Signatures of Rashba-Cavity-Induced Berry-curvature redistribution in the Spin-Hall Conductivity of Semiconductor Artificial Graphene

We investigate the combined effect of a far-infrared cavity field and Rashba spin-orbit interac- tion on the band structure and transport properties of artificial graphene composed of quazi-2D InAs/GaAs quantum dots. The coupling to cavity photons is modeled by constructing a complete basis as the tensor product of the electronic Hilbert space and the Fock space. Our calculations for the system embedded in a linear cavity predict the existence of both type-I and type-II Dirac points which can be distinguished by their response to Rashba interaction. Namely, Rashba coupling opens a gap at type-II Dirac points, while type-I Dirac points remain gapless. For both cylindrical and linear cavities, we demonstrate the formation of electron-photon hybrid states and Rabi oscillations between energy minibands. Multiple splittings, crossings, and anticrossings between Dirac-band replicas produce pronounced modifications of the spin-Hall conductivity, including strong anisotropy and oscillatory behavior controlled by cavity geometry and polarization. Our results show that the interplay between Rashba and cavity couplings governs Dirac-point physics and provides a route toward tunable polaritonic transport and topological phases in engineered nanostructures.