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1. 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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2. Charge-Impurity Effects in Hybrid Majorana Nanowires

   https://doi.org/10.1103/PhysRevApplied.16.054053  

   Woods, Benjamin D.; Das Sarma, Sankar; Stanescu, Tudor D. (November 2021, Physical Review Applied)

   We address an outstanding problem that represents a critical roadblock in the development of the Majorana-based topological qubit using semiconductor-superconductor hybrid structures: the quantitative characterization of disorder effects generated by the unintentional presence of charge impurities within the hybrid device. Given that disorder can have far-reaching consequences for the Majorana physics but is intrinsically difficult to probe experimentally in a hybrid structure, providing a quantitative theoretical description of disorder effects becomes essential. To accomplish this task, we develop a microscopic theory that (i) provides a quantitative characterization of the effective potential generated by a charge impurity embedded inside a semiconductor wire proximity coupled to a superconductor layer by solving selfconsistently the associated three-dimensional Schrödinger-Poisson problem, (ii) describes the low-energy physics of the hybrid structure in the presence of s-wave superconductivity, spin-orbit coupling, Zeeman splitting, and disorder arising from multiple charge impurities by using the results of (i) within a standard free-fermion approach, and (iii) links the microscopic results to experimentally observable features by generating tunneling differential-conductance maps as a function of the control parameters (e.g., Zeeman field and chemical potential). We find that charge impurities lead to serious complications regarding the realization and observation of Majorana zero modes, which have direct implications for the development of Majorana-based qubits. More importantly, our work provides a clear direction regarding what needs to be done for progress in the field, including specific materials-quality and semiconductor-purity targets that must be achieved to create a topological qubit. 

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3. Disentangling types of lattice disorder impacting superconductivity in Sr ₂ RuO ₄ by quantitative local probes

   https://doi.org/10.1063/5.0085279  

   Goodge, Berit H.; Nair, Hari P.; Baek, David J.; Schreiber, Nathaniel J.; Miao, Ludi; Ruf, Jacob P.; Waite, Emily N.; Carubia, Philip M.; Shen, Kyle M.; Schlom, Darrell G.; et al (April 2022, APL Materials)

   The unconventional superconductivity in Sr 2 RuO 4 is infamously susceptible to suppression by small levels of disorder such that it has been most commonly studied in extremely high-purity bulk crystals. Here, we harness local structural and spectroscopic scanning transmission electron microscopy measurements in epitaxial thin films of Sr 2 RuO 4 to disentangle the impact of different types of crystalline disorder on superconductivity. We find that cation off-stoichiometry during growth gives rise to two distinct types of disorder: mixed-phase structural inclusions that accommodate excess ruthenium and ruthenium vacancies when the growth is ruthenium-deficient. Several superconducting films host mixed-phase intergrowths, suggesting this microstructural disorder has relatively little impact on superconductivity. In a non-superconducting film, on the other hand, we measure a high density of ruthenium-vacancies [Formula: see text] with no significant reduction in the crystallinity of the film. The results suggest that ruthenium vacancy disorder, which is hidden to many structural probes, plays an important role in suppressing superconductivity. We discuss the broader implications of our findings to guide the future synthesis of this and other layered systems. 

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4. Josephson Detection of Time Reversal Symmetry Breaking s +/- is Superconductivity in SnTe Nanowires

   Trimble, C.; Wei, M. T.; Kalantre, S. S.; Yuan, N. F.; Liu, P.; Cha, J. J.; Fu, L.; Williams, J. R. (January 2019, ArXiv.org)

   Exotic superconductivity, such as high TC, topological, and heavy-fermion superconductors, often rely on phase sensitive measurements to determine the underlying pairing. Here we investigate the proximity-induced superconductivity in nanowires of SnTe, where a s±is′ superconducting state is produced that lacks the time-reversal and valley-exchange symmetry of the parent SnTe. A systematic breakdown of three conventional characteristics of Josephson junctions -- the DC Josephson effect, the AC Josephson effect, and the magnetic diffraction pattern -- fabricated from SnTe nanowire weak links elucidates this novel superconducting state. Further, the AC Josephson effect reveals evidence of a Majorana bound state, tuned by a perpendicular magnetic field. This work represents the definitive phase-sensitive measurement of novel s±is′ superconductivity, providing a new route to the investigation of fractional vortices, topological superconductivity, topological phase transitions, and new types of Josephson-based devices. 

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5. Observation of a Majorana zero mode in a topologically protected edge channel

   https://doi.org/10.1126/science.aax1444  

   Jäck, Berthold; Xie, Yonglong; Li, Jian; Jeon, Sangjun; Bernevig, B. Andrei; Yazdani, Ali (June 2019, Science)

   null (Ed.)

   Superconducting proximity pairing in helical edge modes, such as those of topological insulators, is predicted to provide a unique platform for realizing Majorana zero modes (MZMs). We used scanning tunneling microscopy measurements to probe the influence of proximity-induced superconductivity and magnetism on the helical hinge states of bismuth(111) films grown on a superconducting niobium substrate and decorated with magnetic iron clusters. Consistent with model calculations, our measurements revealed the emergence of a localized MZM at the interface between the superconducting helical edge channel and the iron clusters, with a strong magnetization component along the edge. Our experiments also resolve the MZM’s spin signature, which distinguishes it from trivial in-gap states that may accidentally occur at zero energy in a superconductor. 

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