Semiconductor Bloch-equations formalism: Derivation and application to high-harmonic generation from Dirac fermions

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.

Automated summary

In this study, we rederive the semiconductor Bloch equations and establish a close link to the Berry connection. Our rigorous derivation reveals the existence of two additional contributions to the current, which significantly impact the emission intensity in situations with strong dephasing or wave-number dependence. The added terms from these contributions can alter the total signal by up to a factor of 10 in high-harmonic generation for a Dirac metal.