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We formulate and apply a low-energy transport theory for hybrid quantumdevices containing junctions of topological superconductor (TS) wires andconventional normal (N) or superconducting (S) leads. We model TS wires asspinless $p$-wave superconductors and derive their boundary Keldysh Green'sfunction, capturing both the Majorana end state and continuum quasiparticleexcitations in a unified manner. We also specify this Green's function for afinite-length TS wire. Junctions connecting different parts of the device aredescribed by the standard tunneling Hamiltonian. Using this Hamiltonianapproach, one also has the option to include many-body interactions in asystematic manner. For N-TS junctions, we provide the current-voltage ($I$-$V$)characteristics at arbitrary junction transparency and give exact results forthe shot noise power and the excess current. For TS-TS junctions, analyticalresults for the thermal noise spectrum and for the $I$-$V$ curve in thehigh-transparency low-bias regime are presented. For S-TS junctions, we computethe entire $I$-$V$ curve and clarify the conditions for having a finiteJosephson current.

Low-energy theory of transport in Majorana wire junctions