Current transport properties and phase diagram of a Kitaev chain with long-range pairing

TL;DR

This paper proposes a method to detect quantum phase transitions in a long-range Kitaev chain using the Fano factor, revealing distinct signatures for different phases and a critical fractionalization effect at the transition.

Contribution

It introduces a novel measurement approach based on the Fano factor to distinguish topological phases in a long-range superconducting chain, including a critical fractionalization signature.

Findings

Fano factor is zero in short-range phase and 2e in long-range phase.

The Fano factor equals e along the quantum critical line.

The method enables detection of phase transitions via measurable transport properties.

Abstract

We describe a method to probe the quantum phase transition between the short-range topological phase and the long-range topological phase in the superconducting Kitaev chain with long-range pairing, both exhibiting subgap modes localized at the edges. The method relies on the effects of the finite mass of the subgap edge modes in the long-range regime (which survives in the thermodynamic limit) on the single-particle scattering coefficients through the chain connected to two normal leads. Specifically, we show that, when the leads are biased at a voltage V with respect to the superconducting chain, the Fano factor is either zero (in the short-range correlated phase) or 2e (in the long-range correlated phase). As a result, we find that the Fano factor works as a directly measurable quantity to probe the quantum phase transition between the two phases. In addition, we note a remarkable "critical fractionalization effect" in the Fano factor, which is exactly equal to e along the quantum critical line. Finally, we note that a dual implementation of our proposed device makes it suitable as a generator of large-distance entangled two-particle states.