[Paper Review] Theory of Andreev Blockade in a Double Quantum Dot with a Superconducting Lead

David Pekker, Po Zhang+1 more|arXiv (Cornell University)|Oct 11, 2018

Quantum and electron transport phenomena41 references4 citations

TL;DR

This paper proposes Andreev blockade in a double quantum dot coupled to a superconducting lead, where two electrons in a spin-triplet state are blocked from forming a Cooper pair due to angular momentum conservation. Unlike Pauli blockade, it occurs for any occupation of the dot adjacent to the superconductor and is lifted when quasiparticles enter the superconductor, making it observable in hard-gap superconductor-semiconductor devices with unique transport signatures in charge stability diagrams.

ABSTRACT

A normal metal source reservoir can load two electrons onto a double quantum dot in the spin-triplet configuration. We show that if the drain lead of the dot is a spin-singlet superconductor, these electrons cannot form a Cooper pair and are blockaded on the double dot. We call this phenomenon Andreev blockade because it arises due to suppressed Andreev reflections. We identify transport characteristics unique to Andreev blockade. Most significantly, it occurs for any occupation of the dot adjacent to the superconductor, in contrast with the well-studied Pauli blockade which requires odd occupations. Andreev blockade is lifted if quasiparticles are allowed to enter the superconducting lead, but it should be observable in the hard gap superconductor-semiconductor devices. A recent experiment tests this model and finds support for several predictions made here~[P. Zhang, H. Wu, J. Chen, S. A. Khan, P. Krogstrup, D. Pekker, and S. M. Frolov, arXiv:2102.03283 (2021)]. Andreev blockade should be considered in the design of topological quantum circuits, hybrid quantum bits and quantum emulators.

Motivation & Objective

• To investigate transport blockade mechanisms specific to Andreev processes in hybrid superconducting quantum dot systems.
• To identify conditions under which Andreev reflection is suppressed due to spin-triplet state formation.
• To distinguish Andreev blockade from Pauli blockade by analyzing its dependence on electron occupation parity and spin configuration.
• To predict observable transport characteristics, such as conductance triangles in charge stability diagrams, under low bias and hard superconducting gap conditions.
• To guide the design of topological quantum circuits and hybrid quantum bits by identifying Andreev blockade as a critical effect to consider.

Proposed method

• Develops a theoretical model of a double quantum dot tunnel-coupled to a normal metal source and a spin-singlet superconducting drain.
• Uses a master equation approach to describe electron tunneling and Andreev reflection processes, incorporating Coulomb blockade and superconducting pairing.
• Analyzes transport using charge stability diagrams in the gate voltage space (Vg1 vs. Vg2), mapping conductance as a function of dot occupations.
• Incorporates particle-hole symmetry in the superconductor to explain the parity dependence of Andreev blockade.
• Performs numerical simulations with parameters including tunneling rates (Γ1, Γ2, Γ12), charging energies (U1, U2, U12), and superconducting gap (Δ2), with bias voltage V1 = −V2 = 0.1.
• Considers the breakdown of blockade when source-drain bias exceeds the superconducting gap, allowing quasiparticle transport.

Experimental results

Research questions

• RQ1 Can Andreev reflection be suppressed in a double quantum dot with a superconducting lead when two electrons occupy a spin-triplet state?
• RQ2 How does Andreev blockade differ from Pauli blockade in terms of occupation dependence and symmetry?
• RQ3 What are the unique transport signatures of Andreev blockade in charge stability diagrams?
• RQ4 Under what conditions does Andreev blockade break down, and how does this affect conductance patterns?
• RQ5 Can Andreev blockade be observed in hard-gap superconductor-semiconductor devices, and what experimental parameters support its detection?

Key findings

• Andreev blockade occurs at (1,odd)→(0,even) charge degeneracy points in the double quantum dot, appearing twice as frequently as Pauli blockade.
• The blockade is sensitive only to the parity of the occupation on the dot adjacent to the superconductor due to particle-hole symmetry in the superconductor.
• Conductance triangles reappear in the stability diagram when the source-drain bias exceeds the superconducting gap (Δ = 0.05U1), indicating breakdown of Andreev blockade.
• The phenomenon is robust in hard-gap superconductors and is lifted when quasiparticles are allowed to enter the superconductor, enabling transport.
• The model's predictions were confirmed in a recent experiment, supporting the existence of Andreev blockade in a double quantum dot with a superconducting lead.
• Andreev blockade should be considered in the design of topological quantum circuits and hybrid quantum bits due to its impact on coherent transport.