Graphene on two-dimensional hexagonal BN, AlN, and GaN: Electronic, spin-orbit, and spin relaxation properties
Klaus Zollner, Aron W. Cummings, Stephan Roche, Jaroslav Fabian
Abstract
We investigate the electronic band structure of graphene on a series of two-dimensional hexagonal nitride insulators $\mathrm{h}X\mathrm{N}, X=\text{B}$, 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 a staggered potential of about 10 meV into the Dirac band structure, less lattice-matched hAlN and hGaN disrupt the Dirac point much less, giving a staggered gap below 100 $\ensuremath{\mu}\mathrm{eV}$. Proximitized intrinsic SOC surprisingly does not increase much above the pristine graphene value of 12 $\ensuremath{\mu}\mathrm{eV}$; it stays in the window of 1--16 $\ensuremath{\mu}\mathrm{eV}$, depending strongly on stacking. However, Rashba SOC increases sharply when increasing the atomic number of the boron group, with calculated maximal values of 8, 15, and 65 $\ensuremath{\mu}\mathrm{eV}$ for B-, Al-, and Ga-based nitrides, respectively. The individual Rashba couplings also depend strongly on stacking, vanishing in symmetrically sandwiched structures, and can be tuned by a transverse electric field. The extracted spin-orbit parameters were used as input for spin transport simulations based on Chebyshev expansion of the time-evolution of the spin expectation values, yielding interesting predictions for the electron spin relaxation. Spin lifetime magnitudes and anisotropies depend strongly on the specific ($\mathrm{h}X\mathrm{N}$)/graphene/$\mathrm{h}X\mathrm{N}$ system, and they 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.