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1. Two superconducting states with broken time-reversal symmetry in FeSe 1−x S x

   https://doi.org/10.1073/pnas.2208276120  

   Matsuura, Kohei ; Roppongi, Masaki ; Qiu, Mingwei ; Sheng, Qi ; Cai, Yipeng ; Yamakawa, Kohtaro ; Guguchia, Zurab ; Day, Ryan P. ; Kojima, Kenji M. ; Damascelli, Andrea ; et al ( May 2023 , Proceedings of the National Academy of Sciences)

   Iron-chalcogenide superconductors FeSe_1−xS_xpossess unique electronic properties such as nonmagnetic nematic order and its quantum critical point. The nature of superconductivity with such nematicity is important for understanding the mechanism of unconventional superconductivity. A recent theory suggested the possible emergence of a fundamentally new class of superconductivity with the so-called Bogoliubov Fermi surfaces (BFSs) in this system. However, such an ultranodal pair state requires broken time-reversal symmetry (TRS) in the superconducting state, which has not been observed experimentally. Here, we report muon spin relaxation (μSR) measurements in FeSe_1−xS_xsuperconductors for0≤x≤0.22covering both orthorhombic (nematic) and tetragonal phases. We find that the zero-field muon relaxation rate is enhanced below the superconducting transition temperatureT_cfor all compositions, indicating that the superconducting state breaks TRS both in the nematic and tetragonal phases. Moreover, the transverse-fieldμSR measurements reveal that the superfluid density shows an unexpected and substantial reduction in the tetragonal phase (x>0.17). This implies that a significant fraction of electrons remain unpaired in the zero-temperature limit, which cannot be explained by the known unconventional superconducting states with point or line nodes. The TRS breaking and the suppressed superfluid density in the tetragonal phase, together with the reported enhanced zero-energy excitations, are consistent with the ultranodal pair state with BFSs. The present results reveal two different superconducting states with broken TRS separated by the nematic critical point in FeSe_1−xS_x, which calls for the theory of microscopic origins that account for the relation between nematicity and superconductivity.

    

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2. 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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3. Optical spectral weight, phase stiffness, and T c bounds for trivial and topological flat band superconductors

   https://doi.org/10.1073/pnas.2106744118  

   Verma, Nishchhal ; Hazra, Tamaghna ; Randeria, Mohit ( August 2021 , Proceedings of the National Academy of Sciences)

   We present exact results that give insight into how interactions lead to transport and superconductivity in a flat band where the electrons have no kinetic energy. We obtain bounds for the optical spectral weight for flat-band superconductors that lead to upper bounds for the superfluid stiffness and the two-dimensional (2D)$T_c$. We focus on on-site attraction$\left|U\right|$on the Lieb lattice with trivial flat bands and on the π-flux model with topological flat bands. For trivial flat bands, the low-energy optical spectral weight${\tilde{D}}_{\text{low}}\le \tilde{n}\left|U\right|\mathrm{\Omega }/2$with$\tilde{n}=min\left(n,2-n\right)$, where n is the flat-band density and Ω is the Marzari–Vanderbilt spread of the Wannier functions (WFs). We also obtain a lower bound involving the quantum metric. For topological flat bands, with an obstruction to localized WFs respecting all symmetries, we again obtain an upper bound for${\tilde{D}}_{low}$linear in$\left|U\right|$. We discuss the insights obtained from our bounds by comparing them with mean-field and quantum Monte Carlo results.

    

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4. Possible transport evidence for three-dimensional topological superconductivity in doped β-PdBi2

   https://doi.org/10.1038/s41598-019-48906-7  

   Kolapo, Ayo ; Li, Tingxin ; Hosur, Pavan ; Miller, Jr., John H. ( August 2019 , Scientific Reports)

   Interest in topological states of matter burgeoned over a decade ago with the theoretical prediction and experimental detection of topological insulators, especially in bulk three-dimensional insulators that can be tuned out of it by doping. Their superconducting counterpart, the fully-gapped three-dimensional time-reversal-invariant topological superconductors, have evaded discovery in bulkintrinsic superconductorsso far. The recently discovered topological metalβ-PdBi₂is a unique candidate for tunable bulk topological superconductivity because of its intrinsic superconductivity and spin-orbit-coupling. In this work, we provide experimental transport signatures consistent with fully-gapped 3D time-reversal-invariant topological superconductivity in K-dopedβ-PdBi₂. In particular, we find signatures of odd-parity bulk superconductivity via upper-critical field and magnetization measurements— odd-parity pairing can be argued, given the band structure ofβ-PdBi₂, to result in 3D topological superconductivity. In addition, Andreev spectroscopy reveals surface states protected by time-reversal symmetry which might be possible evidence of Majorana surface states (Majorana cone). Moreover, we find that the undoped bulk system is a trivial superconductor. Thus, we discoverβ-PdBi₂as a unique bulk material that, on doping, can potentially undergo an unprecedented topological quantum phase transition in the superconducting state.

    

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5. Evidence for an edge supercurrent in the Weyl superconductor MoTe 2

   https://doi.org/10.1126/science.aaw9270  

   Wang, Wudi ; Kim, Stephan ; Liu, Minhao ; Cevallos, F. A. ; Cava, R. J. ; Ong, N. P. ( April 2020 , Science)

   Edge supercurrents in superconductors have long been an elusive target. Interest in them has reappeared in the context of topological superconductivity. We report evidence for the existence of a robust edge supercurrent in the Weyl superconductor molybdenum ditelluride (MoTe₂). In a magnetic fieldB, fluxoid quantization generates a periodic modulation of the edge condensate observable as a “fast-mode” oscillation of the critical currentI_cversusB. The fast-mode frequency is distinct from the conventional Fraunhofer oscillation displayed by the bulk supercurrent. We confirm that the fast-mode frequency increases with crystal area as expected for an edge supercurrent. In addition, weak excitation branches are resolved that display an unusual broken symmetry.

    

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