Can harmonic spectra measure Berry curvature of a crystal? · revision history

Revision 2

Accepted · core change · record

Changes against revision 1:

Title
Can harmonic spectra measure Berry curvature of a crystal?
Plain
In crystals lacking mirror symmetry, electrons pushed by a field also drift sideways because of a geometric property of their bands called Berry curvature. Harmonics polarized at right angles to the laser might read this property out, if other effects can be excluded.
Precise · changed · core
Revision 1: In noncentrosymmetric materials (monolayer MoS2, hBN, $\alpha$-quartz) the anomalous velocity $v = -(e/\hbar)\ E\ x\ \Omega(k)$, with $\Omega(k)$ the Berry curvature, generates even-order harmonics polarized perpendicular to the drive. Question: can the perpendicular even-harmonic amplitudes and phases be inverted to give $\Omega(k)$ along the driven trajectories with a stated accuracy, given interband contributions and propagation. An answer is a retrieval in a material with independently known Omega(k) that agrees within the stated uncertainty, or a proof that the inversion is not unique.
Revision 2: In noncentrosymmetric materials (monolayer $\mathrm{MoS_2}$, hBN, $\alpha$-quartz) the anomalous velocity $v = -(e/\hbar)\ E\ x\ \Omega(k)$, with $\Omega(k)$ the Berry curvature, generates even-order harmonics polarized perpendicular to the drive. Question: can the perpendicular even-harmonic amplitudes and phases be inverted to give $\Omega(k)$ along the driven trajectories with a stated accuracy, given interband contributions and propagation. An answer is a retrieval in a material with independently known Omega(k) that agrees within the stated uncertainty, or a proof that the inversion is not unique.
Settled by
A blind retrieval of $\Omega(k)$ from harmonic data in a material whose Berry curvature is fixed by ab initio band theory and by an independent transport or optical measurement.
Kind
well-posed
Answer type
yes-no
References
(empty)
Literature status
partially-resolved
Status note · changed
Revision 1: Retrievals were reported in $\alpha$-quartz (Luu and Woerner, Nature Communications 2018) and even harmonics attributed to Berry curvature in MoS2 (2017); uniqueness and model dependence of the inversion remain debated.
Revision 2: Retrievals were reported in $\alpha$-quartz (Luu and Woerner, Nature Communications 2018) and even harmonics attributed to Berry curvature in $\mathrm{MoS_2}$ (2017); uniqueness and model dependence of the inversion remain debated.
Posed since
2017

Decisions