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Transport of orbital currents in systems with strong intervalley coupling: the case of Kekulé distorted graphene
by Tarik P. Cysne, R. B. Muniz, Tatiana G. Rappoport
Submission summary
| Authors (as registered SciPost users): | Tatiana Rappoport |
| Submission information | |
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| Preprint Link: | https://arxiv.org/abs/2404.12072v1 (pdf) |
| Date submitted: | 2024-05-03 14:04 |
| Submitted by: | Rappoport, Tatiana |
| Submitted to: | SciPost Physics Core |
| Ontological classification | |
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| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
Abstract
We show that orbital currents can describe the transport of orbital magnetic moments of Bloch states in models where the formalism based on valley current is not applicable. As a case study, we consider Kekul\'e distorted graphene. We begin by analyzing the band structure in detail and obtain the orbital magnetic moment operator for this model within the framework of the modern theory of magnetism. Despite the simultaneous presence of time-reversal and spatial-inversion symmetries, such operator may be defined, although its expectation value at a given energy is zero. Nevertheless, its presence can be exposed by the application of an external magnetic field. We then proceed to study the transport of these quantities. In the Kekul\'e-$O$ distorted graphene model, the strong coupling between different valleys prevents the definition of a bulk valley current. However, the formalism of the orbital Hall effect together with the non-Abelian description of the magnetic moment operator can be directly applied to describe its transport in these types of models. We show that the Kekul\'e-$O$ distorted graphene model exhibits an orbital Hall insulating plateau whose height is inversely proportional to the energy band gap produced by intervalley coupling. Our results strengthen the perspective of using the orbital Hall effect formalism as a preferable alternative to the valley Hall effect
Current status:
Reports on this Submission
Strengths
1- Analytical model, all calculations can be reproduced
2-Addresses a problem which is actively debated
Weaknesses
1-Interpretation - valley currents are meaningless in the considered situation
2-Experimental implications: how is the envisaged situation achieved in the lab - what are the main predictions of this work?
Report
The authors report a theoretical investigation of orbital currents in a Kekulé deformed graphene lattice, occurring when the couplings between carbon atoms are either enhanced or decreased (Figure 1a). How this particular situation is achieved in practice is not discussed in sufficient detail (doesn't the envisaged situation require a very careful fine-tuning?), and the model calculation has the risk of being "just a model" - not relevant to reality. (Later, the paper uses a value for the Kekulé parameter extracted from experiment, but the experiment is itself somewhat unclear.)
But my main point is philosophical. The band structure shown in Fig. 1 c does not have two valleys because the energy minimum is shifted to the Gamma-point - hence it does not make any sense to speak about "valley currents", which are specific to the K and K' points in the undistorted lattice. Thus the authors are considering a situation where, by construction, the valley currents do not give any meaning. This does not remove the reason for doing the calculation, but it removes the foundations of all critical remarks made on using the valley currents as a vehicle of calculation. It also removes the hopes of resolving of some of the difficulties related to the interpretation/observation of valley currents. In my view the authors are presenting a calculation (maybe a model calculation) in a situation where valley currents cannot be defined - and this should be clear in the submitted manuscript.
Requested changes
1- remove "cristal" - it is crystal in English
2-Where does Eq.(11) come from - it is crucial for many subsequent developments. Either give a derivation, or a complete sequence of references.
3) I seem to recognize the expressions for the Berry curvature (e.g., Eq.(20)). Is the expression new, or a reincarnation of well-known results?
Recommendation
Ask for minor revision