SciPost Submission Page
Rashba Spin–Orbit Coupling and Nonlocal Correlations in Disordered 2D Systems
by Yongtai Li, Gour Jana, and Chinedu E. Ekuma
This is not the latest submitted version.
Submission summary
| Authors (as registered SciPost users): | Chinedu E. Ekuma |
| Submission information | |
|---|---|
| Preprint Link: | scipost_202507_00004v1 (pdf) |
| Date submitted: | July 1, 2025, 11:34 p.m. |
| Submitted by: | Chinedu E. Ekuma |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
|
| Approach: | Theoretical |
Abstract
We present an extension of the dynamical cluster approximation (DCA) that incorporates Rashba spin–orbit coupling (SOC) to investigate the interplay between disorder, spin–orbit interaction, and nonlocal spatial correlations in disordered two-dimensional systems. By analyzing the average density of states, momentum-resolved self-energy, and return probability, we demonstrate how Rashba SOC and nonlocal correlations jointly modify single-particle properties and spin-dependent interference. The method captures key features of the symplectic universality class, including SOC-induced delocalization signatures at finite times. We benchmark the DCA results against those obtained from the numerically exact kernel polynomial method, finding good agreement. This validates the computationally efficient, mean-field-based DCA framework as a robust tool for exploring disorder, spin–orbit coupling, and nonlocal correlation effects in low-dimensional systems, and paves the way for simulating multiorbital and strongly correlated systems that were previously inaccessible due to computational limitations.
Author indications on fulfilling journal expectations
- Provide a novel and synergetic link between different research areas.
- Open a new pathway in an existing or a new research direction, with clear potential for multi-pronged follow-up work
- Detail a groundbreaking theoretical/experimental/computational discovery
- Present a breakthrough on a previously-identified and long-standing research stumbling block
Current status:
Reports on this Submission
Report #2 by Anonymous (Referee 2) on 2025-10-3 (Invited Report)
- Cite as: Anonymous, Report on arXiv:scipost_202507_00004v1, delivered 2025-10-03, doi: 10.21468/SciPost.Report.12058
Strengths
-
Opens a new pathway into a new research direction by studying the combined effects of disorder and Rashba spin-orbit coupling, two aspect that are particularly important, for example, in the context of topological phases.
-
The paper is written in a clear and intelligible way, and the results are scientifically sound and clearly presented.
Weaknesses
- Could make better use of previous literature where the dynamical cluster approximation was extended to systems with Rashba spin-orbit coupling.
Report
The paper presents numerical results for the interplay between disorder, SOC, and non-local correlations in a 2D tight-binding model. The main result of this work is that the Rashba SOC counteracts the effects of disorder and drives delocalization. This is interesting, novel, and scientifically sound. I therefore believe that this paper can be recommended for publication.
The only issue to point out is that the statement “We have extended the dynamical cluster approximation to incorporate Rashba spin–orbit coupling” needs better qualification. While this this hasn’t been done before, to the best of my knowledge, in the context of disordered systems, it has been done before in the context of correlated systems and superconductivity in Nagai et al., Phys. Rev. B 93, 220505(R) (2016) (single-site DMFT), Lu and Senechal, Phys. Rev. B 98, 245118 (2018) (clusters), and Doak et al., Phys. Rev. B 107, 224501 (2023) (clusters). Since the basic formalism is the same, the authors should make an effort to acknowledge this.
Requested changes
- Add references to previous work which extended the dynamical cluster approximation to systems with Rashba spin-orbit coupling.
Recommendation
Ask for minor revision
Report #1 by Anonymous (Referee 1) on 2025-9-27 (Invited Report)
- Cite as: Anonymous, Report on arXiv:scipost_202507_00004v1, delivered 2025-09-27, doi: 10.21468/SciPost.Report.12009
Report
Referee report on "Rashba Spin–Orbit Coupling and Nonlocal Correlations in Disordered 2D Systems" by Yongtai Li et al.
The interplay between disorder and spin-orbit coupling is a fundamental problem in modern condensed matter physics. Consequently, the development of novel numerical methods to address Anderson localization in the presence of spin-orbit interaction is highly topical. The manuscript under review makes a valuable contribution to this field. The authors successfully extend the dynamical cluster expansion to incorporate the spin-orbit interaction and demonstrate convincing agreement with exact numerical diagonalization.
I find this work interesting and timely. I recommend it for publication in SciPost. However, the manuscript would be significantly strengthened by including comparison with previous analytical results. My specific suggestions are as follows: - A comparison of the calculated average density of states with the self-consistent Born approximation (SCBA) would be highly instructive. One would expect SCBA to provide a reasonable approximation, at least near the band edge, and demonstrating this agreement (or any deviation) would be valuable. - The presentation and discussion of the return probability in Fig. 3 would benefit from a comparison with the simplest analytical models of diffusive propagation. - Similarly, in standard analytical treatments of electron transport, the Cooperon is used to study quantum corrections to the diffusion coefficient and conductivity. Could the authors comment on whether it is possible to extract the Cooperon matrix from their numerical framework? - The authors present results for only two cluster sizes, N_c = 1 and N_c = 32. The convergence of the method at N_c = 32 is not clear. It would be helpful to demonstrate convergence by plotting the ADOS and return probability P(t) for a series of intermediate N_c values.
Recommendation
Ask for minor revision
We thank the referee for a careful reading of our manuscript and for the constructive suggestions. Below, we carefully address each of the points raised.
On comparison with SBCA:
We thank the referee for this valuable suggestion. We have accordingly included a comparison of SCBA results, mainly self-energy, and results from our DCA-SOC formalism. While studies using SCBA have discovered the role of Rashba SOC to be reducing the effect of disorder scattering, which our results are in agreement to, the incapability of incorporating spatial correlations leads SCBA to fail to predict a softened tail in the imaginary part of self-energy that exists in numerically exact studies. Since the coherent potential approximation (CPA), which is a single-site mean-field description of disorder, provides a close correspondence to the SCBA, it does not capture a soft tail in the self-energy that is manifested in finite-size clusters (Nc = 32). Hence, our DCA formalism is capable of capturing nonlocal correlations that were absent in both CPA and SCBA.
On analytic return probability:
We appreciate the referee for this suggestion. We agree that analytical or numerical comparison for the return probability P(t) with diffusive models would be instructive. However, to our knowledge, no reliable numerical results exist for this quantity in disordered systems with SOC. Developing such a comparison requires additional methodological advances, which we plan to pursue in future work.
About the Cooperon matrix:
This is an insightful observation. Our current mean-field formulation does not explicitly compute the Cooperon matrix. Nonetheless, nonlocal correlations beyond the single-site limit are already embedded in the cluster Green’s functions obtained for Nc > 1, effectively capturing the physics that would otherwise emerge through Cooperon-type corrections.
On N_c convergence:
We thank the referee for this valuable suggestion. In response, we have updated the plots of the average density of states (ADOS) and the return probability P(t) to illustrate convergence with cluster size. For the ADOS, since the results for different cluster sizes largely overlap across most frequencies, we now include data for one intermediate cluster size, Nc = 18, which clearly demonstrates this near-convergence behavior. For the return probability, where the curves for different Nc values show distinct magnitudes but consistent systematic trends, we have added results for two intermediate cluster sizes, Nc = 8 and Nc = 18, to confirm the robustness and convergence of our findings.
Author: Chinedu Ekuma on 2025-10-13 [id 5918]
(in reply to Report 2 on 2025-10-03)We sincerely thank the referee for the careful and thoughtful review of our manuscript, and for recognizing both the novelty and the broader significance of our work. We are also grateful for the insightful suggestion to acknowledge prior studies that have incorporated Rashba spin–orbit coupling (SOC) in the absence of random defects within dynamical mean-field frameworks.
As correctly pointed out, earlier works such as Nagai et al., Phys. Rev. B 93, 220505(R) (2016); Lu and Sénéchal, Phys. Rev. B 98, 245118 (2018); and Doak et al., Phys. Rev. B 107, 224501 (2023) have indeed extended single-site DMFT/CPA formalism and its cluster extensions (CDMFT) to include Rashba SOC in the context of correlated and superconducting systems. We appreciate this valuable clarification and have revised our manuscript accordingly to properly acknowledge these studies. In particular, we will modify the sentence
“We have extended the dynamical cluster approximation to incorporate Rashba spin–orbit coupling,”
to more accurately reflect that,
“We have extended the dynamical cluster approximation (DCA) framework to include Rashba spin–orbit coupling (SOC) in the presence of random disorder—an implementation that, to the best of our knowledge, has not been previously reported”.
We note that while the cited works focused primarily on superconducting or topological phases in clean or correlated systems, our study targets the interplay between disorder, Rashba SOC, and non-local correlations within the TMDCA formalism, specifically addressing the interplay of spatial correlations, strong electron correlation, Rashba SOC, and random disorder in 2D systems. This distinction underscores the novelty of our approach.
Finally, we agree with the referee that the combination of SOC, electronic correlations, and disorder is highly relevant to understanding possible topological phases. This is something we aim to tackle in the future. Although our current focus is on localization physics, we will explicitly mention in the revised manuscript that incorporating a Zeeman field within our extended TMDCA framework would naturally enable future investigations of disorder- and correlation-driven topological phase transitions in 2D systems.