Tunneling between helical Majorana modes and helical Luttinger liquids

Abstract

We propose and study the charge transport through single and double quantum point contacts setup between helical Majorana modes and an interacting helical Luttinger liquid. We show that the differential conductance decreases for stronger repulsive interactions and that the point contacts become insulating above a critical interaction strength. For a single point contact, the differential conductance as a function of bias voltage shows a series of peaks due to Andreev reflection of electrons in the Majorana modes. In the case of two point contacts, interference phenomena make the structure of the individual resonance peaks less universal and show modulations with different separation distance between the contacts. For small separation distance the overall features remain similar to the case of a single point contact.

Detecting Majorana fermions by use of superconductor-quantum Hall liquid junctions

“…Second, whether the superconducting wire is in a topologically nontrivial or trivial phase, the Cooper-pair tunneling may occur. The regular Cooper pairs may hop from the superconducting wire into the QH liquid via the point contact, which is induced locally in the wire by the superconducting pairing [27,32,33,48], similarly to the regular Cooper-pair tunneling in superconductor-Luttinger liquid proximity systems [49][50][51][52][53]. Since the edge states in the QH liquid can only transport spin-up electrons, the regular spin singlet Cooper-pair tunneling process needs to complete two processes [54].…”

“…For a TSC coupled to other materials via point contact, the presence of Majorana fermions can lead to many interesting transport properties [26][27][28][29][30][31][32][33][34][35][36]. When a normal metal lead, either noninteracting or interacting, couples to Majorana fermions through electron tunneling, the Majorana fermions can induce perfect Andreev reflections and may result in a quantized zero-bias conductance 2e 2 /h at low energies [26,27].…”

“…When a normal metal lead, either noninteracting or interacting, couples to Majorana fermions through electron tunneling, the Majorana fermions can induce perfect Andreev reflections and may result in a quantized zero-bias conductance 2e 2 /h at low energies [26,27]. For the normal metal lead, various parameters such as the electronic interaction, disorder, and finite length need to be taken into account [27][28][29][30][31][32][33][34][35][36], and they can result in a drastic departure from the noninteracting cases. These factors have been analyzed by scattering matrix theory [26], Keldysh formalism [34], the Luttinger liquids theory and renormalization group method [37,38].…”

Quantum critical points in tunneling junction of topological superconductor and topological insulator

“…Because of these intrinsically fascinating of Majorana fermions, there are many interesting transport properties and critical points when TSC couples to other materials [20,21,22,23,24,25,26,27,28,29,30,31,32,33]. A junction between a TSC and a Fermi lead (or interacting lead) is predicted to exhibit perfect Andreev reflection at low energies [20,23].…”

“…The localized Majorana modes emerge at interface of superconductor-ferromagnet junction on the edge of 2D TI [6,37]. The different geometries of TSC coupling with the edge of 2D TI have been investigated [28,32,33]. The fractional TI [38,39,40,41,42,43], which is the strongly interacting version of 2D TI, can be regarded as the generalization of the fractional QH liquids to time-reversal-invariant systems.…”