Effects of bulk charged impurities on the bulk and surface transport in three-dimensional topological insulators
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ffects of Bulk Charged Impurities on the Bulk and Surface Transport in ThreeDimensional Topological Insulators1 B. Skinner, T. Chen, and B. I. Shklovskii Fine Theoretical Physics Institute, University of Minnesota, Minneapolis, MN 55455 USA email: [email protected] Received April 1, 2013
Dedicated to the memory of Professor Anatoly Larkin Abstract—In the threedimensional topological insulator (TI), the physics of doped semiconductors exists literally sidebyside with the physics of ultrarelativistic Dirac fermions. This unusual pairing creates a novel playground for studying the interplay between disorder and electronic transport. In this minireview, we focus on the disorder caused by the threedimensionally distributed charged impurities that are ubiquitous in TIs, and we outline the effects it has on both the bulk and surface transport in TIs. We present selfconsistent the ories for Coulomb screening both in the bulk and at the surface, discuss the magnitude of the disorder poten tial in each case, and present results for the conductivity. In the bulk, where the band gap leads to thermally activated transport, we show how disorder leads to a smallerthanexpected activation energy that gives way to variablerange hopping at low temperatures. We confirm this enhanced conductivity with numerical sim ulations that also allow us to explore different degrees of impurity compensation. For the surface, where the TI has gapless Dirac modes, we present a theory of disorder and screening of deep impurities, and we calcu late the corresponding zerotemperature conductivity. We also comment on the growth of the disorder poten tial in passing from the surface of the TI into the bulk. Finally, we discuss how the presence of a gap at the Dirac point, introduced by some source of timereversal symmetry breaking, affects the disorder potential at the surface and the midgap density of states. DOI: 10.1134/S1063776113110150 1
1. INTRODUCTION The threedimensional (3D) topological insulator (TI) [1–5] has generated great excitement in the phys ics community because of its gapless surface states, which host a spectrum of quantum transport phenom ena [6, 7]. Unfortunately, while a number of crystals have been identified to be 3D TIs, most of them are not actually insulators, but instead have a relatively large bulk conductivity that shunts the surface con ductivity for TI crystals of substantial thickness (10 μm). How to achieve a bulkinsulating state is a problem that is widely discussed in the current litera ture [8–16]. Typically, asgrown TI crystals are heavily doped n type semiconductors, such that the Fermi level resides in the bulk conduction band. In order to arrive at a bulk insulating state, such TIs are compensated by acceptors. With increasing the degree of compensation K = NA/ND, where ND and NA are the respective con centrations of monovalent donors and acceptors, the Fermi level shifts from the conduction band to inside the gap and then into the valence band. When com pensation of donors
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