  By eliminating normal fabrication processes, we preserve the bulk insulating
state of calcium-doped Bi2Se3 single crystals in suspended nanodevices, as
indicated by the activated temperature dependence of the resistivity at low
temperatures. We perform low-energy electron beam irradiation (<16 keV) and
electrostatic gating to control the carrier density and therefore the Fermi
level position in the nanodevices. In slightly p-doped Bi2-xCaxSe3 devices,
continuous tuning of the Fermi level from the bulk valence band to the band-gap
reveals dramatic enhancement (> a factor of 10) in the field-effect mobility,
which suggests suppressed backscattering expected for the Dirac fermion surface
states in the gap of topological insulators.
