Spin-resolved Andreev levels and parity crossings in hybrid superconductor-semiconductor nanostructures (1302.2611v3)

Abstract: The hybrid combination of superconductors and low-dimensional semiconductors offers a versatile ground for novel device concepts, such as sources of spin-entangled electrons, nanoscale superconducting magnetometers, or recently proposed qubits based on topologically protected Majorana fermions. The underlying physics behind such hybrid devices ultimately rely on the magnetic properties of sub-gap excitations, known as Andreev levels. Here we report the Zeeman effect on the Andreev levels of a semiconductor nanowire quantum dot (QD) strongly coupled to a conventional superconductor. The combination of the large QD g-factor with the large superconductor critical magnetic field allows spin degeneracy to be lifted without suppressing superconductivity. We show that a Zeeman-split Andreev level crossing the Fermi energy signals a quantum phase transition in the ground state of the superconductivity-induced QD, denoting a change in the fermionic parity of the system. This transition manifests itself as a zero-bias conductance anomaly appearing at a finite magnetic field, with properties that resemble those expected for Majorana fermions in a topological superconductor. Although the herein reported zero-bias anomalies do not hold any relation with topological superconductivity, the observed parity transitions can be regarded as precursors of Majorana modes in the long-wire limit.

• The paper demonstrates that Zeeman splitting lifts the spin degeneracy of Andreev levels, triggering quantum phase transitions via parity crossings.
• The paper correlates experimental nanowire data with Hartree-Fock theory to reveal the interplay between superconducting proximity effects and Coulomb blockade.
• The paper’s insights on magnetic field effects and electron pairing offer practical guidance for optimizing quantum devices and spintronic applications.

Analysis of Spin-Resolved Andreev Levels and Parity Crossings in Hybrid Superconductor-Semiconductor Nanostructures

The paper presented in the paper investigates the spin-resolved Andreev levels and their effects within hybrid superconductor-semiconductor nanostructures, specifically focusing on the manifestation of parity crossings. This research is situated within the broader context of developing advanced quantum devices, including spin-entangled electron sources and potential qubits based on Majorana fermions. The authors utilize semiconductor nanowire quantum dots significantly coupled to superconductors to explore these phenomena.

Key Findings

1. Zeeman Effect on Andreev Levels: The paper examines how the application of a magnetic field lifts the spin degeneracy of Andreev levels within quantum dots that possess large $g$-factors in combination with superconductors having high critical magnetic fields. This splitting leads to distinct quantum phase transitions marked by changes in the fermionic parity of the system.
2. Quantum Phase Transitions and Zero-Bias Conductance: A crucial observation in the work is the quantum phase transition, signaled by Andreev levels crossing the Fermi energy. This transition is associated with a zero-bias conductance peak at finite magnetic fields. The resemblance of this phenomenon to expected properties of Majorana fermions in topological superconductors is noted, though these findings do not directly relate to topological superconductivity.
3. Proximity Effect and Coulomb Blockade: In the superconducting proximity effect within quantum dots, there exists competition with Coulomb blockade phenomena. The paper provides a detailed analysis of this interplay, focusing on how superconductivity-induced electron pairing is counterbalanced by local charge repulsion, stabilizing distinct electronic states within the quantum dot.
4. Experimental and Theoretical Correlation: The research includes experimental data collected from nanowire-based devices, verified against theoretical predictions using self-consistent Hartree-Fock theory. The theoretical framework provides a comprehensive match with the experimental observations, supporting interpretations concerning spin-resolved Andreev states and parity transitions.

Implications and Future Directions

• Quantum Computing: The findings concerning parity crossings in spin-resolved Andreev levels contribute to the ongoing discourse on realizing qubits with topologically protected modes, such as Majorana fermions. While the results do not directly demonstrate topological superconductivity, they offer insights into precursor states that may evolve into long-wire Majorana modes.
• Device Optimization: Understanding the interplay of different energy scales (e.g., $\Delta$, $U$, and $\Gamma_S$) in these structures could lead to the optimization of quantum dots and superconducting device interfaces, crucial for enhancing the operational stability of quantum devices.
• Spintronics: By elucidating the effects of magnetic fields on Andreev levels and ground state parities, this work lays the groundwork for advancements in spintronic applications that exploit quantum coherence at the nanoscale.
• Future Research: Future experimental efforts might focus on extending the length of the nanowires to probe the hypothesized evolution from normal Andreev levels to Majorana bound states. This could advance the design of more robust quantum devices leveraging the unique properties of topologically non-trivial states.

In summary, the paper provides a rigorous examination of the complex interactions in hybrid superconductor-semiconductor systems, revealing critical insights into the quantum mechanics underlying future quantum technologies.