We present an effective low-energy theory of electron-phonon coupling effects for clean cylindrical topological insulator nanowires. Acoustic phonons are modelled by isotropic elastic continuum theory with stress-free boundary conditions. We take into account the deformation potential coupling between phonons and helical surface Dirac fermions, and also include electron-electron interactions within the bosonization approach. For half-integer values of the magnetic flux ΦB along the wire, the low-energy theory admits an exact solution since a topological protection mechanism then rules out phonon-induced 2kF -backscattering processes. We determine the zero-temperature phase diagram and identify a regime dominated by superconducting pairing of surface states. As example, we consider the phase diagram of HgTe nanowires. We also determine the phonon-induced electrical resistivity, where we find a quadratic dependence on the flux deviation δΦB from the nearest half-integer value. arXiv:1911.03300v2 [cond-mat.mes-hall] 5 Jan 2020

We study longitudinal magnetotransport in disorder-free cylindrical Weyl semimetal nanowires. Our theory includes a magnetic flux Φ piercing the nanowire and captures the finite curvature of the Fermi arc in the surface Brillouin zone through a boundary angle α. Electron backscattering by acoustic phonons via the deformation potential causes a finite resistivity which we evaluate by means of the semiclassical Boltzmann approach. We find that low-energy transport is dominated by surface states, where transport observables are highly sensitive to the angle α and to Aharonov-Bohm phases due to Φ. A generic subband dispersion relation allows for either one or two pairs of Fermi points. In the latter case, intra-node backscattering is possible and implies a parametrically larger resistivity than for a single Fermi point pair. As a consequence, large and abrupt resistivity changes take place across the transition points separating parameter regions with a different number of Fermi point pairs in a given subband.

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