SciPost Submission Page
Unifying semiclassics and quantum perturbation theory at nonlinear order
by Daniel Kaplan, Tobias Holder, Binghai Yan
This Submission thread is now published as
Submission summary
| Authors (as registered SciPost users): | Daniel Kaplan · Binghai Yan |
| Submission information | |
|---|---|
| Preprint Link: | https://arxiv.org/abs/2208.00827v2 (pdf) |
| Date accepted: | 2023-01-23 |
| Date submitted: | 2022-12-14 08:09 |
| Submitted by: | Kaplan, Daniel |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approaches: | Theoretical, Computational |
Abstract
Nonlinear electrical response permits a unique window into effects of band structure geometry. It can be calculated either starting from a Boltzmann approach for small frequencies, or using Kubo's formula for resonances at finite frequency. However, a precise connection between both approaches has not been established. Focusing on the second order nonlinear response, here we show how the semiclassical limit can be recovered from perturbation theory in the velocity gauge, provided that finite quasiparticle lifetimes are taken into account. We find that matrix elements related to the band geometry combine in this limit to produce the semiclassical nonlinear conductivity. We demonstrate the power of the new formalism by deriving a quantum contribution to the nonlinear conductivity which is of order $\tau^{-1}$ in the relaxation time $\tau$, which is principally inaccessible within the Boltzmann approach. We outline which steps can be generalized to higher orders in the applied perturbation, and comment about potential experimental signatures of our results.
Author comments upon resubmission
We wish to thank the referees for their diligent and comprehensive review of our paper. We benefited from the suggestions of all referees and were glad to correct the typos that they found. We note that all referees observed the relevance, appropriateness and clear presentation in our work. We carefully followed the suggestions and requests made by all referees and implemented them fully.
We are certain this revised version fixes all remaining typos and answers the clarifications and additional requests put forward by the referees.
List of changes
An extended discussion on the role of $\alpha$ is now in App. A, and we have also answered the referees separately on the submission page.
We have fixed typos in Figure captions as Ref. 2 suggested, that was due to a rendering error. The numerical data was not changed.
We now explicitly expand on the local particle-hole symmetry which is common to many tight-binding models in App. F.
We have fixed all the typos pointed out by both referees.
We have made thee inline equations pointed out by Ref. 2, full ones. They are now Eqs. 16-17.
Published as SciPost Phys. 14, 082 (2023)