Quantum Hall effect in graphene with interface-induced spin-orbit coupling

Cysne, Tarik P.; García, Jose H.; Rocha, Alexandre Reily; Rappoport, Tatiana G.

doi:10.1103/physrevb.97.085413

Cited by 26 publications

(18 citation statements)

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“…In the case of graphene on WS 2 , where λ I < , i.e., the noninverted regime, we see that for small magnetic field values, the Landau levels approach exactly the eigenspectrum at the K point of the bulk spectrum. Further, for small magnetic field values, Zeeman energy is not important and we find two constant eigenvalues of spin-down polarization, as indicated by formulas (18) and (20). The other two eigenvalues (17) and (19) are represented already at very small magnetic fields of about 0.03 T. Zeeman energy and the presence of the linear-in-B low-energy Landau levels become evident for large magnetic fields.…”

Section: Realistic Parameter Values For Graphene On Tmdsmentioning

confidence: 46%

“…It was demonstrated earlier [19] that this method can be used to extract local Rashba parameters in two-dimensional electron gases by comparison to Landau-level models. In this spirit, we focus on single-particle Landau-level spectra (with approximate √ B magnetic field behavior) rather than on transport signatures (with approximate linear-B behavior) [20].…”

Section: Introductionmentioning

confidence: 99%

“…The physics of symmetry-broken honeycomb lattices has been extensively studied theoretically [20][21][22][23][24]. However, the interplay between orbital magnetic fields and proximity SOC is a relatively recent subject; see, for example, Ref.…”

Section: Introductionmentioning

confidence: 99%

“…However, the interplay between orbital magnetic fields and proximity SOC is a relatively recent subject; see, for example, Ref. [20] for monolayer and Ref. [25] for bilayer graphene.…”

Section: Introductionmentioning

confidence: 99%

“…In a recent work [20] properties of proximitized graphene under the influence of orbital magnetic fields was studied, where the emphasis was put on calculations of transport fan diagrams and Hall conductivities [31]. This work finds very rich fan diagrams with characteristic level splittings, allowing one to infer the relative sizes of Rashba and intrinsic SOC from scaling observations.…”

Section: Introductionmentioning

confidence: 99%

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Landau levels in spin-orbit coupling proximitized graphene: Bulk states

Frank

Fabian

2020

Phys. Rev. B

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We study the magnetic-field dependence of Landau levels in graphene proximitized by large spin-orbit coupling materials, such as transition-metal dichalcogenides or topological insulators. In addition to the Rashba coupling, two types of intrinsic spin-orbit interactions, uniform (Kane-Mele type) and staggered (valley Zeeman type), are included to resolve their interplay with magnetic orbital effects. Employing a continuum model approach, we derive analytic expressions for low-energy Landau levels, which can be used to extract local orbital and spin-orbit coupling parameters from scanning probe spectroscopy experiments. We compare different parameter regimes to identify fingerprints of relative and absolute magnitudes of intrinsic spin-orbit coupling in the spectra. The inverted band structure of graphene proximitized by WSe 2 leads to an interesting crossing of Landau states across the bulk gap at a crossover field, providing insights into the size of Rashba spin-orbit coupling. Landau-level spectroscopy can help to resolve the type and signs of the intrinsic spin-orbit coupling by analyzing the symmetry in energy and number of crossings in the Landau fan chart. Finally, our results suggest that the strong response to the magnetic field of Dirac electrons in proximitized graphene can be associated with extremely large self-rotating magnetic moments.

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Section: Realistic Parameter Values For Graphene On Tmdsmentioning

confidence: 46%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

“…However, the interplay between orbital magnetic fields and proximity SOC is a relatively recent subject; see, for example, Ref. [20] for monolayer and Ref. [25] for bilayer graphene.…”

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Landau levels in spin-orbit coupling proximitized graphene: Bulk states

Frank

Fabian

2020

Phys. Rev. B

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Landau‐Level Spectrum and the Effect of Spin–Orbit Coupling in Monolayer Graphene on Transition Metal Dichalcogenides

Rao,

Xue,

2024

Physica Status Solidi (b)

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In graphene on transition metal dichalcogenides, two types of spin–orbit coupling (SOC)—Rashba and spin–valley Zeeman SOCs—can coexist that modify graphene's electronic band differently. Herein, it is shown that the Landau levels (LLs) are also affected by these SOCs distinctively enough to estimate their relative strengths from the Landau fan diagram. A simple theoretical model is used to calculate the LL spectra of graphene for different SOC strengths, revealing that when the total SOC is strong enough (i.e., when it is comparable to the half of the energy gap between the LLs of an intrinsic graphene), the corresponding LLs will split and cross with others depending sensitively on the relative strengths of the SOC terms. To demonstrate how one can use it to estimate the relative SOC strengths, the four key features that are well separated from the complex background are first identified and compared with experiment to show that in the sample investigated, the Rashba SOC is stronger than the spin–valley Zeeman SOC consistent with other spectroscopic measurements. The study therefore provides a simple and practical strategy to analyze the LL spectrum in graphene with SOC before carrying out more in‐depth measurements.

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