Majorana fermions coupled to Luttinger liquids

D.~Pikulin, Y. Komijani, I. Affleck, Luttinger liquids in contact with a Kramers pair of Majorana bound states, Phys. Rev. B 93, 205430 (2016).

Y. Komijani, I. Affleck, Detecting a quantum critical point in topological SN junctions, Phys. Rev. B 90, 115107 (2014).

Y. Komijani, I. Affleck, Effect of disorder on the conductance of (non-) topological SN junctions, J. of Stat. Mech., P11017 (2014).

• The interface between a few 1D wires and a few Majorana fermions contains very rich physics. Such coupling can arise in mutli-band SN junctions in which the gapless normal state is described by a Luttinger liquid due to interactions. This physics turns out to be related to the multichannel Kondo physics. Each normal channel can couple to a Majorana fermion via its real or imaginary parts.

• This table shows a few examples of possible fixed points arising in such interfaces. The vertical direction is number of Majorana zero modes (MZM) and the horizontal direction is the number of gapless channels, described by a Luttinger liquid (LL).
• One MZM coupled to a LL is known to lead to resonant Andreev reflection, unless the repulsive interaction in LL is very large. For one MZM coupled to two LL Affleck and Giuliano discovered a non-trivial fixed point, due to frustration of the MZM between the two LL, similar to the non-trivial fixed point of the two-channel Kondo problem.
• Together with Ian, we were able to show that such critical points can be realized in a simple single-channel nano-wires. the two spin states of the wire, playing the role of the two channels.
• Two MZMs coupled to one LL realize a form of Kondo effect, whereas two MZMs coupled to two LLs have a rich phase diagram, for example realizing a so-called Andreev Transmission state, in which an electron from one channel is reflected as a hole in another channel.