# Modified spin-orbit couplings in uniaxially strained graphene

## TL;DR

This paper investigates how uniaxial strain affects spin-orbit couplings in graphene, proposing a generalized Hamiltonian and demonstrating strain-controlled tuning of spin-orbit interaction strengths and energy gaps.

## Contribution

It introduces a strain-dependent effective Hamiltonian for graphene with spin-orbit couplings, incorporating ab initio data into a tight-binding framework.

## Key findings

- Strain modifies Rashba and intrinsic spin-orbit coupling strengths.
- Energy gap at Dirac points can be tuned by strain.
- Strain slightly alters the low-energy dispersion topology.

## Abstract

Intrinsic and Rashba spin-orbit interactions in strained graphene is studied within the tight-binding (TB) approach. Dependence of Slater-Koster (SK) parameters of graphene on strain are extracted by fitting the \emph{ab initio} band structure to the TB results. A generalized low-energy effective Hamiltonian in the presence of spin-orbit couplings is proposed for strained graphene subjected to an external perpendicular electric field. Dependence of the modified Rashba strength and other parameters of effective Hamiltonian on the strain and electric field are calculated. In order to analyze the influence of the applied strain on the electronic properties of the graphene, one must take into account the lattice deformation, modifications of the hopping amplitudes and shift of the Dirac points. We find that using the strain it is possible to control the strength of Rashba and intrinsic spin-orbit couplings as well as energy gap at the shifted Dirac points. Meanwhile, the strain slightly modifies the topology of low-energy dispersion around the Dirac points. We describe the SOCs induced energy splitting as a function of strain.