Experimental observation of spin−split energy dispersion in high-mobility single-layer graphene/WSe2 heterostructures

Abstract

Proximity-induced spin–orbit coupling in graphene has led to the observation of intriguing phenomena like time-reversal invariant $${{\mathbb{Z}}}_{2}$$ Z 2 topological phase and spin-orbital filtering effects. An understanding of the effect of spin–orbit coupling on the band structure of graphene is essential if these exciting observations are to be transformed into real-world applications. In this research article, we report the experimental determination of the band structure of single-layer graphene (SLG) in the presence of strong proximity-induced spin–orbit coupling. We achieve this in high-mobility hexagonal boron nitride (hBN)-encapsulated SLG/WSe2 heterostructures through measurements of quantum oscillations. We observe clear spin-splitting of the graphene bands along with a substantial increase in the Fermi velocity. Using a theoretical model with realistic parameters to fit our experimental data, we uncover evidence of a band gap opening and band inversion in the SLG. Further, we establish that the deviation of the low-energy band structure from pristine SLG is determined primarily by the valley-Zeeman SOC and Rashba SOC, with the Kane–Mele SOC being inconsequential. Despite robust theoretical predictions and observations of band-splitting, a quantitative measure of the spin-splitting of the valence and the conduction bands and the consequent low-energy dispersion relation in SLG was missing—our combined experimental and theoretical study fills this lacuna.

Ballistic transport spectroscopy of spin-orbit-coupled bands in monolayer graphene on WSe2

“…This is expected as in the density range explored, the Fermi energy is larger than both and , leading to an identical splitting in momentum, with Fermi velocity for both and . This is consistent with the previous SdH oscillations measurements that probe electron bands 3 , 38 .

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“…However, a vast number of previous studies on graphene-TMDC heterostructures have focused on detecting spin relaxation due to electron scattering rather than the ballistic motion 1 – 3 , 7 , 16 , 32 – 37 . Moreover, only a few studies have found direct evidence for the SOC-induced band splitting by measuring beatings in Shubnikov-de Hass (SdH) oscillations (for both mono- and bilayer graphene) 3 , 10 , 38 or tracing changes in quantum capacitance (for bilayer graphene only) 11 . Not only to understand the effect of the SOC on the electronic properties of the system, such as the band topology 39 , 40 but also to exploit its full potential on ballistic spintronics 17 – 22 , it is therefore essential to demonstrate the ballistic transport in graphene on TMDCs while simultaneously probing their band structures and electron dynamics.…”

Observation of room temperature anomalous Hall effect in graphene-WSe2 heterostructures

“…Graphene-based heterostructures offer one such exciting platform for studying band geometric effects. The coupling to the charge, spin, and valley degrees of freedom in graphene gives rise to, among other things, a multitude of Hall effects such as the spin Hall [6][7][8][9] , and the valley Hall effects [10][11][12][13][14][15] . A possible common origin of these effects is the emergence of a nontrivial Berry curvature on breaking the inversion symmetry, which induces opposite anomalous velocity in the two valleys of graphene [16][17][18] .…”

Controlling Umklapp Scattering in a Bilayer Graphene Moiré Superlattice

“…High-quality hBN/BLG/hBN heterostructures were fabricated using the dry transfer technique (section S1 of the Supporting Information). − The top hBN was aligned at nearly 0° with BLG, and the bottom hBN was intentionally misaligned to a large angle to ensure that a moiré pattern forms only between top hBN and BLG (Figure a). The device is in a hall bar geometry (Figure b) with dual gates to tune carrier density n and vertical displacement field D independently via the equations n = ( C tg V tg + C bg V bg )/ e + n r and D = ( C tg V tg – C bg V bg )/2 + D r , respectively.…”