  Nanowires with helical surface states represent key prerequisites for
observing and exploiting phase-coherent topological conductance phenomena, such
as spin-momentum locked quantum transport or topological superconductivity. We
demonstrate in a joint experimental and theoretical study that gated nanowires
fabricated from high-mobility strained HgTe, known as a bulk topological
insulator, indeed preserve the topological nature of the surface states, that
moreover extend phase-coherently across the entire wire geometry. The
phase-coherence lengths are enhanced up to 5 $\mu$m when tuning the wires into
the bulk gap, so as to single out topological transport. The nanowires exhibit
distinct conductance oscillations, both as a function of the flux due to an
axial magnetic field, and of a gate voltage. The observed $h/e$-periodic
Aharonov-Bohm-type modulations indicate surface-mediated quasi-ballistic
transport. Furthermore, an in-depth analysis of the scaling of the observed
gate-dependent conductance oscillations reveals the topological nature of these
surface states. To this end we combined numerical tight-binding calculations of
the quantum magneto-conductance with simulations of the electrostatics,
accounting for the gate-induced inhomogenous charge carrier densities around
the wires. We find that helical transport prevails even for strongly
inhomogenous gating and is governed by flux-sensitive high-angular momentum
surface states that extend around the entire wire circumference.
