Semiconductor Wannier equations: a real-time, real-space approach to the nonlinear optical response in crystals (ATATA)

TL;DR

This paper introduces semiconductor Wannier equations (SWEs), a real-space, real-time method for modeling ultrafast nonlinear optical responses in crystals, overcoming gauge issues and incorporating many-body interactions.

Contribution

The paper presents SWEs as a novel real-space formulation that improves numerical robustness and physical clarity over traditional reciprocal-space methods for nonlinear optical phenomena.

Findings

SWEs effectively model high-harmonic generation in crystals.

The approach removes gauge ambiguities present in reciprocal-space equations.

Inclusion of decoherence channels enhances modeling of ultrafast dynamics.

Abstract

We develop the semiconductor Wannier equations (SWEs), a real-time, real-space formulation of ultrafast light-matter dynamics in crystals, by deriving the equations of motion for the electronic reduced density matrix in a localized Wannier basis. Working in real space removes the structure-gauge ambiguities that hinder reciprocal-space semiconductor Bloch equations. Electron--electron interactions are included at the time-dependent Hartree plus static screened-exchange (TD-HSEX) level. Decoherence is modeled with three complementary channels: pure dephasing, population relaxation, and distance-dependent real-space dephasing; providing physically grounded damping for strong-field phenomena such as high-harmonic generation. Conceptually, the SWEs bridge real-space semiclassical intuition with many-body solid-state optics, offering a numerically robust and gauge-clean alternative to reciprocal-space approaches for nonlinear optical response and attosecond spectroscopy in solids.