Unifying semiclassics and quantum perturbation theory at nonlinear order
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...
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
SciPost
2023-04-01
|
| Series: | SciPost Physics |
| Online Access: | https://scipost.org/SciPostPhys.14.4.082 |
| _version_ | 1797839695677227008 |
|---|---|
| author | Daniel Kaplan, Tobias Holder, Binghai Yan |
| author_facet | Daniel Kaplan, Tobias Holder, Binghai Yan |
| author_sort | Daniel Kaplan, Tobias Holder, Binghai Yan |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-04-09T16:02:18Z |
| format | Article |
| id | doaj.art-defab6e83284464fa4256b63ddbe9c84 |
| institution | Directory Open Access Journal |
| issn | 2542-4653 |
| language | English |
| last_indexed | 2024-04-09T16:02:18Z |
| publishDate | 2023-04-01 |
| publisher | SciPost |
| record_format | Article |
| series | SciPost Physics |
| spelling | doaj.art-defab6e83284464fa4256b63ddbe9c842023-04-25T10:46:48ZengSciPostSciPost Physics2542-46532023-04-0114408210.21468/SciPostPhys.14.4.082Unifying semiclassics and quantum perturbation theory at nonlinear orderDaniel Kaplan, Tobias Holder, Binghai YanNonlinear 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.https://scipost.org/SciPostPhys.14.4.082 |
| spellingShingle | Daniel Kaplan, Tobias Holder, Binghai Yan Unifying semiclassics and quantum perturbation theory at nonlinear order SciPost Physics |
| title | Unifying semiclassics and quantum perturbation theory at nonlinear order |
| title_full | Unifying semiclassics and quantum perturbation theory at nonlinear order |
| title_fullStr | Unifying semiclassics and quantum perturbation theory at nonlinear order |
| title_full_unstemmed | Unifying semiclassics and quantum perturbation theory at nonlinear order |
| title_short | Unifying semiclassics and quantum perturbation theory at nonlinear order |
| title_sort | unifying semiclassics and quantum perturbation theory at nonlinear order |
| url | https://scipost.org/SciPostPhys.14.4.082 |
| work_keys_str_mv | AT danielkaplantobiasholderbinghaiyan unifyingsemiclassicsandquantumperturbationtheoryatnonlinearorder |