SciPost Submission Page
Topological interface states -- a possible path towards a Landau-level laser in the THz regime
by Mark Oliver Goerbig
This Submission thread is now published as
Submission summary
| Authors (as registered SciPost users): | Mark-Oliver Goerbig |
| Submission information | |
|---|---|
| Preprint Link: | https://arxiv.org/abs/2307.05116v4 (pdf) |
| Date accepted: | 2023-12-04 |
| Date submitted: | 2023-11-23 09:28 |
| Submitted by: | Goerbig, Mark-Oliver |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
|
| Approach: | Theoretical |
Abstract
Volkov-Pankratov surface bands arise in smooth topological interfaces, i.e. interfaces between a topological and a trivial insulator, in addition to the chiral surface state imposed by the bulk-surface correspondence of topological materials. These two-dimensional bands become Landau-quantized if a magnetic field is applied perpendicular to the interface. I show that the energy scales, which are typically in the 10-100 meV range, can be controlled both by the perpendicular magnetic field and the interface width. The latter can still be varied with the help of a magnetic-field component in the interface. The Landau levels of the different Volkov-Pankratov bands are optically coupled, and their arrangement may allow one to obtain population inversion by resonant optical pumping. This could serve as the elementary brick of a multi-level laser based on Landau levels. Moreover, the photons are absorbed and emitted either parallel or perpendicular to the magnetic field, respectively in the Voigt and Faraday geometry, depending on the Volkov-Pankratov bands and Landau levels involved in the optical transitions.
Author comments upon resubmission
Dear Editor,
Thank you very much for sending me the second report of Referee 2, who made her/his justified criticism about the definition of the geometry much clearer now. She/he is fully right that in the Voigt geometry, the photon's electric field must be aligned with the external magnetic field to obtain the desired optical selection rules. The main text has been changed in response to the referee's criticism, along with the other two suggestions.
Sincerely yours,
Mark Oliver Goerbig
-------------------------------------------------------------------
Response to the Referee's second report:
I would like to thank the Referee for her/his second report and the helpful clarification of the criticism mentioned in her/his first report. I now understand her/his point better and fully agree that, in the Voigt geometry, also the orientation of the photon's electric field must be specified (in contrast to the more commonly used Faraday geometry, where the direction of the photon's propagation is sufficient). Indeed, in order to obtain the selection rule n->n in Landau-level spectroscopy, one must ensure that the photon's electric field be in the same direction as the external magnetic field. Otherwise, one retrieves the n-> n+-1 selection rules as in the Faraday geometry, which does not have this ambiguity.
In response to the Referee's comment, I have now added this precision of the direction of the photon's electric field in the discussion of the Faraday/Voigt geometry both in the main text as well as in the added footnote [32]. Furthermore, I also mention the polarization in the caption of Table 1.
Furthermore, I have taken into account the Referee's suggestion to make clear the circular polarizations $\sigma^+$ and $\sigma^-$ of the photon in the coupling to the LL transitions in the Faraday geometry.
Finally, I repeat in the caption of Figs. 2 and 3 that the dashed lines correspond to the dispersion of the surface bands in the absence of a magnetic field, as in Fig. 1.
List of changes
* clarification of the orientation of the photon's electric field with respect to the external magnetic field in the Voigt geometry (a) in the main text, (b) in the footnote [32], and (c) in the caption of Table I.
* coupling to the two circular polarizations (for the Faraday geometry) added to the main text (last paragraph of Sec. II)
* meaning of the dashed lines in Figs. 2 and 3 specified in the caption (dispersion in the absence of a magnetic field)
Published as SciPost Phys. 15, 246 (2023)