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Topological-Insulator Nanocylinders

by Michele Governale, Fabio Taddei

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Submission summary

Authors (as Contributors): Michele Governale
Submission information
Arxiv Link: (pdf)
Date submitted: 2022-09-06 10:07
Submitted by: Governale, Michele
Submitted to: SciPost Physics Core
Ontological classification
Academic field: Physics
  • Condensed Matter Physics - Theory
Approach: Theoretical


Nanostructures, such a quantum dots or nanoparticles, made of three-dimensional topological insulators (3DTIs) have been recently attracting increasing interest, especially for their optical properties. In this paper we calculate the energy spectrum, the surface states and the dipole matrix elements for optical transitions with in-plane polarization of 3DTI nanocylinders of finite height L and radius R. We first derive an effective 2D Hamiltonian by exploiting the cylindrical symmetry of the problem. We develop two approaches: the first one is an exact numerical tight-binding model obtained by discretising the Hamiltonian. The second one, which allows us to obtain analytical results, is an approximated model based on a large-R expansion and on an effective boundary condition to account for the finite height of the nanocylinder. We find that the agreement between the two models, as far as eigenenergies and eigenfunctions are concerned, is excellent for the lowest absolute value of the longitudinal component of the angular momentum. Finally, we derive analytical expressions for the dipole matrix elements by first considering the lateral surface alone and the bases alone, and then for the whole nanocylinder. In particular, we focus on the two limiting cases of tall and squat nanocylinders. The latter case is compared with the numerical results finding a good agreement.

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Has been resubmitted

Submission & Refereeing History

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Submission 2209.00890v1 on 6 September 2022

Reports on this Submission

Anonymous Report 1 on 2022-10-13 (Invited Report)

  • Cite as: Anonymous, Report on arXiv:2209.00890v1, delivered 2022-10-13, doi: 10.21468/SciPost.Report.5893


In this work, the authors present a detailed calculation of the spectra and dipole matrix elements of a model for three dimensional topological insulator nanostructures with the form of a finite cylinder. Technically, the manuscript appears correct.


The work is an extension to previous work (Ref. 54) where the same problem was considered for infinite cylinders by the same authors (among others). This work uses the exact same formalism of the continuum model, supplemented now by finite boundary conditions in the z direction. This same approach was followed by Kundu et al (which is not discussed in the paper)

In my opinion, the main problem with this paper is that it does not justify its purpose almost at all. The introduction describes topological insulator nanostructures very generally, and describes honestly the fact that infinite wires were worked out in Ref. 54 among many other references. The only motivation ever offered for the fact that now finite L is considered is “In this paper we focus on TI nanocylinders with finite L”. Why is the finite L case interesting? What does it offer compared to the previous paper? Currently, the paper reads as if the only motivation to do it is because it can be done. The conclusions similarly offer no physical insight, and reduce to describing to what extent numerical and analytical calculations agree. The paper would significantly improve if the authors explained what motivated them to carry out this calculation, what physical problem are they trying to solve, and what conclusions may one draw from their results that will motivate the study of such nanocylinders. In my opinion, these explanations in the introduction would be of much higher value to readers than connections to biomedical applications and cancer therapy.

In my opinion, the paper also falls short of providing any result that is directly relevant to the optics and THz community. The isolated calculation of the dipole matrix element is a very indirect way of approaching this problem, as opposed to providing an actual prediction of the optical conductivity or any other optical response. As provided in Fig. 6, what is the meaning of these results? Is this connected to any observable effect, and of what magnitude? What do we learn about the dependence of the matrix elements as a function of R?

Another pressing problem is that the manuscript does not describe the work of Kundu et al mentioned previously. This work from 2011 solves exactly the same problem and compares surface and bulk theories, compares with a true real space tight binding model, and in my opinion offers significantly more physical insight. The authors should compare their results with this paper and again explain what is the added value of their paper.


In my opinion, the paper does not currently meet the criteria for SciPost Physics Core.

  • validity: ok
  • significance: poor
  • originality: poor
  • clarity: ok
  • formatting: reasonable
  • grammar: excellent

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