The paper by C.L. Kane and E.J. Mele explores the effects of spin-orbit (SO) interactions on the low-energy electronic structure of a single layer of graphene. They find that in a low-temperature regime, the symmetry-allowed SO potential transforms graphene from a two-dimensional semimetallic state to a quantum spin Hall (QSH) insulator. This novel state is gapped in the bulk and supports gapless edge states that transport both spin and charge, which are non-chiral but insensitive to disorder due to their correlation with spin direction. The authors calculate the spin and charge conductances in these edge states and discuss the effects of temperature, chemical potential, Rashba coupling, disorder, and symmetry-breaking fields. They also estimate the magnitude of the SO potential using perturbation theory and renormalization group methods, finding that the QSH effect is robust against small perturbations. The study highlights graphene as a promising material for generating spin currents without dissipation, similar to the spin Hall effect observed in doped semiconductors like GaAs.The paper by C.L. Kane and E.J. Mele explores the effects of spin-orbit (SO) interactions on the low-energy electronic structure of a single layer of graphene. They find that in a low-temperature regime, the symmetry-allowed SO potential transforms graphene from a two-dimensional semimetallic state to a quantum spin Hall (QSH) insulator. This novel state is gapped in the bulk and supports gapless edge states that transport both spin and charge, which are non-chiral but insensitive to disorder due to their correlation with spin direction. The authors calculate the spin and charge conductances in these edge states and discuss the effects of temperature, chemical potential, Rashba coupling, disorder, and symmetry-breaking fields. They also estimate the magnitude of the SO potential using perturbation theory and renormalization group methods, finding that the QSH effect is robust against small perturbations. The study highlights graphene as a promising material for generating spin currents without dissipation, similar to the spin Hall effect observed in doped semiconductors like GaAs.