Berry phases of quantum trajectories in semiconductors under strong terahertz fields

TL;DR

This paper demonstrates that in semiconductors with non-zero Berry curvature, quantum trajectories under strong terahertz fields can accumulate Berry phases, leading to observable Faraday rotation effects in nonlinear optical phenomena.

Contribution

It introduces the concept of Berry phase accumulation along quantum trajectories in semiconductors under strong fields, linking topological properties to nonlinear optical responses.

Findings

Berry phases manifest as Faraday rotation angles in monolayer MoS₂.

Quantum trajectories in semiconductors can carry Berry phases under strong terahertz fields.

The study connects topological band properties with extreme nonlinear optics effects.

Abstract

Quantum evolution of particles under strong fields can be essentially captured by a small number of quantum trajectories that satisfy the stationary phase condition in the Dirac-Feynmann path integrals. The quantum trajectories are the key concept to understand extreme nonlinear optical phenomena, such as high-order harmonic generation (HHG), above-threshold ionization (ATI), and high-order terahertz sideband generation (HSG). While HHG and ATI have been mostly studied in atoms and molecules, the HSG in semiconductors can have interesting effects due to possible nontrivial "vacuum" states of band materials. We find that in a semiconductor with non-vanishing Berry curvature in its energy bands, the cyclic quantum trajectories of an electron-hole pair under a strong terahertz field can accumulate Berry phases. Taking monolayer MoS$_2$ as a model system, we show that the Berry phases appear as the Faraday rotation angles of the pulse emission from the material under short-pulse excitation. This finding reveals an interesting transport effect in the extreme nonlinear optics regime.