  We show, using direct numerical simulations with experimentally realizable
boundary conditions, that wall modes in Rayleigh-B\'enard convection in a
rapidly rotating cylinder persist even very far from their linear onset. These
nonlinear wall states survive in the presence of turbulence in the bulk and are
robust with respect to changes in the shape of the boundary of the container.
In this sense these modes behave much like the topologically protected states
present in two-dimensional chiral systems even though rotating convection is a
three-dimensional nonlinear driven dissipative system. We suggest that the
robustness of this nonlinear mode may provide an explanation for the strong
zonal flows observed recently in simulations and experiments on rapidly
rotating convection at high Rayleigh number.
