Tunable valley Hall effect in gate-defined graphene superlattices

Abstract

We theoretically investigate gate-defined graphene superlattices with broken inversion symmetry as a platform for realizing tunable valley dependent transport. Our analysis is motivated by recent experiments [C. Forsythe et al., Nat. Nanotechnol. 13, 566571 (2018)] wherein gate-tunable superlattice potentials have been induced on graphene by nanostructuring a dielectric in the graphene/patterneddielectric/gate structure. We demonstrate how the electronic tight-binding structure of the superlattice system resembles a gapped Dirac model with associated valley dependent transport using an unfolding procedure. In this manner we obtain the valley Hall conductivities from the Berry curvature distribution in the superlattice Brillouin zone, and demonstrate the tunability of this conductivity by the superlattice potential. Finally, we calculate the valley Hall angle relating the transverse valley current and longitudinal charge current and demonstrate the robustness of the valley currents against irregularities in the patterned dielectric. arXiv:1905.06373v1 [cond-mat.mes-hall]

Orbital Hall effect as an alternative to valley Hall effect in gapped graphene

“…Using Eqs. ( 9) and (10), it is now easy to see that the orbital Berry curvature for the valence band of the valley model has the simple analytical form,…”

“…In other words, the orbital current operator may not have, in general, the simple form as in Eq. (10), where only the intra-band matrix elements of the orbital magnetic moment operator contribute. In general, the inter-band matrix elements may also appear and the orbital Berry curvature should be explicitly computed from Eq.…”

“…2π require the demarcation of the two valley domains, which is quite arbitrary. A frequently used prescription is to consider the Γ − M line in the Brillouin zone (BZ) as the boundary between two valleys [9,10]. However, this choice seems to be suggested by practical rather than fundamental considerations.…”

Spontaneous Valley Spirals in Magnetically Encapsulated Twisted Bilayer Graphene

“…In contrast to spin, valley is an orbital degree of freedom, and thus provides an extra challenge when it comes to interpretation and experimental verification [52,[74][75][76][77][78][79][80][81][82][83]. We propose to make use of the VHE, where band electrons from different valleys flow in opposite directions, leading to transverse charge-neutral valley currents [74,75,84].…”

Spontaneous Valley Spirals in Magnetically Encapsulated Twisted Bilayer Graphene

“…In contrast to spin, valley is an orbital degree of freedom, and thus provides an extra challenge when it comes to interpretation and experimental verification of valley-physics [39,[59][60][61][62][63][64][65][66][67][68]. A promising direction is to make use of the valley Hall effect (VHE), where band electrons from valley K flow in the opposite direction as those from valley K , leading to transverse charge-neutral valley currents [59,60,69].…”