Semiconductor-Bloch Formalism: Derivation and Application to High-Harmonic Generation from Dirac Fermions

TL;DR

This paper rederives the semiconductor Bloch equations highlighting the Berry connection, introduces additional current contributions, and applies the formalism to high-harmonic generation in Dirac metals, revealing significant effects on emission spectra.

Contribution

The paper provides a rigorous derivation of the semiconductor Bloch equations including new current contributions linked to the Berry connection, enhancing understanding of high-harmonic generation in Dirac materials.

Findings

Additional current contributions significantly affect high-harmonic spectra.

Extra terms can alter emission intensity by up to a factor of 10.

The formalism is especially relevant in strong dephasing or wave-number dependent scenarios.

Abstract

We rederive the semiconductor Bloch equations emphasizing the close link to the Berry connection. Our rigorous derivation reveals the existence of two further contributions to the current, in addition to the frequently considered intraband and polarization-related interband terms. The extra contributions become sizable in situations with strong dephasing or when the dipole-matrix elements are strongly wave-number dependent. We apply the formalism to high-harmonic generation for a Dirac metal. The extra terms add to the frequency-dependent emission intensity (high-harmonic spectrum) significantly at certain frequencies changing the total signal up to a factor of 10.