Twist-angle dependent proximity induced spin-orbit coupling in graphene/transition-metal dichalcogenide heterostructures

We investigate the proximity-induced spin-orbit coupling in heterostructures of twisted graphene and monolayers of transition-metal dichalcogenides (TMDCs) MoS$_2$, WS$_2$, MoSe$_2$, and WSe$_2$ from first principles. We identify strain, which is necessary to define commensurate supercells, as the key factor affecting the band offsets and thus magnitudes of the proximity couplings. We establish that for biaxially strained graphene the band offsets between the Dirac point and conduction (valence) TMDC bands vary linearly with strain, regardless of the twist angle. This relation allows to identify the apparent zero-strain band offsets and find a compensating transverse electric field correcting for the strain. The resulting corrected band structure is then fitted around the Dirac point to an established spin-orbit Hamiltonian. This procedure yields the dominant, valley-Zeeman and Rashba spin-orbit couplings. The magnitudes of these couplings do not vary much with the twist angle, although the valley-Zeeman coupling vanishes for 30$^{\circ}$ and Mo-based heterostructures exhibit a maximum of the coupling at around 20$^{\circ}$. The maximum for W-based stacks is at 0$^{\circ}$. The Rashba coupling is in general weaker than the valley-Zeeman coupling, except at angles close to 30$^{\circ}$. We also identify the Rashba phase angle which measures the deviation of the in-plane spin texture from tangential, and find that this angle is very sensitive to the applied transverse electric field. We further discuss the reliability of the supercell approach with respect to atomic relaxation (rippling of graphene), relative lateral shifts of the atomic layers, and transverse electric field.Comment: 14 pages, 9 figures, 7 table

Proximity-enhanced valley Zeeman splitting at the WS2_2/graphene interface

The valley Zeeman physics of excitons in monolayer transition metal dichalcogenides provides valuable insight into the spin and orbital degrees of freedom inherent to these materials. Being atomically-thin materials, these degrees of freedom can be influenced by the presence of adjacent layers, due to proximity interactions that arise from wave function overlap across the 2D interface. Here, we report 60 T magnetoreflection spectroscopy of the A- and B- excitons in monolayer WS$_2$, systematically encapsulated in monolayer graphene. While the observed variations of the valley Zeeman effect for the A- exciton are qualitatively in accord with expectations from the bandgap reduction and modification of the exciton binding energy due to the graphene-induced dielectric screening, the valley Zeeman effect for the B- exciton behaves markedly different. We investigate prototypical WS$_2$/graphene stacks employing first-principles calculations and find that the lower conduction band of WS$_2$ at the $K/K'$ valleys (the $CB^-$ band) is strongly influenced by the graphene layer on the orbital level. This leads to variations in the valley Zeeman physics of the B- exciton, consistent with the experimental observations. Our detailed microscopic analysis reveals that the conduction band at the $Q$ point of WS$_2$ mediates the coupling between $CB^-$ and graphene due to resonant energy conditions and strong coupling to the Dirac cone. Our results therefore expand the consequences of proximity effects in multilayer semiconductor stacks, showing that wave function hybridization can be a multi-step process with different bands mediating the interlayer interactions. Such effects can be exploited to resonantly engineer the spin-valley degrees of freedom in van der Waals and moir\'e heterostructures.Comment: 14 pages, 6 figures, 3 table

Proximity-enhanced valley Zeeman splitting at the WS2/graphene interface

The valley Zeeman physics of excitons in monolayer transition metal dichalcogenides provides valuable insight into the spin and orbital degrees of freedom inherent to these materials. Being atomically-thin materials, these degrees of freedom can be influenced by the presence of adjacent layers, due to proximity interactions that arise from wave function overlap across the 2D interface. Here, we report 60 T magnetoreflection spectroscopy of the A- and B- excitons in monolayer WS2, systematically encapsulated in monolayer graphene. While the observed variations of the valley Zeeman effect for the A- exciton are qualitatively in accord with expectations from the bandgap reduction and modification of the exciton binding energy due to the graphene-induced dielectric screening, the valley Zeeman effect for the B- exciton behaves markedly different. We investigate prototypical WS2/graphene stacks employing first-principles calculations and find that the lower conduction band of WS2 at the $K/K^{^{\prime}}$ valleys (the $\mathrm{CB}^-$ band) is strongly influenced by the graphene layer on the orbital level. Specifically, our detailed microscopic analysis reveals that the conduction band at the Q point of WS2 mediates the coupling between $\mathrm{CB}^-$ and graphene due to resonant energy conditions and strong coupling to the Dirac cone. This leads to variations in the valley Zeeman physics of the B- exciton, consistent with the experimental observations. Our results therefore expand the consequences of proximity effects in multilayer semiconductor stacks, showing that wave function hybridization can be a multi-step energetically resonant process, with different bands mediating the interlayer interactions. Such effects can be further exploited to resonantly engineer the spin-valley degrees of freedom in van der Waals and moiré heterostructures

Educational readiness among health professionals in rheumatology: Low awareness of EULAR offerings and unfamiliarity with the course content as major barriers—results of a EULAR-funded European survey

Background Ongoing education of health professionals in rheumatology (HPR) is critical for high-quality care. An essential factor is education readiness and a high quality of educational offerings. We explored which factors contributed to education readiness and investigated currently offered postgraduate education, including the European Alliance of Associations for Rheumatology (EULAR) offerings.Methods and participants We developed an online questionnaire, translated it into 24 languages and distributed it in 30 European countries. We used natural language processing and the Latent Dirichlet Allocation to analyse the qualitative experiences of the participants as well as descriptive statistics and multiple logistic regression to determine factors influencing postgraduate educational readiness. Reporting followed the Checklist for Reporting Results of Internet E-Surveys guideline.Results The questionnaire was accessed 3589 times, and 667 complete responses from 34 European countries were recorded. The highest educational needs were ‘professional development’, ‘prevention and lifestyle intervention’. Older age, more working experience in rheumatology and higher education levels were positively associated with higher postgraduate educational readiness. While more than half of the HPR were familiar with EULAR as an association and the respondents reported an increased interest in the content of the educational offerings, the courses and the annual congress were poorly attended due to a lack of awareness, comparatively high costs and language barriers.Conclusions To promote the uptake of EULAR educational offerings, attention is needed to increase awareness among national organisations, offer accessible participation costs, and address language barriers

Twist-angle dependent proximity induced spin-orbit coupling in graphene/topological insulator heterostructures

The proximity-induced spin-orbit coupling (SOC) in heterostructures of twisted graphene and topological insulators (TIs) Bi2Se3 and Bi2Te3 is investigated from first principles. To build commensurate supercells, we strain graphene and correct thus resulting band offsets by applying a transverse electric field. We then fit the low energy electronic spectrum to an effective Hamiltonian that comprises orbital and spin-orbit terms. For twist angles 0°≤θ≤20°, we find the dominant spin-orbit couplings to be of the valley-Zeeman and Rashba types, both a few meV strong. We also observe a sign change in the induced valley-Zeeman SOC at θ≈ 10°. Additionally, the in-plane spin structure resulting from the Rashba SOC acquires a nonzero radial component, except at 0° or 30°. At 30° the graphene Dirac cone interacts directly with the TI surface state. We therefore explore this twist angle in more detail, studying the effects of gating, TI thicknesses, and lateral shifts on the SOC parameters. We find, in agreement with previous results, the emergence of the proximitized Kane-Mele SOC, with a change in sign possible by electrically tuning the Dirac cone within the TI bulk band gap

Tuning proximity spin-orbit coupling in graphene/NbSe₂ heterostructures via twist angle

We investigate the effect of the twist angle on the proximity spin-orbit coupling (SOC) in graphene/NbSe2 heterostructures from first principles. The low-energy Dirac bands of several different commensurate twisted supercells are fitted to a model Hamiltonian, allowing us to study the twist-angle dependency of the SOC in detail. We predict that the magnitude of the Rashba SOC can triple, when going from Θ=0° to Θ=30° twist angle. Furthermore, at a twist angle of Θ≈23° the in-plane spin texture acquires a large radial component, corresponding to a Rashba angle of up to Φ=25°. The twist-angle dependence of the extracted proximity SOC is explained by analyzing the orbital decomposition of the Dirac states to reveal with which NbSe2 bands they hybridize strongest. Finally, we employ a Kubo formula to evaluate the efficiency of conventional and unconventional charge-to-spin conversion in the studied heterostructures

Twist-angle dependent proximity induced spin-orbit coupling in graphene/transition metal dichalcogenide heterostructures

We investigate the proximity-induced spin-orbit coupling in heterostructures of twisted graphene and monolayers of transition metal dichalcogenides (TMDCs) MoS_2, WS_2, MoSe_2 and WSe_2 from first principles. We identify strain, which is necessary to define commensurate supercells, as the key factor affecting the band offsets and thus magnitudes of the proximity couplings. We establish that for biaxially strained graphene the band offsets between the Dirac point and conduction (valence) TMDC bands vary linearly with strain, regardless of the twist angle. This relation allows us to identify the apparent zero-strain band offsets and find a compensating transverse electric field correcting for the strain. The resulting corrected band structure is then fitted around the Dirac point to an established spin-orbit Hamiltonian. This procedure yields the dominant, valley-Zeeman, and Rashba spin-orbit couplings. The magnitudes of these couplings do not vary much with the twist angle, although the valley-Zeeman coupling vanishes for 30◦ and Mo-based heterostructures exhibit a maximum of the coupling at around 20◦. The maximum for W-based stacks is at 0◦. The Rashba coupling is in general weaker than the valley-Zeeman coupling, except at angles close to 30◦. We also identify the Rashba phase angle which measures the deviation of the in-plane spin texture from tangential, and find that this angle is very sensitive to the applied transverse electric field. We further discuss the reliability of the supercell approach with respect to atomic relaxation (rippling of graphene), relative lateral shifts of the atomic layers, and transverse electric field