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 (Bi1−x Sbx)2 Te3 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 ∼ 3 Δ . 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 .