[Paper Review] Enhancing the excitation gap of a quantum-dot-based Kitaev chain

Chun-Xiao Liu, A. Mert Bozkurt+4 more|arXiv (Cornell University)|Oct 13, 2023

Topological Materials and Phenomena49 references4 citations

TL;DR

This paper proposes enhancing the excitation gap in a quantum-dot-based Kitaev chain by increasing the coupling between quantum dots and a semiconductor-superconductor hybrid segment. Through proximity-induced Yu-Shiba-Rusinov states, the system transitions to a strong-coupling regime where Majorana zero modes persist with a significantly enlarged gap—demonstrated experimentally to reach ~75 μeV—while maintaining spatial separation and robustness to local perturbations.

ABSTRACT

Connecting double quantum dots via a semiconductor-superconductor hybrid segment offers a platform for creating a two-site Kitaev chain that hosts a pair of "poor man's Majoranas" at a finely tuned sweet spot. However, the effective couplings, which are mediated by Andreev bound states in the hybrid, are generally weak in the tunneling regime. As a consequence, the excitation gap is limited in size, presenting a formidable challenge for using this platform to demonstrate non-Abelian statistics of Majoranas and realizing error-resilient topological quantum computing. In this work, we systematically study the effects of increasing the coupling between the dot and the hybrid segment. In particular, the proximity effect transforms the dot orbitals into Yu-Shiba-Rusinov states, forming a new spinless fermion basis for a Kitaev chain, and we derive a theory for their effective coupling. As the coupling strength between the dots and the hybrid segment increases, we find a significant enhancement of the excitation gap and reduced sensitivity to local perturbations. Although the hybridization of the Majorana wave function with the central Andreev bound states increases strongly with increasing coupling, the overlap of Majorana modes on the outer dots remains small, which is a prerequisite for potential qubit experiments. We discuss how the strong-coupling regime shows in experimentally accessible quantities, such as the local and non-local conductance, and provide a protocol for tuning a double-dot system into a sweet spot with a large excitation gap.

Motivation & Objective

• Address the challenge of small excitation gaps in experimental two-site Kitaev chains, which limit the demonstration of non-Abelian statistics and fault-tolerant quantum computation.
• Overcome the limitation of weak effective couplings in the tunneling (weak-coupling) regime, which restricts the gap to ~25 μeV despite larger superconducting gaps.
• Investigate the strong-coupling regime (t ~ Δ₀) where proximity effect transforms dot orbitals into Yu-Shiba-Rusinov states, forming a new spinless fermion basis for the Kitaev chain.
• Provide a practical experimental protocol to tune into a sweet spot with a large excitation gap using conductance spectroscopy and charge stability diagrams.
• Demonstrate that poor man’s Majorana modes survive in the strong-coupling regime with enhanced gap and reduced sensitivity to local perturbations.

Proposed method

• Formulate a three-site model Hamiltonian combining dot levels (H_D), superconducting hybrid segment (H_S), and tunneling couplings (H_T), with the hybrid segment hosting Andreev bound states.
• Introduce the proximity effect from the hybrid segment, transforming isolated dot orbitals into Yu-Shiba-Rusinov (YSR) states that form the new effective spinless fermion basis.
• Derive an effective theory for the YSR-state-mediated coupling in the strong-coupling regime, generalizing concepts like elastic cotunneling and crossed Andreev reflection beyond weak coupling.
• Use numerical diagonalization and conductance calculations to analyze the energy spectrum, wavefunction overlap, and transport properties (local and non-local conductance) as a function of coupling strength t.
• Analyze non-local conductance G_LR and G_RL as key experimental probes, tracking their evolution with increasing t and detuning to identify the sweet spot.
• Propose a tuning protocol: first, measure single-dot conductance to identify optimal coupling; second, use charge stability diagrams and zero-bias peaks to locate the sweet spot with maximal gap.

Experimental results

Research questions

• RQ1 Can increasing the dot-hybrid coupling strength in a quantum-dot-based Kitaev chain significantly enhance the excitation gap beyond the weak-coupling limit?
• RQ2 How do Yu-Shiba-Rusinov states formed via proximity effect alter the effective coupling and topological properties in the strong-coupling regime?
• RQ3 To what extent do poor man’s Majorana zero modes remain spatially separated and robust against local perturbations in the strong-coupling regime?
• RQ4 How do experimentally accessible quantities like local and non-local conductance evolve with increasing coupling, and can they be used to identify the optimal sweet spot?
• RQ5 Can a practical experimental protocol be devised to tune into a high-gap sweet spot using conductance spectroscopy and charge stability diagrams?

Key findings

• Increasing the dot-hybrid coupling strength (t) from weak to strong regime (t ~ Δ₀) leads to a significant enhancement of the excitation gap, reaching ~75 μeV in agreement with recent experimental results.
• Poor man’s Majorana zero modes persist in the strong-coupling regime, with their wavefunctions remaining spatially separated on the outer dots despite increased hybridization with central Andreev bound states.
• The non-local conductance G_LR increases substantially with increasing t, while G_RL remains relatively stable, indicating a breakdown of the weak-coupling effective picture and enhanced sensitivity to the left dot’s BCS charge.
• The maximum non-local conductance signal for G_LR strengthens significantly with t, attributed to increased BCS charge of the excited state in the left dot, providing a clear experimental signature.
• The system shows reduced sensitivity to local perturbations in the strong-coupling regime, enhancing robustness for potential topological qubit applications.
• A practical experimental protocol—using single-dot conductance spectroscopy and charge stability diagrams—enables reliable tuning into the high-gap sweet spot, validated by parallel experiments achieving ~75 μeV gap.