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We investigate the conductivity of charge carriers confined to atwo-dimensional system with the non-parabolic dispersion $k^N$ with $N$ beingan arbitrary natural number. A delta-shaped scattering potential is assumed asthe major source of disorder. We employ the exact solution of theLippmann-Schwinger equation to derive an analytical Boltzmann conductivityformula valid for an arbitrary scattering potential strength. The range ofapplicability of our analytical results is assessed by a numerical study basedon the finite size Kubo formula. We find that for any $N>1$, the conductivitydemonstrates a linear dependence on the carrier concentration in the limit of astrong scattering potential strength. This finding agrees with the conductivitymeasurements performed recently on chirally stacked multilayer graphene wherethe lowest two bands are non-parabolic and the adsorbed hydrocarbons might actas strong short-range scatterers.

Charge transport in two dimensions limited by strong short-range scatterers: Going beyond parabolic dispersion and Born approximation