Disorder effects in topological insulator nanowires

Three-dimensional topological insulator (TI) nanowires with quantized surface subband spectra are studied as a main component of Majorana bound states (MBS) devices. However, such wires are known to have large concentration  N ~ 10¹⁹ cm^-3 of Coulomb impurities. It is believed that a MBS device can function only if the amplitude of long-range fluctuations of the random Coulomb potential Γ is smaller than the subband gap Δ. Here we calculate Γ for recently experimentally studied large-dielectric-constant (Bi_1-xSb_x)₂Te₃ wires in a small-dielectric-constant environment (no superconductor). We show that provided by such a dielectric-constant contrast, the confinement of electric field of impurities within the wire allows more distant impurities to contribute into Γ, leading to Γ ~ 3Δ. We also calculate a TI wire resistance as a function of the Fermi level and carrier concentration due to scattering on Coulomb and neutral impurities, and do not find observable discrete subband-spectrum related oscillations at N ≥ 10¹⁸ cm^-3.