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

Abstract

The proximity-induced spin-orbit coupling (SOC) in heterostructures of twisted graphene and topological insulators (TIs) Bi 2 Se 3 and Bi 2 Te 3 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 • 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 ≈ 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.

Chiral spin channels in curved graphenepnjunctions

“…( 10) and (11b). The selection of substrates inducing the weakest possible VZSOC [35,36] is thus essential to observing the effects described in this work.…”

“…The terms H R , H KM , and H VZ are the Rashba, Kane-Mele, and valley-Zeeman SOC, respectively [24,26,49]. Precise estimates for the SOCs depend on the specific heterostructure, e.g., the relative orientation between graphene and substrate [35,36]. The RSOC and the VZSOC range from few hundredths of meV up to few meV, while the KMSOC is typically much smaller [35,37].…”

“…The electronic spin degree of freedom is usually neglected in the study of graphene pn junctions because of the weak atomic spin-orbit coupling (SOC) of carbon [24][25][26][27]. However, theoretical predictions followed by experimental realizations proved that strong SOCs can be induced, e.g., by proximity with transition metal dichalcogenide (TMD) substrates [28][29][30][31][32][33][34][35][36][37]. These advances open the exciting possibility of including the spin functionality in graphene-based electron optics, with the further benefit that the versatility of pn junctions allows for the design of curved waveguides for spin and charge carriers.…”

Moiré-enabled topological superconductivity in twisted bilayer graphene

“…The two-dimensional nature of van der Waals materials provides a unique playground to engineer emergent states [1][2][3]. Among others, their 2D nature allows to induce ferromagnetic exchange [4][5][6][7][8], superconductivity and spin-orbit coupling (SOC) [9][10][11][12][13] through proximity to other 2D materials. This versatility increases considerably the range of phenomena that can be explored in van der Waals materials.…”

Giant asymmetric proximity-induced spin–orbit coupling in twisted graphene/SnTe heterostructure

“…In contrast, heterostructures with no common symmetry are expected to induce fully three-dimensional spin relaxation anisotropy. This is a strong motivation to explore beyond the well-investigated graphene/T-MDC stacks [26][27][28][29][30][31][32][33][34] in the search for novel materials [35,36] that could be used as an alternative to induce both strong spin-orbit coupling and exotic spin textures in graphene. Particularly interesting are mixed-lattice heterostructures with incompatible symmetries, expected to give rise to novel spin textures.…”