Signatures of Majorana Kramers pairs in superconductor-Luttinger liquid and superconductor-quantum dot-normal lead junctions

TL;DR

This paper explores the transport signatures and stability of Majorana Kramers pairs in topological superconductors, analyzing electron interactions in Luttinger liquids and quantum dot systems to identify new fixed points and conductance behaviors.

Contribution

It provides a detailed phase diagram for Majorana Kramers pairs in interacting Luttinger liquids and reveals a new fixed point dominated by Majorana interactions in quantum dot setups.

Findings

Quantized conductance of 4e^2/h in superconductor-normal lead junctions.

Low-energy properties governed by spin-triplet Andreev reflection.

Identification of a Majorana-controlled fixed point in quantum dot systems.

Abstract

Time-reversal invariant topological superconductors are characterized by the presence of Majorana Kramers pairs localized at defects. One of the transport signatures of Majorana Kramers pairs is the quantized differential conductance of $4e^2/h$ when such a one-dimensional superconductor is coupled to a normal-metal lead. The resonant Andreev reflection, responsible for this phenomenon, can be understood as the boundary condition change for lead electrons at low energies. In this paper, we study the stability of the Andreev reflection fixed point with respect to electron-electron interactions in the Luttinger liquid. We first calculate the phase diagram for the Luttinger liquid-Majorana Kramers pair junction and show that its low-energy properties are determined by Andreev reflection scattering processes in the spin-triplet channel, i.e. the corresponding Andreev boundary conditions are similar to that in a spin-triplet superconductor - normal lead junction. We also study here a quantum dot coupled to a normal lead and a Majorana Kramers pair and investigate the effect of local repulsive interactions leading to an interplay between Kondo and Majorana correlations. Using a combination of renormalization group analysis and slave-boson mean-field theory, we show that the system flows to a new fixed point which is controlled by the Majorana interaction rather than the Kondo coupling. This Majorana fixed point is characterized by correlations between the localized spin and the fermion parity of each spin sector of the topological superconductor. We investigate the stability of the Majorana phase with respect to Gaussian fluctuations.