We numerically investigated the effect of chemical potential on Dyakonov–Tamm waves (DTWs) guided by a graphene-coated structurally chiral medium in the terahertz and the visible spectral regimes. Only one DTW can propagate in a specific direction in wide angular sectors, but multiple DTWs can propagate in a specific direction in narrow angular sectors, in both spectral regimes. Although the phase speed of a DTW depends weakly on the chemical potential in both spectral regimes, the propagation distance can be strongly dependent on the chemical potential in the terahertz regime but not in the visible regime. This difference can be attributed to the real part of the surface conductivity of graphene, which varies significantly with the chemical potential in the terahertz regime but not in the visible regime.