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We study disorder effects on the surface states of the topological insulatorBi$_2$Se$_3$ close to the topologically protected crossing point. Close tocharge neutrality, local fluctuations in carrier density arising from therandom charged disorder in the environment result in electron and hole puddlesthat dominate the electronic properties of these materials. By calculating thepolarizability of the surface state using the random phase approximation, anddetermining the characteristics of puddles using the self-consistentapproximation, we find that band asymmetry plays a crucial role in determiningexperimentally measured quantities including the conductivity and the puddleautocorrelation length.

2D transport and screening in topological insulator surface states