Robust poor man's Majorana zero modes using Yu-Shiba-Rusinov states

Majorana bound states (MBSs), exotic quasiparticles predicted to be their own antiparticles, are highly sought after for their potential in fault-tolerant quantum computing. Kitaev chains, theoretical one-dimensional structures consisting of spinless fermions with superconducting pairing and hopping terms, are a promising platform for creating and manipulating MBSs. Even a minimal two-site Kitaev chain can host Majorana zero modes, known as "poor man's Majoranas" (PMMs). While PMMs lack the topological protection of longer chains, they already exhibit robustness to local perturbations and quadratic protection against global chemical potential fluctuations. This makes them attractive for near-term quantum information processing experiments. Previous attempts to realize PMMs using coupled quantum dots (QDs) in hybrid semiconductor-superconductor nanowires faced challenges in achieving a sufficient energy gap between the PMM and excited states, as well as significant sensitivity to charge fluctuations, hindering their application as qubits. This research explores the use of spin-polarized YSR states, which form when QDs are strongly hybridized with a superconductor, as a more robust platform for creating PMMs. The expectation is that this approach will enhance the energy gap, reduce charge noise sensitivity and lead to a higher yield of functional devices.

The theoretical foundation for PMMs lies in the Kitaev chain model and its minimal two-site realization. Previous experimental work has demonstrated the creation of PMMs in coupled QDs, but these implementations suffered from limitations in energy scale and noise sensitivity. The use of YSR states as building blocks for topological superconductivity has been proposed theoretically, with several studies exploring the formation and properties of YSR states in various systems, including quantum dots coupled to superconductors. However, the creation of robust PMMs leveraging the properties of YSR states has not yet been successfully demonstrated. This work aims to bridge this gap and demonstrate the advantages of using YSR states in creating more robust and scalable PMM-based qubits.

The researchers fabricated a hybrid InSb nanowire device partly covered with a superconducting Al film. Two QDs were defined on either side of the superconducting segment using gate-defined tunnel barriers. The electrochemical potentials of the QDs were controlled by plunger gates, and the couplings between the QDs and the superconductor were controlled by tunnel gates. The device was characterized using a combination of techniques: scanning electron microscopy for imaging, charge stability diagrams (CSDs) and differential conductance spectroscopy to probe the energy levels and couplings. The CSDs were obtained by measuring the zero-bias conductance as a function of the QD plunger gate voltages. Differential conductance spectroscopy provided detailed information on the energy spectrum. A three-site model was used to describe the system, treating the superconducting hybrid segment as a single Andreev bound state (ABS) coupled to the two QDs. The model incorporated spin-conserving and spin-flipping tunneling, which are crucial for mediating the hopping and pairing terms of the Kitaev Hamiltonian. Importantly, the researchers systematically tuned the hybridization between the QDs and the superconductor to achieve strong coupling and formation of YSR states. The amplitudes of elastic cotunneling (ECT) and crossed Andreev reflection (CAR), which determine the hopping and pairing terms respectively, were extracted by analyzing the energy splitting in the measured spectra. To mitigate the effects of series resistance, the researchers employed a correction method based on the observed superconducting gap. They use a model that simplifies the low-energy spectrum of the coupled YSR system to a spinless PMM model, enabling extraction of the relevant coupling parameters (ECT and CAR) from the energy eigenvalues. The experimental data were analyzed by fitting the measured spectra with Gaussian functions and comparing the results with theoretical calculations. The robustness of the PMM states against local and global perturbations was assessed by systematically varying the gate voltages.

The research successfully created and characterized PMMs using YSR states. The key findings include: 1. **Large Energy Gap:** The observed energy gap between the PMM ground state and excited states reached 76 μeV, a significant improvement compared to previous experiments. This substantial gap is crucial for protecting the PMM from thermal excitations and enabling faster quantum operations. 2. **Reduced Sensitivity to Charge Fluctuations:** The sensitivity of the PMM states to charge noise affecting the QDs was reduced by two orders of magnitude compared to PMMs based on non-proximitized QDs. This robustness is a major step towards building stable Majorana-based qubits. 3. **Systematic Control of Couplings:** By tuning the electrochemical potential of the ABS, the researchers could systematically control the amplitudes of ECT and CAR couplings between the YSR states. This precise control allowed them to reach the PMM sweet spot (t ≈ Δ), where the hopping and pairing terms are balanced. 4. **Confirmation by Theoretical Model:** The experimental observations were consistent with theoretical predictions based on a three-site model incorporating the YSR states and their strong coupling to the ABS. The model accurately reproduced the evolution of the CSDs and the energy spectra. 5. **Improved Robustness:** The PMMs formed using YSR states exhibited enhanced stability against local perturbations of the QDs electrochemical potential. This improved robustness is attributed to the stronger coupling between the YSR states and the reduced charge dispersion compared to non-proximitized QDs.

The results demonstrate the significant advantage of using YSR states as building blocks for creating robust PMMs. The improved energy scale and reduced noise sensitivity achieved in this work represent major steps towards realizing scalable Majorana-based qubits. The observed robustness suggests that even short Kitaev chains, such as those with 3-5 sites, could potentially achieve coherence times comparable to those predicted for longer continuous nanowires. The ability to systematically control the couplings between the YSR states provides a powerful tool for further research on Majorana qubits and other quantum phenomena. The findings are also relevant to the development of Andreev spin qubits, long-distance spin qubit coupling, and analog quantum simulations of Fermi-Hubbard systems with superconductivity.

This research successfully demonstrated a significant improvement in the robustness and scalability of PMMs using YSR states. The larger energy gap and reduced noise sensitivity offer compelling advantages for the development of Majorana-based qubits. The systematic control of couplings opens avenues for exploring longer Kitaev chains and realizing more complex quantum circuits. Future research could focus on increasing the number of sites in the Kitaev chain to further enhance topological protection and investigate the non-Abelian exchange statistics of these improved PMMs.

While this study demonstrated a significant improvement in PMM robustness, some limitations remain. The PMMs are not fully topologically protected against noise affecting the tunnel couplings. Further studies are needed to fully understand and mitigate the effects of such noise. Although the device architecture and methodolgy are potentially scalable, the fabrication process remains complex and may still present challenges for larger-scale integration.