Theoretical study of carrier transport and screening in topological insulator Bi$_{2}$Se$_{3}$

This theoretical work is motivated by two recent experiments on Bi$_{2}$Se$_{3}$ examining the charge inhomogeneity [1-2] close to the topologically protected crossing point of surface bands in these bulk topological insulators. Reminiscent of graphene close to charge neutrality [3-4], the energy landscape becomes highly inhomogeneous, forming a sea of electron and hole puddles, which determine the properties at low carrier density. Here, we show that the induced carrier density fluctuations are of order 1 {\%} of the impurity density, providing a small-parameter with which we can perform a controlled perturbation theory. Analytic results are obtained for the minimum conductivity and puddle auto-correlation length. We also find that the band asymmetry between electron and holes states is a necessary ingredient to understand the aforementioned experiments. \textbf{References: } [1] H. Beidenkopf \textit{et al,} ``\textit{Spatial fluctuations of helical Dirac fermions on the surface of topological insulators},'' Nat. Phys.\textit{ online publ.}, (2011) [2] D. Kim \textit{et al.,} ``\textit{Minimum conductivity and charge inhomogeneity in Bi}$_{2}$\textit{Se}$_{3}$,'' arXiv:1105.1410. [3] S. Adam \textit{et al.}, ``\textit{A self-consistent theory for graphene transport},'' PNAS \textbf{104}, 18392 (2007). [4] S. Das Sarma \textit{et al., ``Electronic transport in 2D graphene},'' \textit{Rev. Mod. Phys.} \textbf{83}, 407 (2011).