Electronic and spin-orbit properties of h -BN encapsulated bilayer graphene

Abstract

Van der Waals heterostructures consisting of Bernal bilayer graphene (BLG) and hexagonal boron nitride (hBN) are investigated. By performing first-principles calculations, we capture the essential BLG band structure features for several stacking and encapsulation scenarios. A low-energy model Hamiltonian, comprising orbital and spin-orbit coupling (SOC) terms, is employed to reproduce the hBN-modified BLG dispersion, spin splittings, and spin expectation values. Most important, the hBN layers open an orbital gap in the BLG spectrum, which can range from zero to tens of meV, depending on the precise stacking arrangement of the individual atoms. Therefore, large local band gap variations may arise in experimentally relevant moiré structures. Moreover, the SOC parameters are small (few to tens of µeV), just as in bare BLG, but are markedly proximity modified by the hBN layers. Especially when BLG is encapsulated by monolayers of hBN, such that inversion symmetry is restored, the orbital gap and spin splittings of the bands vanish. In addition, we show that a transverse electric field mainly modifies the potential difference between the graphene layers, which perfectly correlates with the orbital gap for fields up to about 1 V/nm. Moreover, the layer-resolved Rashba couplings are tunable by ∼5 µeV per V/nm. Finally, by investigating twisted BLG/hBN structures, with twist angles between 6 • -20 • , we find that the global band gap increases linearly with the twist angle. The extrapolated 0 • band gap is about 23 meV and results roughly from the average of the stacking-dependent local band gaps. Our investigations give insights into proximity spin physics of hBN/BLG heterostructures, which should be useful for interpreting experiments on extended as well as confined (quantum dot) systems.

Strain-controlled charge and spin current rectifications in spin–orbit coupled graphene nano-ribbon: A new proposition

“…Graphene, a single layer of carbon atoms grouped in a twodimensional honeycomb lattice, on the other hand, has exceptional mechanical, electrical, thermal, and optoelectronic properties, largest carrier mobility, a very long carrier mean free path longer than 1 μm in room temperature limit, [33][34][35] and a long spin coherence length, [36][37][38] making it a very promising 2D material for electronics and spintronics research. [39][40][41][42][43][44][45][46][47] Furthermore, it is known that, strain engineering in graphene can modify its distances between ions in graphene-lattice sites, electronic structure, create polarized carrier puddles, induce pseudomagnetic fields, 48,49 and alter surface properties, which have been well investigated and summarized in previous studies and reviews. [50][51][52][53] The incredible elastic deformability of graphene, [54][55][56] capable of tolerating nondestructive reversible deformations up to extraordinarily high failure limits ( 25%, 57,58 26:5%, 59 or even 27% 60 ), prompted a series of studies on strain effects on graphene's electronic characteristics, notably bandgap engineering.…”