Graphene on two-dimensional hexagonal BN, AlN, and GaN: Electronic, spin-orbit, and spin relaxation properties

Abstract

We investigate the electronic band structure of graphene on a series of two-dimensional hexagonal nitride insulators hXN, X = B, Al, and Ga, with first principles calculations. A symmetry-based model Hamiltonian is employed to extract orbital parameters and spin-orbit coupling (SOC) from the low-energy Dirac bands of the proximitized graphene. While commensurate hBN induces the staggered potential of about 10 meV into the Dirac band structure, less lattice-matched hAlN and hGaN disrupt the Dirac point much less, giving the staggered gap below 100 µeV. Proximitized intrinsic SOC surprisingly does not increase much above the pristine graphene value of 12 µeV, it stays in the window of (1-16) µeV, depending strongly on stacking. However, Rashba SOC increases sharply with increasing the atomic number of the boron group, with calculated maximal values of 8, 15, and 65 µeV for B, Al, and Ga-based nitrides, respectively. The individual Rashba couplings depend also strongly on stacking, vanishing in symmetrically-sandwiched structures, and can also be tuned by a transverse electric field. The extracted spin-orbit parameters were used as input for spin transport simulations based on Chebyschev expansion of the time-evolution operator, yielding interesting predictions for the electron spin relaxation. Spin lifetime magnitudes and anisotropies depend strongly on the specific (hXN)/graphene/hXN system, and can be efficiently tuned by an applied external electric field as well as the carrier density in the graphene layer. A particularly interesting case for experiments is graphene/hGaN, in which the giant Rashba coupling is predicted to induce spin lifetimes of 1-10 ns, short enough to dominate over other mechanisms, and lead to the same spin relaxation anisotropy as that observed in conventional semiconductor heterostructures: 50%, meaning that out-of-plane spins relax twice as fast as in-plane spins.