Levitons in helical liquids with Rashba spin-orbit coupling probed by a superconducting contact

Maura Sassetti,Matteo Carrega,Flavio Ronetti

doi:10.1103/physrevresearch.2.013203

Abstract

We consider transport properties of a single edge of a two-dimensional topological insulators, in presence of Rashba spin-orbit coupling, driven by two external time-dependent voltages and connected to a thin superconductor. We focus on the case of a train of Lorentzian-shaped pulses, which are known to generate coherent single-electron excitations in two-dimensional electron gas, and prove that they are minimal excitations for charge transport also in helical edge states, even in the presence of spin-orbit interaction. Importantly, these properties of Lorentzian-shaped pulses can be tested computing charge noise generated by the scattering of particles at the thin superconductor. This represents a novel setup where electron quantum optics experiments with helical states can be implemented, with the superconducting contact as an effective beamsplitter. By elaborating on this configuration, we also evaluate charge noise in a collisional Hong-Ou-Mandel configuration, showing that, due to the peculiar effects induced by Rashba interaction, a non-vanishing dip at zero delay appears.

Highlights

The exciting progress in quantum electronics gathered during the last decade has yielded an impressive level of experimental control such that even single-electron scale can be properly attained
The setup usually employed to prove that levitons are minimal excitation states is the so called Hanbury-BrownTwiss (HBT) configuration, where a single drive is applied to a quantum conductor in a quantum point contact (QPC) geometry [32,35]
We want to demonstrate that levitons are minimal excitations even for helical edge states in the presence of Rashba spin-orbit coupling and show that evidence for this result could be achieved in a HBT-like configuration, i.e., with a single drive applied to the system, where instead of the partitioning at the QPC one can employ the scattering induced by a thin superconductor tunnel-coupled to the helical edge

Summary

Introduction

The exciting progress in quantum electronics gathered during the last decade has yielded an impressive level of experimental control such that even single-electron scale can be properly attained. The first implementation of a singleelectron source, known as mesoscopic capacitor, has been accomplished by periodically driving a quantum dot, alternatively emitting an electron and a hole along the ballistic channels of a quantum Hall system [8,9,10,11,12,13] Another injection scheme, proposed by Levitov and co-workers [14,15,16], is based on the idea of applying to a quantum conductor a periodic train of quantized Lorentzian-shaped pulses, carrying an integer number of particles.

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Conclusion