From Andreev to Majorana bound states in hybrid superconductor-semiconductor nanowires (1911.04512v3)

Abstract: Electronic excitations above the ground state must overcome an energy gap in superconductors with spatially-homogeneous s-wave pairing. In contrast, inhomogeneous superconductors such as those with magnetic impurities or weak links, or heterojunctions containing normal metals or quantum dots, can host subgap electronic excitations that are generically known as Andreev bound states (ABSs). With the advent of topological superconductivity, a new kind of ABS with exotic qualities, known as Majorana bound state (MBS), has been discovered. We review the main properties of ABSs and MBSs, and the state-of-the-art techniques for their detection. We focus on hybrid superconductor-semiconductor nanowires, possibly coupled to quantum dots, as one of the most flexible and promising experimental platforms. We discuss how the combined effect of spin-orbit coupling and Zeeman field in these wires triggers the transition from ABSs into MBSs. We show theoretical progress beyond minimal models in understanding experiments, including the possibility of different types of robust zero modes that may emerge without a band-topological transition. We examine the role of spatial non-locality, a special property of MBS wavefunctions that, together with non-Abelian braiding, is the key to realizing topological quantum computation.

• The paper demonstrates how tuning spin-orbit coupling and magnetic fields in hybrid nanowires enables the transition from Andreev to Majorana bound states.
• It employs tunneling spectroscopy, Josephson junction experiments, and advanced device fabrication to distinguish between trivial and topological states.
• The study outlines key challenges and strategies for integrating Majorana bound states into scalable topological quantum computing architectures.

Insights into Andreev and Majorana Bound States in Hybrid Superconductor-Semiconductor Nanowires

The paper "From Andreev to Majorana bound states in hybrid superconductor-semiconductor nanowires" provides an extensive exploration of the electronic states that exist in hybrid systems formed by combining superconductors (SCs) with semiconductors. The paper primarily focuses on two types of bound states: Andreev bound states (ABSs) and Majorana bound states (MBSs). The work highlights experimental and theoretical advances that delineate the formation, properties, and detection methodologies of these states, which are fundamental to the pursuit of topological quantum computing.

Andreev Bound States (ABSs)

Invariants of superconductors, Andreev-bound states are subgap states associated with inhomogeneous superconductors and are pivotal to understanding superconductor-semiconductor hybrids. These states arise from Andreev reflections, where an electron entering a superconductor from a normal region is reflected as a hole, facilitating the formation of Cooper pairs in the superconductor. ABSs manifest in devices where such reflections occur multiple times, such as in short superconductor-normal-superconductor (SNS) junctions. The dynamics of ABSs, particularly how their energies depend on phase differences across these junctions, offer key insights into Josephson effects and superconducting quantum bits.

Transition to Majorana Bound States (MBSs)

The pursuit of exotic Majorana bound states, which exhibit non-Abelian statistics, occupies a central place in advancing quantum computing due to their proposed capability for topological quantum computation. The paper elaborates on the transition from ABSs to MBSs facilitated by enhanced spin-orbit coupling and an external Zeeman field. In appropriate conditions, such as low electron densities and specific phase transitions driven by magnetic fields, these hybrid systems can evolve into topological superconductors. This scenario leads to the formation of MBSs at the ends of the superconducting segment, making them distinctly robust against certain types of local perturbations and noise.

Theoretical and Experimental Techniques

Key theoretical models that guide these investigations involve manipulating semiconductor nanowire systems with varying operational parameters such as chemical potential, effective mass, and spin-orbit coupling. The paper demonstrates how these parameters impact both the formation of MBSs and the manifestation of the topological phase transition. From an experimental perspective, several sophisticated techniques are employed:

1. Tunneling Spectroscopy: Used prevalently to observe zero-energy states indicative of MBSs. Tunneling conductance measurements reveal specific signatures that suggest topological phase transitions, often correlated with the applied magnetic field.
2. Josephson Junction Experiments: Phase-dependent properties of ABSs and MBSs are scrutinized through supercurrent measurements, probing their energy levels using microwave spectroscopy techniques.
3. Device Fabrication Techniques: Advances in device fabrication, such as epitaxial growth of superconductors on semiconductors, have led to more robust induced superconductivity, crucial for distinguishing between trivial Andreev processes and genuine Majorana signatures.

Implications and Future Directions

Despite significant progress, the challenge of conclusively distinguishing true MBSs from other trivial zero-energy states remains. This distinction is critical for realizing the non-Abelian braiding operations that are essential for practical implementations of topological quantum computers. The paper also underscores the impact of device imperfections and other inhomogeneities that can lead to misleading signals. Hence, increasing the understanding of quasi-MBSs and exceptional point realized states, among other quasi-phenomena, is imperative.

Future research directions are likely to focus on refining detection methods to unambiguously confirm MBSs' presence and to engineer devices that harness their non-local quantum information properties. This will likely involve further integration of hybrid devices into scalable quantum networks incorporating quantum dots, nanowire junctions, and advanced topological materials.

In summary, this paper provides a pathway towards realizing MBSs in semiconductor-superconductor hybrids and illuminates both the promises and challenges that accompany the technological leap towards fault-tolerant quantum computing. The insights gained from these nanowire systems continue to enrich the field of condensed matter physics and quantum technology.