Phase diagram and phonon-induced backscattering in topological insulator nanowires

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 ${\mathrm{\Phi }}_B$ along the wire, the low-energy theory admits an exact solution since a topological protection mechanism then rules out phonon-induced $2k_F$-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 $\delta {\mathrm{\Phi }}_B$ from the nearest half-integer value.