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Landau levels in curved space realized in strained graphene

by Glenn Wagner, Fernando de Juan, Dung X. Nguyen

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Submission summary

Authors (as registered SciPost users): Dung Nguyen · Glenn Wagner · Fernando de Juan
Submission information
Preprint Link: scipost_202204_00009v1  (pdf)
Date accepted: 2022-04-13
Date submitted: 2022-04-06 09:22
Submitted by: Wagner, Glenn
Submitted to: SciPost Physics Core
Ontological classification
Academic field: Physics
  • Condensed Matter Physics - Theory
Approach: Theoretical


The quantum Hall effect in curved space has been the subject of many theoretical investigations in the past, but devising a physical system to observe this effect is hard. Many works have indicated that electronic excitations in strained graphene realize Dirac fermions in curved space in the presence of a background pseudo-gauge field, providing an ideal playground for this. However, the absence of a direct matching between a numerical, strained tight-binding calculation of an observable and the corresponding curved space prediction has hindered realistic predictions. In this work, we provide this matching by deriving the low-energy Hamiltonian from the tight-binding model analytically to second order in the strain and mapping it to the curved-space Dirac equation. Using a strain profile that produces a constant pseudo-magnetic field and a constant curvature, we compute the Landau level spectrum with real-space numerical tight-binding calculations and find excellent agreement with the prediction of the quantum Hall effect in curved space. We conclude discussing experimental schemes for measuring this effect.

Author comments upon resubmission

We thank the referee for their careful reading of our manuscript and for their endorsement for publication in SciPost Physics Core (“Once these changes have been made, I expect the manuscript to be suitable for publication in SciPost Physics Core.”).

List of changes

We have made the following changes in response to the referee's comments:
1) We added Refs. [41,48,49] after the statement "are used interchangeably in the literature". Appendix A serves for self-completeness with additional discussions on the boundary conditions and the spin connection term of the 2+1D Dirac action in a static curved space, which was not discussed in the literature. Therefore we would like to keep it after shortening it. We have substantially shortened Appendix A and quote Ref. 49 for the details of the calculation, we do not reproduce the calculation anymore and instead focus on the details of the boundary conditions which are specific to our work.
We added the clarifying statement at the beginning of App. A “Let us start by reproducing the argument for why S and S’ are used interchangeably in the literature [41,48,49].”
And before the section about the boundary conditions, we added the statement “Let us now focus on the boundary conditions specific to the set-up of our study.”
2) In the revised manuscript, we use the valley dual transformation, defined in the new equation (B.11), to map the effective Hamiltonian near the K point to the effective Hamiltonian near K’. The transformation provides the matching of energy levels near K and K’ without using the Schrodinger equation (old equation B.17). We substantially shortened Appendix B by removing unnecessary equations and compressed subsections B.2 and B.3 to one paragraph and equation B.12.
3) We moved the discussion of App. C to the end of section 3.1 such that it appears after the discussion of App. B.
4) We added a discussion of App. D to the end of section 3.1.
5) There was a typo in Eq. (3.6) that has now been fixed, the correct indices for the vielbein \tilde v is one coordinate frame index (i) and one local frame index (a).
6) The confusion was probably due to the typo in Eq. (3.6). We have nevertheless relabelled the dummy index “i” to “j” in Eqs. (3.7)-(3.9). That way one avoids the need for a relabeling of dummy indices, which should make the line of manipulations easier to follow.
7) We updated the figure with the axes switched.
8) We fixed all these typos and some additional ones that were found upon careful proof-reading of the manuscript.
9) We added a reference to Eqs. (3.3) and (3.4) and removed equations (F.15) and (F.16).
10) We added the missing DOI numbers.
11) We updated the references with the journal reference.
12) We fixed an issue in the bibstyle file that was causing the titles to appear completely in lowercase.

Published as SciPost Phys. Core 5, 029 (2022)

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