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The joint effects of Kekul\'e lattice distortions and Rashba-type spin-orbitcoupling on the electronic properties of graphene are explored. We modeled theposition dependence of the Rashba energy term in a manner that allows itsseamless integration into the scheme introduced by Gamayun et al.[New J. Phys.20, 023016 (2018)] to describe graphene with Kekul\'e lattice distortion.Particularly for the Kekul\'e-Y texture, the effective low energy DiracHamiltonian contains a new spin-valley locking term, in addition to thewell-known Rashba-induced momentum-pseudospin and spin-pseudospin couplings,and the Kekul\'e-induced momentum-valley coupling term. We report on thelow-energy band structure and Landau level spectra of Rashba-spin-orbit-coupledKek-Y graphene, and propose an experimental scheme to discern between thepresence of Rashba spin-orbit coupling, Kek-Y lattice distortion, and both,based on doping-dependent magnetotransport measurements.

Spin-valley locking in Kekul\'e-distorted graphene with Dirac-Rashba interactions