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1. Signature of a pair of Majorana zero modes in superconducting gold surface states

   https://doi.org/10.1073/pnas.1919753117  

   Manna, Sujit ; Wei, Peng ; Xie, Yingming ; Law, Kam Tuen ; Lee, Patrick A. ; Moodera, Jagadeesh S. ( April 2020 , Proceedings of the National Academy of Sciences)

   Under certain conditions, a fermion in a superconductor can separate in space into two parts known as Majorana zero modes, which are immune to decoherence from local noise sources and are attractive building blocks for quantum computers. Promising experimental progress has been made to demonstrate Majorana zero modes in materials with strong spin–orbit coupling proximity coupled to superconductors. Here we report signatures of Majorana zero modes in a material platform utilizing the surface states of gold. Using scanning tunneling microscope to probe EuS islands grown on top of gold nanowires, we observe two well-separated zero-bias tunneling conductance peaks aligned along the direction of the applied magnetic field, as expected for a pair of Majorana zero modes. This platform has the advantage of having a robust energy scale and the possibility of realizing complex designs using lithographic methods.

    

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2. Flux-induced topological superconductivity in full-shell nanowires

   https://doi.org/10.1126/science.aav3392  

   Vaitiekėnas, S. ; Winkler, G. W. ; van Heck, B. ; Karzig, T. ; Deng, M. -T. ; Flensberg, K. ; Glazman, L. I. ; Nayak, C. ; Krogstrup, P. ; Lutchyn, R. M. ; et al ( March 2020 , Science)

   Hybrid semiconductor-superconductor nanowires have emerged as a promising platform for realizing topological superconductivity (TSC). Here, we present a route to TSC using magnetic flux applied to a full superconducting shell surrounding a semiconducting nanowire core. Tunneling into the core reveals a hard induced gap near zero applied flux, corresponding to zero phase winding, and a gapped region with a discrete zero-energy state around one applied flux quantum, corresponding to 2π phase winding. Theoretical analysis indicates that the winding of the superconducting phase can induce a transition to a topological phase supporting Majorana zero modes. Measured Coulomb blockade peak spacing around one flux quantum shows a length dependence that is consistent with the existence of Majorana modes at the ends of the nanowire.

    

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3. The demonstration of Majorana zero modes in scalable gold nanowires

   https://doi.org/10.1117/12.2565976  

   Wei, Peng ; Manna, Sujit ; Xie, Yingming ; Law, Kam Tuen ; Lee, Patrick ; Moodera, Jagadeesh ( August 2020 , Spintronics XIII)

   Drouhin, Henri-Jean M. ; Wegrowe, Jean-Eric ; Razeghi, Manijeh (Ed.)

   Majorana zero modes (MZMs) are expected to emerge in material heterostructures combining superconductivity, ferromagnetism, and spin-orbit coupling (SOC). Particularly, inducing superconductivity and magnetic exchange interactions in well-defined Shockley surface states (SS) of high quality ultrathin Au(111) layers, which intrinsically have strong SOC, has been predicted as an excellent platform for MBS. In this talk, our success in creating such heterostructure in epitaxially grown Au(111) heterostructures will be presented. Signatures of superconductivity induced in the two-dimensional SS of Au(111) thin film are observed by means of electron tunneling spectroscopy. The behavior of such superconducting state under a planar Zeeman field will be shown. Evidence of a pair of MZMs in a fabricated Au(111) nanowire system will be demonstrated. 

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4. Tuning interactions between spins in a superconductor

   https://doi.org/10.1073/pnas.2024837118  

   Ding, Hao ; Hu, Yuwen ; Randeria, Mallika T. ; Hoffman, Silas ; Deb, Oindrila ; Klinovaja, Jelena ; Loss, Daniel ; Yazdani, Ali ( March 2021 , Proceedings of the National Academy of Sciences)

   Novel many-body and topological electronic phases can be created in assemblies of interacting spins coupled to a superconductor, such as one-dimensional topological superconductors with Majorana zero modes (MZMs) at their ends. Understanding and controlling interactions between spins and the emergent band structure of the in-gap Yu–Shiba–Rusinov (YSR) states they induce in a superconductor are fundamental for engineering such phases. Here, by precisely positioning magnetic adatoms with a scanning tunneling microscope (STM), we demonstrate both the tunability of exchange interaction between spins and precise control of the hybridization of YSR states they induce on the surface of a bismuth (Bi) thin film that is made superconducting with the proximity effect. In this platform, depending on the separation of spins, the interplay among Ruderman–Kittel–Kasuya–Yosida (RKKY) interaction, spin–orbit coupling, and surface magnetic anisotropy stabilizes different types of spin alignments. Using high-resolution STM spectroscopy at millikelvin temperatures, we probe these spin alignments through monitoring the spin-induced YSR states and their energy splitting. Such measurements also reveal a quantum phase transition between the ground states with different electron number parity for a pair of spins in a superconductor tuned by their separation. Experiments on larger assemblies show that spin–spin interactions can be mediated in a superconductor over long distances. Our results show that controlling hybridization of the YSR states in this platform provides the possibility of engineering the band structure of such states for creating topological phases.

    

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5. Spectral properties, topological patches, and effective phase diagrams of finite disordered Majorana nanowires

   https://doi.org/10.1103/PhysRevB.108.085416  

   Das Sarma, Sankar ; Sau, Jay D. ; Stanescu, Tudor D. ( August 2023 , Physical Review B)

   We consider theoretically the physics of bulk topological superconductivity accompanied by boundary non- Abelian Majorana zero modes in semiconductor-superconductor (SM-SC) hybrid systems consisting of finite wires in the presence of correlated disorder arising from random charged impurities. We find the system to manifest a highly complex behavior due to the subtle interplay between finite wire length and finite disorder, leading to copious low-energy in-gap states throughout the wire and considerably complicating the interpretation of tunneling spectroscopic transport measurements used extensively to search forMajorana modes. The presence of disorder-induced low-energy states may lead to the nonexistence of end Majorana zero modes even when tunneling spectroscopy manifests zero-bias conductance peaks in local tunneling and signatures of bulk gap closing/reopening in the nonlocal transport. In short wires within the intermediate disorder regime, apparent topology may manifest in small ranges (“patches”) of parameter values, which may or may not survive the longwire limit depending on various details. Because of the dominance of disorder-induced in-gap states, the system may even occasionally have an appropriate topological invariant without manifesting isolated end Majorana zero modes. We discuss our findings in the context of a recent breakthrough experiment from Microsoft reporting the simultaneous observations of zero-bias conductance peaks in local tunneling and gap opening in nonlocal transport within small patches of parameter space. Based on our analysis, we believe that the disorder strength to SC-gap ratio must decrease further for the definitive realization of non-Abelian Majorana zero modes in SM-SC devices. 

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