Modification of mixed Berry curvature under AC electric fields

Characterize the modification of the mixed Berry curvature Ω_n^{k t} (defined in momentum–time space for Bloch band n) by a time-dependent uniform electric field E(t), and ascertain whether this modification leads to new physical phenomena in semiclassical electron dynamics and transport.

Background

The paper extends the semiclassical wavepacket formalism to include time-dependent (AC) electric fields up to second order, where the momentum–time mixed Berry curvature Ω_n^{k t} naturally appears in the equations of motion. While corrections to the conventional (momentum–momentum) Berry curvature Ω_n from electric fields are known to induce intrinsic nonlinear Hall effects, the role and possible modifications of the mixed Berry curvature under AC driving had not been clearly established.

Understanding how Ω_n^{k t} is altered by E(t) is crucial because mixed Berry curvature governs phenomena such as adiabatic pumping and emergent electromagnetic induction. Clarifying its field-induced modification and any resulting novel responses would unify and deepen the connection between semiclassical transport and quantum response approaches in AC regimes.