field light-dressed solids: prevalence of the adiabatic band picture
• Relativistic Spin-Lattice Interaction Compatible with Discrete Translation Symmetry in Solids