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

Abstract

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 non-zero radial component, except at 0°o r 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.

Omnidirectional spin-to-charge conversion in graphene/NbSe$_2$ van der Waals heterostructures

“…4b (see Supplementary Information section S11 for a detailed symmetry discussion). Furthermore, recent first-principles calculations on twisted graphene/transition metal dichalcogenide heterostructures [43,44] have shown that the radial component of the in-plane SOC can have a similar magnitude as the conventional Rashba SOC component [43] depending on the electric field and twist angle, indicating that the measured component is likely to arise from the EE in the graphene channel. Finally, shear strain could also break enough symmetries in the NbSe 2 flake, enabling a SCC component where y-polarized spins flow in the z direction in NbSe 2 (Fig.…”

Impurity-induced excitations in twisted topological van der Waals superconductors

“…In this material, the relative lattice mismatch and rotation between the CrBr 3 ferromagnet and the NbSe 2 superconductor leads to the emergence of a moire pattern, as shown in 1a. In particular, moire pattern is expected to directly impact underlying Hamiltonian of the system due to the local structural modulation [54][55][56][57][58] . Due to the structural modulation, both the local hoppings 59 , induced spin-orbit coupling 54 , chemical potential 60 , exchange field 61 and superconducting proximity 62 will be modulated.…”

“…In particular, moire pattern is expected to directly impact underlying Hamiltonian of the system due to the local structural modulation [54][55][56][57][58] . Due to the structural modulation, both the local hoppings 59 , induced spin-orbit coupling 54 , chemical potential 60 , exchange field 61 and superconducting proximity 62 will be modulated. For the sake of concreteness, here we will focus on the two parameters whose modulation is expected to be most sizable, the local superconducting order and the proximity-induced exchange field.…”

“…With the previous platforms in mind, we now turn to address a minimal effective model for the previous heterostructures. While the specific parameters of the model for each material combination should be estimated using first-principles calculations [54][55][56][57][58] , here we will focus on addressing the universal features that arise due the interplay of the moire superconductor and the local impurities [50][51][52][53] . The structure moire pattern directly gives rise to a modulation in the induced exchange coupling and an s-wave superconductivity, whose spatial profiles are shown in Fig.…”

Proximity spin-orbit and exchange coupling in ABA and ABC trilayer graphene van der Waals heterostructures

“…Recently, it has been demonstrated that superconductivity [8][9][10], magnetism [11][12][13][14][15][16][17][18][19][20][21][22][23], and spin-orbit coupling (SOC) [24][25][26][27][28][29][30][31][32][33], can be induced on demand in such weakly glued vdW multilayers. In addition, gating, twisting, stacking, and straining are efficient tunability knobs to tailor these spin interactions [13,28,30,[34][35][36][37][38][39][40][41], while the individual materials also preserve a great degree of autonomy.…”