[Paper Review] Strong nonlocal tuning of the current-phase relation of a quantum dot based Andreev molecule

Mátyás Kocsis, Zoltán Scherübl+3 more|arXiv (Cornell University)|Mar 26, 2023

Quantum and electron transport phenomena4 citations

TL;DR

This paper proposes a quantum dot-based Andreev molecule in a dual-SQUID configuration that enables strong nonlocal tuning of the current-phase relation (CPR) via superconducting phase differences and electrostatic gating. By embedding two quantum dots in separate superconducting loops sharing a common side, the system exhibits tunable $0$–$ar{ au}$ transitions and a nonlocally controlled $ar{ au}_0$ phase shift without relying on spin-orbit coupling or Zeeman fields, demonstrating a robust, nonlocal Josephson effect and a tunable superconducting diode effect.

ABSTRACT

Multiple systems hosting Andreev molecular states have been proposed and studied, consisting of closely spaced Josephson junctions modeled as ballistic channels. We show that replacing the ballistic channels in the weak link of the Josephson junctions with quantum dots (QD), leads to a very exciting, rich phase diagram. It shows a strong nonlocal Josephson effect: as one junction is tuned the current-phase relation of the other junction is modified. This architecture hosts $0 - π$ transitions and shows a tunable anomalous phase-shift $ϕ_0$ , nonlocally controlled in both cases, without relying on spin-orbit interaction or Zeeman fields. In addition significant superconducting diode effect can also be observed. The presented non-local current-phase relation can be used as a signature of the formation of an Andreev molecular state, as well as to introduce new ways to tune quantum architectures.

Motivation & Objective

• To investigate the role of Coulomb interactions in an Andreev molecule by enabling independent electrostatic and phase tuning of two quantum dots.
• To realize a nonlocal Josephson effect where tuning one quantum dot modulates the CPR of the other, enabling control over supercurrent phase relations.
• To demonstrate tunable $ar{ au}_0$ phase shifts and $ar{ au}$-periodic CPRs without relying on spin-orbit interaction or Zeeman fields.
• To explore the emergence of a nonlocally tunable superconducting diode effect in a correlated, non-Abelian platform.
• To provide a robust signature of Andreev molecular states through nonlocal CPR engineering in a minimal Kitaev chain architecture.

Proposed method

• Designing a dual-SQUID architecture with two superconducting loops sharing a common side, each hosting a quantum dot in a Josephson junction.
• Applying independent magnetic fluxes ($\varphi_L, \varphi_R$) to control the superconducting phase difference across each quantum dot.
• Using side gates to electrostatically tune the on-site energy ($\varepsilon_L, \varepsilon_R$) of each quantum dot independently.
• Employing a five-site tight-binding model with on-site Coulomb repulsion ($U$) and equal hopping ($t$) to simulate the Andreev molecular states.
• Performing Fourier decomposition of the current-phase relation (CPR) to extract first and second harmonic components for phase and amplitude analysis.
• Analyzing the CPR under varying $\varepsilon_R$ and $\varphi_L$ to identify $0$–$\pi$ transitions, $\varphi_0$ shifts, and harmonic contributions.

Experimental results

Research questions

• RQ1 Can the current-phase relation of one quantum dot in an Andreev molecule be strongly nonlocally tuned by adjusting the parameters of the other dot?
• RQ2 Does the presence of Coulomb interactions enable new types of nonlocal Josephson effects not accessible in non-interacting models?
• RQ3 Can a tunable $\varphi_0$ phase shift be achieved without spin-orbit coupling or Zeeman fields?
• RQ4 What role do higher-order harmonic components (first and second) of the CPR play in identifying $0$–$\pi$ transitions and $\varphi_0$ states?
• RQ5 Can the system exhibit a nonlocally tunable superconducting diode effect due to asymmetric CPRs?

Key findings

• The system exhibits a strong nonlocal Josephson effect: tuning the on-site energy $\varepsilon_R$ of one quantum dot induces measurable changes in the CPR of the other dot, even without direct coupling.
• A $0$–$\pi$ transition is observed in the CPR of one dot when $\varepsilon_R \approx -1U$, with a $\pi$ phase jump in the first harmonic component confirmed by Fourier analysis.
• A tunable $\varphi_0$ phase shift is achieved nonlocally by adjusting $\varepsilon_R$, with the phase shift varying continuously from $0$ to $\pi$ as $\varepsilon_R$ is tuned, even without a ground state transition.
• The second harmonic component of the CPR reaches a local maximum at the same point where the first harmonic vanishes, explaining the skewing of CPR curves and enabling $\pi$-periodic behavior in certain regimes.
• The first harmonic amplitude does not vanish at the $\varphi_0$ point when $\varphi_L = 0.8\pi$, indicating robustness against phase noise compared to $\cos 2\varphi$ qubits.
• A significant nonlocally tunable superconducting diode effect is observed, with asymmetric current flow dependent on the applied phase bias and gate voltage.