Theory of noninteger highharmonic generation in a topological surface state
Abstract
High harmonic generation is a versatile experimental technique for probing ultrafast electron dynamics. While in the past it has been employed typically in dielectrics and semiconductors, recently high harmonic generation was also observed from a topological surface [Schmid et al., Nature 593, 385 (2021)]. It has been found that harmonic orders in the intermediate range of 1318 continuously shift when the carrier envelope phase (CEP) is varied. In this work, we adopt a minimal model of the topological surface state and calculate analytically the highharmonic spectrum. We derive formulae describing the parametric dependencies of CEP shifts in high harmonics; in particular, we have a transparent result for the shift of the (peak) frequency $\omega$ when changing the CEP $\varphi$: $d\omega/d\varphi = 2 \bar{\mathfrak f}' \omega/\omega_0$, where $\omega_0$ describes the fundamental driving frequency and $\bar{\mathfrak f}'$ characterizes the chirp of the driving laser pulse. We compare the analytical formula to fullfledged numerical simulations finding only 17% average absolute deviation in $d\omega/d\varphi$. Our analytical result is fully consistent with experimental observations. It therefore provides the first understanding of the phenomenon of CEP shifts in solids based on analytically derived parametric dependencies.
 Publication:

arXiv eprints
 Pub Date:
 May 2022
 arXiv:
 arXiv:2205.02631
 Bibcode:
 2022arXiv220502631G
 Keywords:

 Physics  Optics;
 Condensed Matter  Mesoscale and Nanoscale Physics