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1. Observation of backscattering induced by magnetism in a topological edge state

   https://doi.org/10.1073/pnas.2005071117  

   Jäck, Berthold; Xie, Yonglong; Andrei Bernevig, B.; Yazdani, Ali (June 2020, Proceedings of the National Academy of Sciences)

   The boundary modes of topological insulators are protected by the symmetries of the nontrivial bulk electronic states. Unless these symmetries are broken, they can give rise to novel phenomena, such as the quantum spin Hall effect in one-dimensional (1D) topological edge states, where quasiparticle backscattering is suppressed by time-reversal symmetry (TRS). Here, we investigate the properties of the 1D topological edge state of bismuth in the absence of TRS, where backscattering is predicted to occur. Using spectroscopic imaging and spin-polarized measurements with a scanning tunneling microscope, we compared quasiparticle interference (QPI) occurring in the edge state of a pristine bismuth bilayer with that occurring in the edge state of a bilayer, which is terminated by ferromagnetic iron clusters that break TRS. Our experiments on the decorated bilayer edge reveal an additional QPI branch, which can be associated with spin-flip scattering across the Brioullin zone center between time-reversal band partners. The observed QPI characteristics exactly match with theoretical expectations for a topological edge state, having one Kramer’s pair of bands. Together, our results provide further evidence for the nontrivial nature of bismuth and in particular, demonstrate backscattering inside a helical topological edge state induced by broken TRS through local magnetism. 

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2. Detecting and distinguishing Majorana zero modes with the scanning tunnelling microscope

   https://doi.org/10.1038/s42254-021-00328-z  

   Jäck, Berthold; Xie, Yonglong; Yazdani, Ali (January 2021, Nature Reviews Physics)

   null (Ed.)

   One of the most exciting areas of research in quantum condensed matter physics is the push to create topologically protected qubits using non-Abelian anyons. The focus of these efforts has been Majorana zero modes (MZMs), which are predicted to emerge as localized zero-energy states at the ends of 1D topological superconductors. A key role in the search for experimental signatures of these quasiparticles has been played by the scanning tunnelling microscope (STM). The power of high-resolution STM techniques is perhaps best illustrated by their application in identifying MZMs in 1D chains of magnetic atoms on the surface of a superconductor. In this platform, STM spectroscopic mapping has demonstrated the localized nature of MZM zero-energy excitations at the ends of such chains, and experiments with superconducting and magnetic STM tips have been used to uniquely distinguish them from trivial edge modes. Beyond the atomic chains, STM has also uncovered signatures of MZMs in 2D materials and topological surface and boundary states, when they are subjected to the superconducting proximity effect. Looking ahead, future STM experiments may be able to demonstrate the non-Abelian statistics of MZMs. 

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3. 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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4. Topological superconductor candidates PdBi2Te4 and PdBi2Te5 from a generic ab initio strategy

   https://doi.org/10.1038/s41524-023-01144-y  

   Luo, Aiyun; Li, Ying; Qin, Yi; Hu, Jingnan; Wang, Xiaoxu; Zou, Jinyu; Lian, Biao; Xu, Gang (December 2023, npj Computational Materials)

   Abstract Superconducting topological metals (SCTMs) have recently emerged as a promising platform of topological superconductivity (TSC) and Majorana zero modes for quantum computation. Despite their importance in both fundamental research and applications, SCTMs are very rare in nature. Here, we propose a strategy to design SCTMs by intercalating the superconducting units into the topological insulators. A program that characterizes the superconducting BdG Chern number of 2D BdG Hamiltonian from ab initio calculations is also developed. Following this strategy, PdBi₂Te₅and PdBi₂Te₄are found to be experimentally synthesizable and ideal SCTMs. Chiral TSC could be realized in such SCTMs by incorporating topological surface states with Zeeman effect, which can be realized by an external magnetic field or in proximity to ferromagnetic insulator. Our strategy provides a new method for identifying the SCTMs and TSC candidates, and the program makes it possible to design and modulate the TSC candidates from ab initio calculations. 

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5. Engineering parafermions in helical Luttinger liquids

   https://doi.org/10.1117/12.2595632  

   Lyanda-Geller, Yuli; Ponomarenko, Vadim; Wang, Ying; Rokhinson, Leonid (August 2021, SPIE Nanoscience + Engineering)

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

   Parafermions or Fibonacci anyons leading to universal quantum computing, require strongly interacting systems. A leading contender is the fractional quantum Hall effect, where helical channels can arise from counterpropagating chiral modes. These modes have been considered weakly interacting. However, experiments on transport in helical channels in the fractional quantum Hall effect at a 2/3 filling shows current passing through helical channels on the boundary between polarized and unpolarized quantum Hall liquids nine-fold smaller than expected. This current can increase three-fold when nuclei near the boundary are spin polarized. We develop a microscopic theory of strongly interacting helical states and show that emerging helical Luttinger liquid manifests itself as unequally populated charge, spin and neutral modes in polarized and unpolarized fractional quantum Hall liquids. We show that at strong coupling counter-propagating modes of opposite spin polarization emerge at the sample edges, providing a viable path for generating proximity topological superconductivity and parafermions. Current, calculated in strongly interacting picture is in agreement with the experimental data. 

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