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1. 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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2. Hunting for Majoranas

   https://doi.org/10.1126/science.ade0850  

   Yazdani, Ali ; von Oppen, Felix ; Halperin, Bertrand I. ; Yacoby, Amir ( June 2023 , Science)

   BACKGROUND The past decade has witnessed considerable progress toward the creation of new quantum technologies. Substantial advances in present leading qubit technologies, which are based on superconductors, semiconductors, trapped ions, or neutral atoms, will undoubtedly be made in the years ahead. Beyond these present technologies, there exist blueprints for topological qubits, which leverage fundamentally different physics for improved qubit performance. These qubits exploit the fact that quasiparticles of topological quantum states allow quantum information to be encoded and processed in a nonlocal manner, providing inherent protection against decoherence and potentially overcoming a major challenge of the present generation of qubits. Although still far from being experimentally realized, the potential benefits of this approach are evident. The inherent protection against decoherence implies better scalability, promising a considerable reduction in the number of qubits needed for error correction. Transcending possible technological applications, the underlying physics is rife with exciting concepts and challenges, including topological superconductors, non-abelian anyons such as Majorana zero modes (MZMs), and non-abelian quantum statistics.­­ ADVANCES In a wide-ranging and ongoing effort, numerous potential material platforms are being explored that may realize the required topological quantum states. Non-abelian anyons were first predicted as quasiparticles of topological states known as fractional quantum Hall states, which are formed when electrons move in a plane subject to a strong perpendicular magnetic field. The prediction that hybrid materials that combine topological insulators and conventional superconductors can support localized MZMs, the simplest type of non-abelian anyon, brought entirely new material platforms into view. These include, among others, semiconductor-superconductor hybrids, magnetic adatoms on superconducting substrates, and Fe-based superconductors. One-dimensional systems are playing a particularly prominent role, with blueprints for quantum information applications being most developed for hybrid semiconductor-superconductor systems. There have been numerous attempts to observe non-abelian anyons in the laboratory. Several experimental efforts observed signatures that are consistent with some of the theoretical predictions for MZMs. A few extensively studied platforms were subjected to intense scrutiny and in-depth analyses of alternative interpretations, revealing a more complex reality than anticipated, with multiple possible interpretations of the data. Because advances in our understanding of a physical system often rely on discrepancies between experiment and theory, this has already led to an improved understanding of Majorana signatures; however, our ability to detect and manipulate non-abelian anyons such as MZMs remains in its infancy. Future work can build on improved materials in some of the existing platforms but may also exploit new materials such as van der Waals heterostructures, including twisted layers, which promise many new options for engineering topological phases of matter. OUTLOOK Experimentally establishing the existence of non-abelian anyons constitutes an outstandingly worthwhile goal, not only from the point of view of fundamental physics but also because of their potential applications. Future progress will be accelerated if claims of Majorana discoveries are based on experimental tests that go substantially beyond indicators such as zero-bias peaks that, at best, suggest consistency with a Majorana interpretation. It will be equally important that these discoveries build on an excellent understanding of the underlying material systems. Most likely, further material improvements of existing platforms and the exploration of new material platforms will both be important avenues for progress toward obtaining solid evidence for MZMs. Once that has been achieved, we can hope to explore—and harness—the fascinating physics of non-abelian anyons such as the topologically protected ground state manifold and non-abelian statistics. Proposed topological platforms. (Left) Proposed state of electrons in a high magnetic field (even-denominator fractional quantum Hall states) are predicted to host Majorana quasiparticles. (Right) Hybrid structures of superconductors and other materials have also been proposed to host such quasiparticles and can be tailored to create topological quantum bits based on Majoranas. 

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3. Feasibility of measurement-based braiding in the quasi-Majorana regime of semiconductor-superconductor heterostructures

   https://doi.org/10.1103/PhysRevB.102.205101  

   Zeng, Chuanchang ; Sharma, Girish ; Stanescu, Tudor D. ; Tewari, Sumanta ( November 2020 , Physical Review B)

   We discuss the feasibility of measurement-based braiding in semiconductor-superconductor (SM-SC) heterostructures in the so-called quasi-Majorana regime—the topologically-trivial regime characterized by robust zero-bias conductance peaks (ZBCPs) that are due to partially-separated Andreev bound states (ps-ABSs). These low energy ABSs consist of component Majorana bound states (also called quasi-Majorana modes) that are spatially separated by a length scale smaller than the length of the system, in contrast with the Majorana zero modes (MZMs) emerging in the topological regime, which are separated by the length of the wire. In the quasi-Majorana regime, the ZBCPs appear to be robust to various perturbations as long as the energy splitting of the ps-ABS is less than the typical width Ew of the low-energy conductance peaks (Ew ∼ 10–20 μeV). However, the feasibility of measurement-based braiding depends on a different, much smaller, energy scale Em ∼ 0.1 μeV. This energy scale is given by the typical fermion parity-dependent ground state energy shift due to virtual electron transfer between the SM-SC system and a quantum dot used for parity measurements. In this paper we show that it is possible to prepare the SM-SC system in the quasi-Majorana regime with energy splittings below the Em threshold, so that measurement-based braiding is possible in principle. However, despite the apparent robustness of the corresponding ZBCPs, ps-ABSs are in reality topologically unprotected. Starting with ps-ABSs with energy below Em, we identify the maximum amplitudes of different types of (local) perturbations that are consistent with perturbation-induced energy splittings not exceeding the Em limit.We argue that measurements generating perturbations larger than the threshold amplitudes appropriate for Em cannot realize measurement-based braiding in SM-SC heterostructures in the quasi-Majorana regime. We find that, if possible at all, quantum computation using measurement-based braiding in the quasi-Majorana regime would be plagued with errors introduced by the measurement processes themselves, while such errors are significantly less likely in a scheme involving topological MZMs. 

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4. Superconductivity enhancement in phase-engineered molybdenum carbide/disulfide vertical heterostructures

   https://doi.org/10.1073/pnas.2003422117  

   Zhang, Fu ; Zheng, Wenkai ; Lu, Yanfu ; Pabbi, Lavish ; Fujisawa, Kazunori ; Elías, Ana Laura ; Binion, Anna R. ; Granzier-Nakajima, Tomotaroh ; Zhang, Tianyi ; Lei, Yu ; et al ( August 2020 , Proceedings of the National Academy of Sciences)

   Stacking layers of atomically thin transition-metal carbides and two-dimensional (2D) semiconducting transition-metal dichalcogenides, could lead to nontrivial superconductivity and other unprecedented phenomena yet to be studied. In this work, superconducting α-phase thin molybdenum carbide flakes were first synthesized, and a subsequent sulfurization treatment induced the formation of vertical heterolayer systems consisting of different phases of molybdenum carbide—ranging from α to γ′ and γ phases—in conjunction with molybdenum sulfide layers. These transition-metal carbide/disulfide heterostructures exhibited critical superconducting temperatures as high as 6 K, higher than that of the starting single-phased α-Mo 2 C (4 K). We analyzed possible interface configurations to explain the observed moiré patterns resulting from the vertical heterostacks. Our density-functional theory (DFT) calculations indicate that epitaxial strain and moiré patterns lead to a higher interfacial density of states, which favors superconductivity. Such engineered heterostructures might allow the coupling of superconductivity to the topologically nontrivial surface states featured by transition-metal carbide phases composing these heterostructures potentially leading to unconventional superconductivity. Moreover, we envisage that our approach could also be generalized to other metal carbide and nitride systems that could exhibit high-temperature superconductivity. 

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5. Interface-induced superconductivity in magnetic topological insulators

   https://doi.org/10.1126/science.adk1270  

   Yi, Hemian ; Zhao, Yi-Fan ; Chan, Ying-Ting ; Cai, Jiaqi ; Mei, Ruobing ; Wu, Xianxin ; Yan, Zi-Jie ; Zhou, Ling-Jie ; Zhang, Ruoxi ; Wang, Zihao ; et al ( February 2024 , Science)

   The interface between two different materials can show unexpected quantum phenomena. In this study, we used molecular beam epitaxy to synthesize heterostructures formed by stacking together two magnetic materials, a ferromagnetic topological insulator (TI) and an antiferromagnetic iron chalcogenide (FeTe). We observed emergent interface-induced superconductivity in these heterostructures and demonstrated the co-occurrence of superconductivity, ferromagnetism, and topological band structure in the magnetic TI layer—the three essential ingredients of chiral topological superconductivity (TSC). The unusual coexistence of ferromagnetism and superconductivity is accompanied by a high upper critical magnetic field that exceeds the Pauli paramagnetic limit for conventional superconductors at low temperatures. These magnetic TI/FeTe heterostructures with robust superconductivity and atomically sharp interfaces provide an ideal wafer-scale platform for the exploration of chiral TSC and Majorana physics. 

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