Tuning proximity-induced spin-orbit coupling in graphene/WSe$_{2}$ heterostructures

TL;DR

The paper investigates how proximity-induced spin-orbit coupling (SOC) in graphene/WSe$_{2}$ heterostructures is controlled by twist angle and interlayer distance. Using weak anti-localization (WAL) measurements, the authors extract Rashba-type ($λ_R$) and valley-Zeeman-type ($λ_{VZ}$) SOC, and demonstrate a strong dependence on twist angle with reproducible SOC values at fixed angles; notably, $α=30^ imes$ suppresses $λ_{VZ}$. They fabricate two sample types to enable unambiguous angle determination and confirm the angle dependence across a set of devices. Moreover, applying hydrostatic pressure up to 1.9 GPa increases SOC strengths by about 40%, illustrating tunability via interlayer distance. These findings advance controlled design of graphene-based spintronic devices by enabling reproducible and tunable proximity SOC through both angular alignment and mechanical compression.

Abstract

Recently, proximity-induced spin-orbit coupling (SOC) has been observed in heterostructures consisting of monolayer graphene (ML-G) and transition metal dichalcogenides (TMDCs) such as WSe$_{2}$. Successful tuning of SOC in graphene/WSe$_{2}$ heterostructures by applying mechanical pressure and electric fields was also demonstrated in previous studies. In addition, theoretical calculations predicted a strong dependence of the proximity-induced SOC on the twist angle between graphene and TMDC. Here, we put these predictions to experimental test in ML-G/ML-WSe$_{2}$/hBN-heterostructures, where the twist angle is determined by aligning fractured edges, and by crystallographic etching of graphene. By performing weak anti-localization measurements, we determine the strength of the Rasbha-type SOC ($λ_\mathrm{R}$) and the valley-Zeeman-type SOC ($λ_\mathrm{VZ}$). Our experiments confirm a strong twist angle dependence of the proximity-induced SOC in agreement with theoretical predictions. Finally, we demonstrate the tunability of the SOC strength via mechanical pressure, which is in agreement with earlier findings.

Figures (12)

• Figure 1: (a) ML-G/ML-WSe$_{2}$/hBN heterostructure with Cr/Au edge contacts on a Si/SiO$_{2}$ substrate. (b) Optical microscope image of sample 6. The heterostructure is etched in a Hall-bar geometry and contacted with Cr/Au edge contacts. The white box highlights the Hall bar.
• Figure 2: (a) Schematic representation of a ML-WSe$_{2}$ flake (blue) placed on a ML-G flake (gray). The lattices of the two flakes are rotated by the angle $\alpha$. (b) Graphite flake with a part of ML-G. The two white parallel lines mark specific edges, which are most likely of zigzag or armchair type. (c) WSe$_{2}$ flake is shown, part of which consists of ML-WSe$_{2}$. The orange lines here also mark specific edges with an angle of $60^\circ$ to each other. (d) Finished heterostructure. The ML-G and ML-WSe$_{2}$ flakes were superimposed in such a way that the specific edges enclose an angle of $0^\circ$. However, since the structure of the edges (zigzag or armchair) is not known, two possible rotation angles between the two lattices, $\alpha=0^\circ$ and $\alpha^\prime=30^\circ$, must be assumed here.
• Figure 3: Different stages of a ML-G flake before and after anisotropic etching. (a) ML-G/graphite flakes in their original shape after exfoliation. (b) remaining parts of the flakes after the other part has been removed to form the heterostructure. (c) AFM z-topography of the anisotropically etched flakes (approximate position: blue frame in panels (a) and (b)). (d) Enlarged view of the area outlined in white showing anisotropically etched holes. The crystal orientation at sharp edges of the holes (black lines) becomes apparent.
• Figure 4: (a) Four-point resistance $R_{xx}$ and conductivity $\sigma_{xx}$ near the Dirac point for sample 1 as a function of gate voltage $U_{g}$. (b) Diffusion coefficient $D$ for samples 1-3 as a function of the charge carrier density $n$.
• Figure 5: Measurements of the quantum mechanical correction of the conductivity $\Delta\sigma_{xx}$ for different charge carrier densities $n$ as a function of the out-of-plane magnetic field $B_{z}$. Curves are offset for clarity. SOC-WAL is mainly responsible for the small significant peak near $B_{z}=0\,$T, while Berry-WAL, results in the decreasing conductivity towards larger magnetic fields. WL is not detected here due to the dominant Berry-WAL. Red lines: Fits to Eq. \ref{['WAL_groß']} with fitting parameters given in Fig. \ref{['Fig. 6.']}.