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New aspects of Nonadiabatic Geometric Effects --- Application to Twisted Schwinger Effect in Dirac and Weyl Fermions

by Shintaro Takayoshi, Jianda Wu, Takashi Oka

This is not the current version.

Submission summary

As Contributors: Takashi Oka
Preprint link: scipost_202104_00022v2
Date submitted: 2021-05-17 04:47
Submitted by: Oka, Takashi
Submitted to: SciPost Physics
Academic field: Physics
  • Condensed Matter Physics - Theory
Approach: Theoretical


We study geometric effects in nonadiabatic quantum tunneling and derive the tunneling formula within the quadratic expansion of the Hamiltonian. In addition to the rectification effect known previously, we find two novel effects, namely perfect tunneling and counterdiabaticity at fast sweep speed. As an application, we study the twisted Schwinger effect, i.e., nonadiabatic pair production of particles induced by a rotating electric field. In 2D and 3D Dirac and Weyl fermions, this gives a nonperturbative generation mechanism for valley polarization and current.

Current status:
Has been resubmitted

Author comments upon resubmission

Dear Editor,

Thank you very much for your careful reading and important comments.

We are grateful for giving us the opportunity to clarify the following point.

The "twisted" Landau-Zener model refers to a Hamiltonian with a linear dispersion in one direction and a parabolic dispersion in the perpendicular direction. This is not applicable to the Dirac or Weyl fermions one typically encounters in graphene or Weyl semimetals (although there do exist more complex models where this might apply).

We are afraid that there might be a misunderstanding in the interpretation of our Hamiltonian (1) that defines the twisted Landau-Zener problem. Our target systems are indeed the Dirac and Weyl fermions encountered in graphene or Weyl semimetals and NOT the semi-Dirac materials (= linear + quadratic band touching). The Hamiltonian (1) for the twisted Landau-Zener model is a quadratic time-dependent Hamiltonian, which can be realized in many different situations. The situation we consider is realized when a circularly polarized laser field is applied to graphene or Weyl semimetals as is described in Hamiltonian (11). This Hamiltonian (11) can be mapped to the twisted Landau Zener problem (1) (and its generalization (4)). In order to clarify this point, we added Figure 2 “Mapping from the twisted Schwinger effect to the twisted Landau Zener problem” to the manuscript.

As a computational exercise it may well be publishable, but for SciPost Physics the physical significance of the analysis is an essential ingredient.

The problem of Dirac and Weyl semimetals in a circularly polarized laser field has physical significance, which has led to important experiments such as Y. H. Wang, H. Steinberg, P. Jarillo-Herrero, and N. Gedik, “Observation of Floquet-Bloch states on the surface of a topological insulator”, Science 342, 453 (2013) and J. W. McIver, B. Schulte, F.-U. Stein, T. Matsuyama, G. Jotzu, G. Meier and A. Cavalleri, “Light-induced anomalous Hall effect in graphene”, Nat. Phys. 16(1), 38 (2020). Our work is expected to shed new light on these experiments.

Thus, we believe that our paper is suited for SciPost Physics rather than SciPost Physics Core.

List of changes

We added Figure 2.

Submission & Refereeing History

Resubmission scipost_202104_00022v3 on 10 September 2021

Reports on this Submission

Anonymous Report 2 on 2021-7-13 (Invited Report)

  • Cite as: Anonymous, Report on arXiv:scipost_202104_00022v2, delivered 2021-07-13, doi: 10.21468/SciPost.Report.3226


The Authors study the problem of a fast sweep of an external parameter across an energy barrier. The probability of particle tunneling is calculated. Their calculations are based on a simple two-band model. Applications to the case of driven 2D Dirac fermions and 3D Weyl fermions with circularly polarized light are presented. The main difference with respect to the usual Landau-Zener problem is that the parameter space is curved. They found interesting effects namely, asymmetrical tunneling probability with respect to direction of drive, perfect tunneling at finite sweep rate, and exponentially decreasing tunneling probability for large sweep rate. I find the paper results worth of publication in SciPost Physics. I however have few comments that should be addressed before publication.

1. The Tunneling probability in Eq. 10 should be defined.

2. Comment about v \kappa_{\parallel} `corresponding to the shift vector’ should be either fully explained or removed. Page 5.

3. Why should the expansion of Eq.11 in powers of \Omega to second order be equivalent to the model Eq. 4 on which the results of this paper as based? E.g., why cubic terms in expansion of Eq. 11 are not important near the band minimum?

4. Give an order of magnitude estimate of the value of the electric field and \Omega need to observe these effects for a realistic condensed matter realization.

  • validity: -
  • significance: -
  • originality: -
  • clarity: -
  • formatting: -
  • grammar: -

Anonymous Report 1 on 2021-6-21 (Invited Report)

  • Cite as: Anonymous, Report on arXiv:scipost_202104_00022v2, delivered 2021-06-21, doi: 10.21468/SciPost.Report.3090


1- This paper identifies a new aspect of Bloch function quantum geometry, namely strong corrections to the valley polarization and valley currents in the presence of nonlinear terms in a Dirac Hamiltonian. A simple and transparent derivation is provided, with a new formula for the Landau-Zener tunneling problem (eq. 2, the main result of this work).

2- Predictions are made for 2D and 3D systems, which can be tested experimentally (e.g., discussion on page 14).


1- Maybe a minor weakness is that the paper does not mention and discuss the role of dissipation and decoherence in the quantum tunneling process, which is known to be relevant in light-driven Dirac systems, and can be modelled by a relatively simple extension of their model(s). See, e.g., the relevance of dissipation and decoherence discussed in a theory work related to the anomalous Hall effect measurement in driven graphene,


Overall, I think that the paper clearly meets the acceptance criteria for SciPost Physics. This is an original theoretical proposal which highlights the importance of quantum geometric effects for strong-field phenomena in general and specifically for the Landau-Zener problem, which opens a new pathway in an existing or a new research direction, with clear potential for multipronged follow-up work. (Criterion #3 for Acceptance in SciPost Physics). All of the necessary criteria are fulfilled.

Requested changes

1- I would like to see a discussion of the expected impact of dissipation and decoherence effects, as outlined above; I believe that such effects could be the study of a follow-up work.

  • validity: top
  • significance: high
  • originality: top
  • clarity: high
  • formatting: excellent
  • grammar: excellent

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