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Rashba Spin–Orbit Coupling and Nonlocal Correlations in Disordered 2D Systems
by Yongtai Li, Gour Jana, and Chinedu E. Ekuma
This Submission thread is now published as
Submission summary
| Authors (as registered SciPost users): | Chinedu E. Ekuma |
| Submission information | |
|---|---|
| Preprint Link: | scipost_202507_00004v2 (pdf) |
| Date accepted: | Oct. 28, 2025 |
| Date submitted: | Oct. 13, 2025, 4:01 a.m. |
| Submitted by: | Chinedu E. Ekuma |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approaches: | Theoretical, Computational |
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
Author comments upon resubmission
We have carefully addressed each of the comments raised by the reviewers. We appreciated the feedback.
List of changes
We added some new citations in the manuscript listed below:
Ref 42: Nagai, Yuki et al, Phys. Rev. B 93, 220505 (R) (2016)
Ref 43: Lu, Xiancong et al, Phys. Rev. B 98, 2451118 (2018)
Ref 44: Doak, Peter et al, Phys. Rev. B 107, 224501 (2023)
Ref 51: Langenbuch, M et al, Phys. Rev. B 69, 125303 (2004)
Ref 52: Brosco, V. et al, Phys. Rev. Lett. 116, 166602 (2016)
Ref 53: H. Bruus and K. Flensberg, Introduction to Many-body Quantum Theory in Condensed Matter Physics (Oxford University Press, 2016)
We included in the Introduction section, “While previous studies have incorporated Rashba spin–orbit coupling (SOC) into strongly correlated systems within single-site mean-field approaches such as the DMFT and CPA [42], as well as their cluster extensions [43, 44] to investigate its role in topological superconductivity, to the best of our knowledge, no work has yet examined the competition between random disorder and Rashba SOC using a nonlocal mean-field framework.”
We added at the end of Sec. III A, “We further provide a qualitative comparison between our DCA-SOC framework and a commonly used approximation in impurity scattering problems, the self-consistent Born approximation (SCBA) [29, 51–53]...This demonstrates the ability of our DCA-SOC method to incorporate nonlocal correlation effects that are absent in both CPA and SCBA, especially in the strong disorder limit.”
We adjusted our description of return probability with respect to cluster sizes in Sec. III B, “In contrast, for Nc > 1, the inclusion of nonlocal correlations significantly slows the decay of P (t) at α = 0, and this effect becomes more pronounced as Nc systematically increases…”
We modified the beginning of Sec. IV, “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 replotted Fig. 1, the average density of states (ADOS) to include data calculated for Nc = 18. We also modified its caption, “Panels (a)–(f) compare results for Nc = 1 (CPA, black solid curves), Nc = 18 (green dot-dashed curves) and Nc = 32 (red dashed curves) at increasing disorder strengths: W = 0.20 ((a), (b)), W = 0.50 ((c), (d)), and W = 1.00 ((e), (f)).”
We replotted Fig. 3, the return probability to include data calculated for Nc = 8 and Nc = 18. We also modified its caption, “Return probability P (t) as a function of time at fixed disorder strength W = 0.50 for Nc = 1 (black curves), Nc = 8 (red curves), Nc = 18 (green curves), Nc = 32 (blue curves), with Rashba SOC (α = 0.25, solid) and without SOC (α = 0, dashed).”
Minor modifications in the main text:
In Sec. III, we changed the original text “we performed DCA calculations for a finite cluster size of Nc = 32…” to, “we perform DCA calculations for finite-size clusters up to Nc = 32…”
In Sec. III A, we changed the original text “the ADOS curves for Nc = 1 and Nc = 32 overlap…” to, “the ADOS curves for all the cluster sizes studied in this work overlap…”
In Sec. III A, we changed the original text “This trend, more pronounced for Nc = 32…” to, “This trend is more pronounced for both Nc = 18 and Nc = 32…”
In Sec. III A, we changed the original text “the ADOS exhibits softened tails…especially for Nc = 32…” to, “the ADOS exhibits softened tails…especially for finite-size clusters…”
In Sec III B, we changed the original text “Figure 3(a) shows P(t) at W = 0.50 for both Nc = 1 and Nc = 32,” to, “Figure 3(a) shows P(t) at W = 0.50for cluster sizes ranging from Nc = 1 and Nc = 32.”
In Sec. IV, we changed the original text “These effects become more pronounced for larger clusters (Nc = 32),” to “These effects become more pronounced for larger clusters (up to Nc = 32).”
Ref 42: Nagai, Yuki et al, Phys. Rev. B 93, 220505 (R) (2016)
Ref 43: Lu, Xiancong et al, Phys. Rev. B 98, 2451118 (2018)
Ref 44: Doak, Peter et al, Phys. Rev. B 107, 224501 (2023)
Ref 51: Langenbuch, M et al, Phys. Rev. B 69, 125303 (2004)
Ref 52: Brosco, V. et al, Phys. Rev. Lett. 116, 166602 (2016)
Ref 53: H. Bruus and K. Flensberg, Introduction to Many-body Quantum Theory in Condensed Matter Physics (Oxford University Press, 2016)
We included in the Introduction section, “While previous studies have incorporated Rashba spin–orbit coupling (SOC) into strongly correlated systems within single-site mean-field approaches such as the DMFT and CPA [42], as well as their cluster extensions [43, 44] to investigate its role in topological superconductivity, to the best of our knowledge, no work has yet examined the competition between random disorder and Rashba SOC using a nonlocal mean-field framework.”
We added at the end of Sec. III A, “We further provide a qualitative comparison between our DCA-SOC framework and a commonly used approximation in impurity scattering problems, the self-consistent Born approximation (SCBA) [29, 51–53]...This demonstrates the ability of our DCA-SOC method to incorporate nonlocal correlation effects that are absent in both CPA and SCBA, especially in the strong disorder limit.”
We adjusted our description of return probability with respect to cluster sizes in Sec. III B, “In contrast, for Nc > 1, the inclusion of nonlocal correlations significantly slows the decay of P (t) at α = 0, and this effect becomes more pronounced as Nc systematically increases…”
We modified the beginning of Sec. IV, “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 replotted Fig. 1, the average density of states (ADOS) to include data calculated for Nc = 18. We also modified its caption, “Panels (a)–(f) compare results for Nc = 1 (CPA, black solid curves), Nc = 18 (green dot-dashed curves) and Nc = 32 (red dashed curves) at increasing disorder strengths: W = 0.20 ((a), (b)), W = 0.50 ((c), (d)), and W = 1.00 ((e), (f)).”
We replotted Fig. 3, the return probability to include data calculated for Nc = 8 and Nc = 18. We also modified its caption, “Return probability P (t) as a function of time at fixed disorder strength W = 0.50 for Nc = 1 (black curves), Nc = 8 (red curves), Nc = 18 (green curves), Nc = 32 (blue curves), with Rashba SOC (α = 0.25, solid) and without SOC (α = 0, dashed).”
Minor modifications in the main text:
In Sec. III, we changed the original text “we performed DCA calculations for a finite cluster size of Nc = 32…” to, “we perform DCA calculations for finite-size clusters up to Nc = 32…”
In Sec. III A, we changed the original text “the ADOS curves for Nc = 1 and Nc = 32 overlap…” to, “the ADOS curves for all the cluster sizes studied in this work overlap…”
In Sec. III A, we changed the original text “This trend, more pronounced for Nc = 32…” to, “This trend is more pronounced for both Nc = 18 and Nc = 32…”
In Sec. III A, we changed the original text “the ADOS exhibits softened tails…especially for Nc = 32…” to, “the ADOS exhibits softened tails…especially for finite-size clusters…”
In Sec III B, we changed the original text “Figure 3(a) shows P(t) at W = 0.50 for both Nc = 1 and Nc = 32,” to, “Figure 3(a) shows P(t) at W = 0.50for cluster sizes ranging from Nc = 1 and Nc = 32.”
In Sec. IV, we changed the original text “These effects become more pronounced for larger clusters (Nc = 32),” to “These effects become more pronounced for larger clusters (up to Nc = 32).”
Published as SciPost Phys. 19, 135 (2025)
Reports on this Submission
Report
I am happy with the revisions made by the authors and by their response to my questions. While not all my suggestions were directly incorporated in the manuscript (in particular, for the systems with weak disorder and Rashba coupling the SCBA density of states and return probabilities can be easily found in the literature), I think that current manuscript fully matches the SciPost Physics acceptance criteria.
Recommendation
Publish (meets expectations and criteria for this Journal)
Report
I believe that the revisions made by the authors sufficiently address the first round criticism, and the revised manuscript can be recommended for publication.
Recommendation
Publish (easily meets expectations and criteria for this Journal; among top 50%)
Author: Chinedu Ekuma on 2025-10-17 [id 5942]
(in reply to Report 2 on 2025-10-17)We sincerely thank the referee for their positive assessment and constructive feedback. We are pleased that the revisions have addressed the earlier concerns and appreciate the recommendation for publication.