We study the quantum point contact between the topological superconductor and
the helical Luttinger liquid. The effects of the electron-electron interactions
in the helical Luttinger liquid on the low-energy physics of this system are
analyzed by the renormalization group. Among the various couplings at the point
contact which arise from the tunneling via the Majorana edge channel, the
induced backscattering in the helical Luttinger liquid is the most relevant for
repulsive interactions. Hence, at low temperatures, the helical Luttinger
liquid is effectively cut into two separated half wires. As a result, the
low-temperature physics is described by a fixed point consisting of two leads
coupled to the topological superconductor, and the electrical transport
properties through the point contact at low temperature and low bias are
dominated by the tunneling via the Majorana edge channel. We compute the
temperature dependence of the zero-bias tunneling conductance and study the
full counting statistics for the tunneling current at zero temperature.Comment: 7 pages, 2 figur
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