Ambipolar surface state transport in nonmetallic stoichiometric ${\mathrm{Bi}}_2{\mathrm{Se}}_3$ crystals

Achieving true bulk insulating behavior in ${\mathrm{Bi}}_2{\mathrm{Se}}_3$, the archetypal topological insulator with a simplistic one-band electronic structure and sizable band gap, has been prohibited by a well-known self-doping effect caused by selenium vacancies, whose extra electrons shift the chemical potential into the bulk conduction band. We report a synthesis method for achieving stoichiometric ${\mathrm{Bi}}_2{\mathrm{Se}}_3$ crystals that exhibit nonmetallic behavior in electrical transport down to low temperatures. Hall-effect measurements indicate the presence of both electron- and holelike carriers, with the latter identified with surface state conduction and the achievement of ambipolar transport in bulk ${\mathrm{Bi}}_2{\mathrm{Se}}_3$ crystals without gating techniques. With carrier mobilities surpassing the highest values yet reported for topological surface states in this material, the achievement of ambipolar transport via upward band bending is found to provide a key method to advancing the potential of this material for future study and applications.

Figure 1

Electrical resistivity of stoichiometric ${\mathrm{Bi}}_2{\mathrm{Se}}_3$ crystals with varying carrier concentrations resulting from variations in sample growth conditions. Samples A, F, and D all show an overall increase in $\rho$ between 300 K and 2 K. Samples V and H, shown for comparison, have semimetallic and metallic behavior.

Figure 2

Analysis of quantum oscillations observed in ${\mathrm{Bi}}_2{\mathrm{Se}}_3$ sample H, a high-carrier-density crystal. Panel (a) presents the background-subtracted longitudinal resistance as a function of inverse magnetic field, with a fitted model (solid line) that incorporates the presence of two oscillation frequencies (85 T and 95 T) with a $1.24\pi$ phase shift between them. Panel (b) presents a plot of the Hall resistivity for the same sample measured in situ, along with a two-carrier model fit shown as a solid line. The resultant carrier densities and mobilities are shown in the inset, with carrier densities that match the values expected for the two oscillation frequencies noted above (see text for details).

Figure 3

Hall-effect data and analysis of single-crystal ${\mathrm{Bi}}_2{\mathrm{Se}}_3$ obtained for two characteristic samples V and A, shown in panels (a–c) and (d–f), respectively. Transverse Hall resistance is presented in panels (a) and (d), with Drude model fits (see text) shown as solid lines. Panels (b) and (e) present the carrier densities extracted from the two-carrier analysis, and panels (c) and (f) present the resultant mobilities for each carrier type. The presence of two carrier contributions is easily discerned by the nonlinear behavior of ${\rho }_{xy}\left(H\right)$, in particular for sample A, which presents a crossover from electron- to hole-dominated conduction as a function of temperature. As described in the text, the two carrier types are ascribed to bulk and surface state carriers present in each sample, with holelike conduction necessarily originating from surface states in sample A.

Figure 4

(a) Electronic band structure of ${\mathrm{Bi}}_2{\mathrm{Se}}_3$ obtained from photoemission experiments [44], showing the positioning of bulk (dashed lines) and surface (dotted lines) chemical potential values $E_F$ extracted from two-carrier analysis of data for samples A and V (see text). Panel (b) presents a schematic of the difference between downward and upward band bending near the surface, providing an explanation for the positioning of surface chemical potentials of samples V and A near the Dirac point, consistent with an upward-band-bending picture.