Real-time observation of Berry curvature and nonlinear Hall effect in insulators

Berry curvature is the key component for various geometric properties of energy bands in many solid-state systems, such as the topological invariance of linear Hall conductivity with broken time-reversal symmetry [1]. Beyond the linear response, the nonlinear Hall effect of time-reversal symmetric materials has attracted significant interest in the last decade [2]. Here, we propose a real-time propagation framework of Bloch wavefunctions to observe linear and nonlinear Hall currents. Together with perturbation analysis of the theoretical Hamiltonian models, we performed real-time time-dependent density functional theory (rt-TDDFT) calculations to investigate an insulator’s first- and second-order optical responses. We show that the topological nature of Bloch states is directly reflected in the real-time responses. Moreover, our implementation is capable of reproducing perturbative second harmonic generation (SHG) spectra [3], polarization anisotropy of SHG signals, and intensity dependence on high harmonic generation for a nonlinear Hall response. We present an rt-TDDFT method that can analyze the band geometry of solid states through real-time simulations of linear and nonlinear optical Hall effects.



References

[1] M. V. Berry, Quantal Phase-Factors Accompanying Adiabatic Changes, Proc R Soc Lon Ser-A 392, 45 (1984).

[2] Q. Ma et al., Observation of the nonlinear Hall effect under time-reversal-symmetric conditions, Nature 565, 337 (2019).

[3] J. E. Sipe and A. I. Shkrebtii, Second-order optical response in semiconductors, Phys Rev B 61, 5337 (2000).