Fig. 1

The helical gap in a one-dimensional nanowire device. a An indium antimonide (InSb) nanowire device with a Rashba spin-orbit field B _SO perpendicular to the wave vector k and the electric field E. A voltage is sourced to one contact, and the resulting conductance measured from the second contact. A degenerately doped wafer acts as global backgate V _g. b A quantum point contact (QPC) of length L is defined by the two contacts. Underneath the nanowire contacts, many subbands are occupied as the contacts screen the gate electric field. In the nanowire channel away from the contacts, the chemical potential in the wire, μ, is tuned with V _g. The onset shape of V _g with a lengthscale λ is set by the dielectric and screening of the electric field from the metallic contacts resulting in an effective QPC length L _QPC = L−2λ. c The energy dispersion of the first two subbands for a system with spin-orbit interaction (SOI) at external magnetic field B = 0 T. The SOI causes subbands to shift by k _SO in momentum space, as electrons with opposite spins carry opposite momentum. When the electrochemical potential μ in the wire is tuned conductance plateaus will occur at integer values of G ₀. d At finite magnetic field B perpendicular to B _SO, the spin polarized bands hybridize opening a helical gap of size E _Z (green). In this region the conductance reduces from 1·G ₀ to 0.5·G ₀ when μ is positioned inside the gap. e When the magnetic field is orientated at an angle θ to B _SO, the size of the helical gap decreases to only include the component of the magnetic field perpendicular to B _SO and the two subbands split by an additional Zeeman gap (purple). The color scheme illustrating different conductance regimes is also used in Figs. 2d and 3b. For all angles the re-entrant conductance feature at 0.5·G ₀ in the 1·G ₀ plateau will scale linearly with Zeeman energy