Majorana modes as electrical switches: computing the conductance of a junction between a Topological superconductor and a multi-channel Luttinger liquid

Motivated by the experimental confirmation of topological superconductivity in semiconducting nanowires, I study the transport properties of a junction of three wires (T-junction), which provides the simplest nontrivial example of wire network, as well as an important building block for topological quantum computing architectures. I show how to compute the electrical conductance of a T-junction between a Topological superconductor and two normal interacting nanowires using the Density Matrix Renormalization Group (DMRG) method [1] that allows one to extract the conductance in the thermodynamic limit from static ground-state DMRG computations in closed finite systems [2]. As main result, I numerically demonstrate that the T-junction can act as an electrical switch in the presence of a localized Majorana mode in agreement with field theory predictions [3]. I finally focus on the regime where the tunnel couplings between the superconductor and the nanowires is fine tuned to the same value, and compare the numerical results to the field theory calculations that predict a non-trivial critical point with an unusual conductance tensor.

[1] A. Nocera et al (in preparation)
[2] A. Rahmani et al. Phys. Rev. B 85, 045120 (2012)
[3] I. Affleck and D. Giuliano, J. Stat. Mech. P06011 (2013)