Tunneling in the topological mechanism of superconductivity

TL;DR

This paper investigates tunneling phenomena in a topological superconductor model, revealing unique features like a complex d-wave pairing and asymmetric tunneling peaks, distinct from conventional BCS superconductivity.

Contribution

It introduces a novel topological model of superconductivity incorporating orthogonality catastrophe and soft modes, providing new insights into pairing and tunneling mechanisms.

Findings

Wave function of pairs is dressed by soft modes

Tunneling amplitude exhibits an asymmetric broad peak

Superconductivity physics differs from BCS theory due to orthogonality catastrophe

Abstract

We compute the two-particle matrix element and Josephson tunneling amplitude in a two-dimensional model of topological superconductivity which captures the physics of the doped Mott insulator. The hydrodynamics of topological electronic liquid consists of the compressible charge sector and the incompressible chiral topological spin liquid. We show that ground states differing by an odd number of particles are orthogonal and insertion of two extra electrons is followed by the emission of soft modes of the transversal spin current. The orthogonality catastrophe makes the physics of superconductivity drastically different from the BCS-theory but similar to the physics of one-dimensional electronic liquids. The wave function of a pair is dressed by soft modes. As a result the two particle matrix element forms a complex d-wave representation (i.e., changes sign under $90^o$ degree rotation), although the gap in the electronic spectrum has no nodes. In contrast to the BCS-theory the tunneling amplitude has an asymmetric broad peak (much bigger than the gap) around the Fermi surface. We develop an operator algebra, that allows one to compute other correlation functions.