Surface conduction of topological Dirac electrons in bulk insulating Bi ₂ Se ₃

The newly discovered three-dimensional strong topological insulators (STIs) exhibit topologically protected Dirac surface states. Although the STI surface state has been studied spectroscopically, for example, by photoemission and scanned probes, transport experiments have failed to demonstrate the most fundamental signature of the STI: ambipolar metallic electronic transport in the topological surface of an insulating bulk. Here we show that the surfaces of thin (∼ 10ĝ€‰nm), low-doped Bi 2 Se 3 (≈10 17 ĝ€‰cm -3) crystals are strongly electrostatically coupled, and a gate electrode can completely remove bulk charge carriers and bring both surfaces through the Dirac point simultaneously. We observe clear surface band conduction with a linear Hall resistivity and a well-defined ambipolar field effect, as well as a charge-inhomogeneous minimum conductivity region. A theory of charge disorder in a Dirac band explains well both the magnitude and the variation with disorder strength of the minimum conductivity (2 to 5 e 2 /h per surface) and the residual (puddle) carrier density (0.4×10 12 to 4×10 12 ĝ€‰cm -2). From the measured carrier mobilities 320-1,500ĝ€‰cm 2 ĝ€‰V -1 ĝ€‰s -1, the charged impurity densities 0.5×10 13 to 2.3×10 13 ĝ€‰cm -2 are inferred. They are of a similar magnitude to the measured doping levels at zero gate voltage (1×10 13 to 3×10 13 ĝ€‰cm -2), identifying dopants as the charged impurities.