# Heterostructures of graphene and hBN: electronic, spin-orbit, and spin relaxation properties from first principles

## TL;DR

This paper uses first-principles calculations to analyze the electronic and spin relaxation properties of graphene/hBN heterostructures, revealing tunable spin lifetimes and anisotropy influenced by stacking, interlayer distance, and electric fields.

## Contribution

It introduces a minimal tight-binding model for graphene/hBN heterostructures and explores how stacking, interlayer distance, and electric fields affect spin-orbit coupling and spin relaxation.

## Key findings

- Spin lifetimes are in the nanosecond range, matching experiments.
- Spin relaxation anisotropy is giant near charge neutrality and tunable by electric field.
- Orbital and SOC parameters depend strongly on stacking and electric field.

## Abstract

We perform extensive first-principles calculations for heterostructures composed of monolayer graphene and hexagonal boron nitride (hBN). Employing a symmetry-derived minimal tight-binding model, we extract orbital and spin-orbit coupling (SOC) parameters for graphene on hBN, as well as for hBN encapsulated graphene. Our calculations show that the parameters depend on the specific stacking configuration of graphene on hBN. We also perform an interlayer distance study for the different graphene/hBN stacks to find the corresponding lowest energy distances. For very large interlayer distances, one can recover the pristine graphene properties, as we find from the dependence of the parameters on the interlayer distance. Furthermore, we find that orbital and SOC parameters, especially the Rashba one, depend strongly on an applied transverse electric field, giving a rich playground for spin physics. Armed with the model parameters, we employ the Dyakonov-Perel formalism to calculate the spin relaxation in graphene/hBN heterostructures. We find spin lifetimes in the nanosecond range, in agreement with recent measurements. The spin relaxation anisotropy, being the ratio of out-of-plane to in-plane spin lifetimes, is found to be giant close to the charge neutrality point, decreasing with increasing doping, and being highly tunable by an external transverse electric field. This is in contrast to bilayer graphene in which an external field saturates the spin relaxation anisotropy.