Topological phases and twisting of graphene on a dichalcogenide monolayer

Abstract

Depositing monolayer graphene on a transition metal dichalcogenide (TMD) semiconductor substrate has been shown to change the dynamics of the electronic states in graphene, inducing spin orbit coupling (SOC) and staggered potential effects. Theoretical studies on commensurate supercells have demonstrated the appearance of interesting phases, as different materials and relative gate voltages are applied. Here we address the effects of the real incommensurability between lattices by implementing a continuum model approach that does not require small-period supercells. The approach allows us to study the role of possible relative twists of the layers, and verify that the SOC transfer is robust to twists, in agreement with observations. We characterize the nature of the different phases by studying an effective Hamiltonian that fully describes the graphene-TMD heterostructure. We find the system supports topologically non-trivial phases over a wide range of parameter ranges, which require the dominance of the intrinsic SOC over the staggered and Rashba potentials. This tantalizing result suggests the possible experimental realization of a tunable quantum spin Hall phase under suitable conditions. We estimate that most TMDs used to date likely result in weak intrinsic SOC that would not drive the heterostructure into topologically non-trivial phases. Additional means to induce a larger intrinsic SOC, such as strain fields or heavy metal intercalation may be required.

Van Der Waals Heterostructures with Spin‐Orbit Coupling

“…For the case of graphene-WSe 2 vdW systems the SOC induced by proximity in graphene is sufficient to create a band inversion of the spin-split bands close to the original graphene's Dirac point. Such a band inversion could lead to topological phases exhibiting the quantum spin Hall effect in SLG-TMD [110,112,113] or BLG-TMD [114] heterostructures. The enhancement of the SOC in graphene-TMD vdW systems has been observed, indirectly, via weak antilocalization [115][116][117][118][119][120][121] and spin-relaxation measurements.…”

Inducing chiral superconductivity on honeycomb lattice systems

“…In contrast, the proximitized honeycomb lattice of graphene may result in broken lattice inversion symmetry and strong spin-orbit coupling that induces an effective Ising (or Zeeman-like) spin field that preserves TRS. Such an effect results in the spin projection perpendicular to the plane being a good quantum number but with opposite value in each valley to preserve TRS [12][13][14][15][16]. Such a situation could be induced in graphene deposited on a transition metal dichalcogenide substrate, for example [14][15][16].…”

“…Such an effect results in the spin projection perpendicular to the plane being a good quantum number but with opposite value in each valley to preserve TRS [12][13][14][15][16]. Such a situation could be induced in graphene deposited on a transition metal dichalcogenide substrate, for example [14][15][16]. Considering the effect of superconducting correlations on such Zeeman-like system is expected to provide non-trivial Chern numbers and complex Berry curvatures that should affect the resulting symmetries of the quasiparticle excitations [10].…”

Quantum interference tuning of spin-orbit coupling in twisted van der Waals trilayers

“…Recently, Refs. [46][47][48][49] have also discussed the interlayer twist angle dependence of the induced SOC in graphene/TMDC. In particular, it has been noted [47,48] that the most general form of the induced Rashba-SOC in twisted graphene/TMDC heterostructures that obeys time reversal T and three-fold rotation C 3 symmetries can be written as…”