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Transitions in Xenes between excitonic, topological and trivial insulator phases: influence of screening, band dispersion and external electric field
by Olivia Pulci, Paola Gori, Davide Grassano, Marco D'Alessandro, Friedhelm Bechstedt
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Authors (as registered SciPost users):  Marco D'Alessandro 
Submission information  

Preprint Link:  https://arxiv.org/abs/2301.08601v1 (pdf) 
Date submitted:  20230206 10:26 
Submitted by:  D'Alessandro, Marco 
Submitted to:  SciPost Physics 
Ontological classification  

Academic field:  Physics 
Specialties: 

Approaches:  Theoretical, Computational 
Abstract
Using a variational approach, the binding energies $E_b$ of the lowest bound excitons in Xenes under varying electric field are investigated. The internal exciton motion is described both by Dirac electron dispersion and in effectivemass approximation, while the screened electronhole attraction is modeled by a RytovaKeldysh potential with a 2D electronic polarizability $\alpha_{2{\rm D}}$. The most important parameters as spinorbitinduced gap $E_g$, Fermi velocity $v_F$ and $\alpha_{2{\rm D}}$ are taken from ab initio density functional theory calculations. In addition, $\alpha_{2{\rm D}}$ is approximated in two different ways. The relation of $E_b$ and $E_g$ is ruled by the screening. The existence of an excitonic insulator phase with $E_b>E_g$ sensitively depends on the chosen $\alpha_{2{\rm D}}$. The values of $E_g$ and $\alpha_{2{\rm D}}$ are strongly modified by a vertical external electric bias $U$, which defines a transition from the topological into a trivial insulator at $U=E_g/2$, with the exception of plumbene. Within the Dirac approximation, but also within the effective mass description of the kinetic energy, the treatment of screening dominates the appearance or nonappearance of an excitonic insulator phase. Gating does not change the results: the prediction done at zero electric field is confirmed when a vertical electric field is applied. Finally, ManyBody perturbation theory approaches based on the Green's function method, applied to stanene, confirm the absence of an excitonic insulator phase, thus validating our results obtained by ab initio modeling of $\alpha_{2{\rm D}}$.
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Submission & Refereeing History
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Reports on this Submission
Report
The problem considered in the manuscript arXiv:2301.08601vI is interesting and recommend the manuscript "Transitions in Xenes between excitonic, topological and trivial insulator phases: influence of screening, band dispersion and external electric field" by Olivia Pulci et al., for publication.
Anonymous Report 1 on 2023320 (Invited Report)
 Cite as: Anonymous, Report on arXiv:2301.08601v1, delivered 20230320, doi: 10.21468/SciPost.Report.6932
Strengths
1) topic is important
2) approach is pertinent and (for the validation) state of the art
Weaknesses
1) presentation of results
Report
In this article, the authors present a study to evaluate the
exciton properties of xenes. In particular, they study the
influence of the eh screening (and band dispersion and the
role of an external electric field) in discriminating between
an insulator and a candidate topological insulator.
The analysis of the screening is of great importance in the
description of optical properties. But in these systems
(2D, small bandgap, spinorbit coupling) it becomes a very
cumbersome part of the calculation if the ab initio approach
is uniquely considered. The proposition of models is then more
than welcome. For this reason, I believe the results shown
in the article deserve publication.
I find however the presentation unclear. I believe a little effort
would permit the article to be better structured, with a clear
discussion of the results, a summary of the different models, etc.
The article should be published only after this work has been
carried out.
Requested changes
1) the discussion of the different models, their physical meaning,
the advantages and the limits should been highlighted, within a
summary. I would expect much clearer indication where a model
makes sense, where we should expect problems, etc.
All this is sort of diluted all along the text and not very clear.
2) at the beginning of II.B, the authors mention the ingredients
of the problem in BSE: electron(hole) energy bands, statically screened
Coulomb interaction W and bare repulsive eh exchange. I do not
find the latter term in Eq.3, while I find the first two terms.
Is it embedded in W? Is it excluded from the model?
3) In the ab initio calculation, it is mentioned a cutoff in the
Coulomb interaction. I understand this as a mean to overcome the
problem of a supercell replica. But I would like more details, for
the use of a cutoff introduce a parameter. The problem of calculating
surfaces or slabs in periodic boundary conditions is a long standing one,
often treated very unsatisfactorily. Recently an article shed a bit
of light in this matter: Phys. Rev. B 106, 035431. Maybe it relates.
4) Slightly related to point 1 above: the ab initio 'validation' comes
only from the case of stanene. Considering the variation of results
of the models and the comparison with only one case, I would tone
down the validation. What is the amount of calculation here involved
(in terms of computational resources) and how much would be required to do an extra case ?
Here, I want to stress that I totally am in favour of the objective
of the article: to offer a much cheaper alternative (by using
models) to the ab initio brute force approach of exciton binding
energy. But a validation has to be meaningful.
Author: Marco D'Alessandro on 20230428 [id 3624]
(in reply to Report 1 on 20230320)**The referee writes:**
_The analysis of the screening is of great importance in the
description of optical properties. But in these systems
(2D, small bandgap, spinorbit coupling) it becomes a very
cumbersome part of the calculation if the ab initio approach
is uniquely considered. The proposition of models is then more
than welcome. For this reason, I believe the results shown
in the article deserve publication_
**Our response:**
We thank the reviewer for his/her clear and positive characterization of our work and the recommendation of publication of our manuscript.
**The referee writes:**
_I find however the presentation unclear. I believe a little effort
would permit the article to be better structured, with a clear
discussion of the results, a summary of the different models, etc.
The article should be published only after this work has been
carried out._
**Our response:**
We thank the reviewer for his/her suggestions and have correspondingly improved the structure, discussion and summary in the resubmitted manuscript.
__Requested changes__
**The referee writes:**
_1)The discussion of the different models, their physical meaning,
the advantages and the limits should been highlighted, within a
summary. I would expect much clearer indication where a model
makes sense, where we should expect problems, etc.
All this is sort of diluted all along the text and not very clear._
**Our response:**
We thank the reviewer for this suggestion. The different models are discussed in the new text under varying aspects.
**The referee writes:**
_2)at the beginning of II.B, the authors mention the ingredients
of the problem in BSE: electron(hole) energy bands, statically screened
Coulomb interaction W and bare repulsive eh exchange. I do not
find the latter term in Eq.3, while I find the first two terms.
Is it embedded in W? Is it excluded from the model?_
**Our response:**
In the investigated limit of the description of the electronhole interaction within a twoband model and vanishing translation of the excitons the electronhole exchange is vanishing as well known from the description of the WannierMott excitons. We mention this fact now in the text of the resubmitted manuscript.
**The referee writes:**
_3) In the ab initio calculation, it is mentioned a cutoff in the
Coulomb interaction. I understand this as a mean to overcome the
problem of a supercell replica. But I would like more details, for
the use of a cutoff introduce a parameter. The problem of calculating
surfaces or slabs in periodic boundary conditions is a long standing one,
often treated very unsatisfactorily. Recently an article shed a bit
of light in this matter: Phys. Rev. B 106, 035431. Maybe it relates._
**Our response:**
The treatment of the artificial Coulomb interaction between different slabs in the supercell arrangement is now discussed describing the ab initio treatment of quasiparticle GW and excitonic BSE. Moreover, details and references are given. Referring to possible effects on optical properties and screening of 2D objects, the abovementioned reference is cited.
**The referee writes:**
_4) Slightly related to point 1 above: the ab initio 'validation' comes
only from the case of stanene. Considering the variation of results
of the models and the comparison with only one case, I would tone
down the validation. What is the amount of calculation here involved
(in terms of computational resources) and how much would be required to do an extra case ?
Here, I want to stress that I totally am in favour of the objective
of the article: to offer a much cheaper alternative (by using
models) to the ab initio brute force approach of exciton binding
energy. But a validation has to be meaningful._
**Our response:**
We understand the point arised by the Referee. An extra case would have been useful to further support the validation. However, silicene and germanene have spinorbit gaps that are extremely small, a few meV. This creates severe problems of convergence and requires a very fine sampling of the Brillouin zone, thus requiring a huge amount of computational resources. Indeed, calculations for stanene (with a DFT gap of about 77 meV) have been already very demanding, requiring around 40.000 CPU hours and the use of massive parallel supercomputers.
The idea is to investigate plumbene, although the honeycomb structure is not the most stable one. This fact, and the presence of an indirect gap, makes plumbene not an ideal test case, and for sure not a good case for possible comparison with experiments. Nevertheless, we plan to perform calculations on plumbene, but due to the very large computational cost, it will the subject of a separate future publication.