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arXiv · 2510.22064

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

Eduardo B. Molinero·Bruno Amorim·Misha Ivanov·Graham G. Brown·Giovanni Cistaro·João M. Viana Parente Lopes·Álvaro Jiménez-Galán·Pablo San-Jose·Rui E. F. Silva
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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.

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Eduardo B. Molinero, Bruno Amorim, Misha Ivanov, Graham G. Brown, Giovanni Cistaro, João M. Viana Parente Lopes, Álvaro Jiménez-Galán, Pablo San-Jose, Rui E. F. Silva. 2025-10-24. Semiconductor Wannier equations: a real-time, real-space approach to the nonlinear optical response in crystals (ATATA). https://doi.org/10.1103/sxcl-yqs7

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