Session X58: Distinguishing Trivial and Topological Superconducting States in Hybrid Devices

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Josephson junctions hosting Majorana fermions have been predicted to exhibit a 4π periodic current phase relation. One experimental consequence of this periodicity is the disappearance of odd steps in Shapiro steps experiments. Experimentally, missing odd Shapiro steps have been observed in a number of materials systems with strong spin-orbit coupling and have been interpreted in the context of topological superconductivity. We report on missing odd steps in topologically trivial Josephson junctions fabricated on InAs quantum wells. We ascribe our observations to the high transparency of our junctions allowing Landau-Zener transitions. The probability of these processes is shown to be independent of the drive frequency. We analyze our results using a bi-modal transparency distribution which demonstrates that only few modes carrying 4π periodic current are sufficient to describe the disappearance of odd steps. Our findings highlight the elaborate circumstances that have to be considered in the investigation of the 4π Josephson junctions in relationship to topological superconductivity.   

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Understanding excitations of the Cooper pair condensate in a superconductor is crucial for many applications in quantum information processing. A remarkable example is the possibility of creating topologically-protected non-local qubits based on quasiparticle excitations at no energy cost, so-called Majorana zero modes. Their unambiguous detection has been impeded by the ubiquitous presence of non-topological Andreev bound states pinned to zero energy. It has thus become of utmost importance to find ways to experimentally establish the physical origin of subgap states in a controlled way. Here we show that the magnetic flux tunability of full-shell nanowires allows to clearly identify subgap levels as Andreev bound states. Transport spectroscopy reveals them as Yu-Shiba-Rusinov bound states, resulting from a quantum spin impurity --a quantum dot forming within the tunneling region-- that forms Kondo-like singlets with quasiparticles in the superconductor. The magnetic flux, both through the Little-Parks modulation of the gap and the Zeeman effect, induces quantum phase transitions between physically-different ground states, resulting in subgap level crossings at zero energy -zero bias peaks in tunneling conductance- unrelated to Majoranas. Our understanding of the complex interplay of different physical effects, fully supported by theory, offers a starting point for systematic experiments towards an unambiguous topological classification of zero modes.   

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Semiconductor nanowires with proximity-induced superconductivity are leading contenders for manifesting Majorana fermions in condensed matter. However, unambiguous detection of these quasiparticles is controversial, and one proposed method is to show that the peak in the conductance at zero applied bias is quantized to the value of 2e^2/h. Here, we fabricate devices that feature tunnel probes on both ends of a nanowire and observe zero-bias peaks that are close to the quantized value. These peaks evolve with the tunnel barrier strength and magnetic field in a way that is consistent with Majorana zero modes. However, we only find nearly-quantized zero-bias peaks localized to one end of the nanowire, while conductance dips are observed for the same parameters at the other end. Yet if peaks come from Majorana modes they should be observed at both ends simultaneously. These results imply either a topological segment shorter than the superconducting segment which is 400 nm, or a non-Majorana origin of the observed quantized zero-bias peaks. We also lay out procedures for assessing the nonlocality of subgap wave functions and provide a classification of nanowire bound states based on their localization.   

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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 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 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. In particular, we focus on states created in wires with smooth confinement, known in the field as a quasi-MBSs, partially-separated ABSs, non-topological MBSs, or exceptional-point MBSs in systems open to reservoirs. We examine the role of their spatial non-locality, a special property of MBS wavefunctions that, together with non-Abelian braiding, is the key to realizing topological quantum computation.

This work has been published as a review in Nature Reviews Physics 2, 575–594 (2020).   

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A quantum anomalous Hall (QAH) insulator coupled to an s-wave superconductor is predicted to harbor chiral Majorana fermions, excitations that could serve as topological qubits. A recent experiment interprets the half-quantized two-terminal conductance plateau as evidence for these excitations in a millimeter-size QAH-Nb hybrid device. However, non-Majorana mechanisms can also generate similar signatures, especially in disordered samples. In this talk, I will introduce our recent progress in this direction. We first studied the contact transparency between the QAH insulator and Nb layers using Andreev reflection spectroscopy measurements. In the QAH-Nb devices with high interface transparency, we found that the two-terminal conductance across the QAH insulator-Nb hybrid device is always half-quantized throughout the entire magnetic field range with well-aligned magnetization. Our systematic measurements and careful analysis of the data showed that the half-quantized two-terminal conductance plateau observed in such a QAH-Nb device is unlikely to arise from chiral Majorana fermion excitations.