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1. Chiral and counter-propagating Majorana fermions in a p-wave superconductor

   https://doi.org/10.1088/1367-2630/ab5cad  

   Hu, Haiping; Satija, Indubala I.; Zhao, Erhai (December 2019, New Journal of Physics)

   Abstract Chiral and helical Majorana fermions are two archetypal edge excitations in two-dimensional topological superconductors. They emerge from systems of different Altland–Zirnbauer symmetries and characterized by $\mathbb{Z}$and ${\mathbb{Z}}_2$topological invariants respectively. It seems improbable to tune a pair of co-propagating chiral edge modes to counter-propagate in a single system without symmetry breaking. Here, we explore the peculiar behaviors of Majorana edge modes in topological superconductors with an additional ‘mirror’ symmetry which changes the bulk topological invariant to $\mathbb{Z}\oplus \mathbb{Z}$type. A theoretical toy model describing the proximity structure of a Chern insulator and ap_x-wave superconductor is proposed and solved analytically to illustrate a direct transition between two topologically nontrivial phases. The weak pairing phase has two chiral Majorana edge modes, while the strong pairing phase is characterized by mirror-graded Chern number and hosts a pair of counter-propagating Majorana fermions protected by the mirror symmetry. The edge theory is worked out in detail, and implications to braiding of Majorana fermions are discussed. 

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2. Designing phase sensitive probes of monopole superconducting order

   https://doi.org/10.1103/PhysRevResearch.6.043189  

   Frazier, Grayson R; Zhang, Junjia; Zhang, Junyi; Sun, Xinyu; Li, Yi (November 2024, Physical Review Research)

   Distinct from familiar $s$-, $p$-, or $d$-wave pairings, the monopole superconducting order represents a novel class of pairing order arising from nontrivial monopole charge of the Cooper pair. In the weak-coupling regime, this order can emerge when pairing occurs between Fermi surfaces with different Chern numbers in, for example, doped Weyl semimetal systems. However, the phase of monopole pairing order is not well-defined over an entire Fermi surface, making it challenging to design experiments sensitive to both its symmetry and topology. To address this, we propose a scheme based on symmetry and topological principles to identify this elusive pairing order through a set of phase-sensitive Josephson experiments. By examining the discrepancy between global and local angular momentum of the pairing order, we can unveil the monopole charge of the pairing order, including for models with higher pair monopole charge $|q_p|=1,2$, and 3. We demonstrate the proposed probe of monopole pairing order through analytic and numerical studies of Josephson coupling in models of monopole superconductor junctions. This work opens a promising avenue to uncover the unique topological properties of monopole pairing orders and to distinguish them from known pairing orders based on spherical harmonic symmetry. Published by the American Physical Society2024 

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3. Chern Insulators at Integer and Fractional Filling in Moiré Pentalayer Graphene

   https://doi.org/10.1103/PhysRevX.15.011045  

   Waters, Dacen; Okounkova, Anna; Su, Ruiheng; Zhou, Boran; Yao, Jiang; Watanabe, Kenji; Taniguchi, Takashi; Xu, Xiaodong; Zhang, Ya-Hui; Folk, Joshua; et al (February 2025, Physical Review X)

   The advent of moiré platforms for engineered quantum matter has led to discoveries of integer and fractional quantum anomalous Hall effects, with predictions for correlation-driven topological states based on electron crystallization. Here, we report an array of trivial and topological insulators formed in a moiré lattice of rhomobohedral pentalayer graphene (R5G). At a doping of one electron per moiré unit cell ( $\nu =1$), we see a correlated insulator with a Chern number that can be tuned between $C=0$and $+1$by an electric displacement field. This is accompanied by a series of additional Chern insulators with $C=+1$originating from fractional fillings of the moiré lattice— $\nu =1/4$, $1/3$, and $2/3$—associated with the formation of moiré-driven topological electronic crystals. At $\nu =2/3$the system exhibits an integer quantum anomalous Hall effect at zero magnetic field, but further develops hints of an incipient $C=2/3$fractional Chern insulator in a modest field. Our results establish moiré R5G as a fertile platform for studying the competition and potential intertwining of integer and fractional Chern insulators. Published by the American Physical Society2025 

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4. Controllable suppression of the unconventional superconductivity in bulk and thin-film ${\mathrm{Sr}}_2{\mathrm{RuO}}_4$ via high-energy electron irradiation

   https://doi.org/10.1103/PhysRevResearch.6.033178  

   Ruf, Jacob P; Noad, Hilary_M L; Grasset, Romain; Miao, Ludi; Zhakina, Elina; McGuinness, Philippa H; Nair, Hari P; Schreiber, Nathaniel J; Kikugawa, Naoki; Sokolov, Dmitry; et al (August 2024, Physical Review Research)

   In bulk ${\mathrm{Sr}}_2{\mathrm{RuO}}_4$, the strong sensitivity of the superconducting transition temperature $T_{\text{c}}$to nonmagnetic impurities provides robust evidence for a superconducting order parameter that changes sign around the Fermi surface. In superconducting epitaxial thin-film ${\mathrm{Sr}}_2{\mathrm{RuO}}_4$, the relationship between $T_{\text{c}}$and the residual resistivity ${\rho }_0$, which in bulk samples is taken to be a proxy for the low-temperature elastic scattering rate, is far less clear. Using high-energy electron irradiation to controllably introduce point disorder into bulk single-crystal and thin-film ${\mathrm{Sr}}_2{\mathrm{RuO}}_4$, we show that $T_{\text{c}}$is suppressed in both systems at nearly identical rates. This suggests that part of ${\rho }_0$in films comes from defects that do not contribute to superconducting pairbreaking and establishes a quantitative link between the superconductivity of bulk and thin-film samples. Published by the American Physical Society2024 

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5. Orbital Ingredients and Persistent Dirac Surface State for the Topological Band Structure in ${\mathrm{FeTe}}_{0.55}{\mathrm{Se}}_{0.45}$

   https://doi.org/10.1103/PhysRevX.14.021043  

   Li, Y-F; Chen, S-D; García-Díez, M; Iraola, M I; Pfau, H; Zhu, Y-L; Mao, Z-Q; Chen, T; Yi, M; Dai, P-C; et al (June 2024, Physical Review X)

   ${\mathrm{FeTe}}_{0.55}{\mathrm{Se}}_{0.45}$(FTS) occupies a special spot in modern condensed matter physics at the intersections of electron correlation, topology, and unconventional superconductivity. The bulk electronic structure of FTS is predicted to be topologically nontrivial due to the band inversion between the $d_{xz}$and $p_z$bands along $\mathrm{\Gamma }\text{−}Z$. However, there remain debates in both the authenticity of the Dirac surface states (DSSs) and the experimental deviations of band structure from the theoretical band inversion picture. Here we resolve these debates through a comprehensive angle-resolved photoemission spectroscopy investigation. We first observe a persistent DSS independent of $k_z$. Then, by comparing FTS with FeSe, which has no band inversion along $\mathrm{\Gamma }\text{−}Z$, we identify the spectral weight fingerprint of both the presence of the $p_z$band and the inversion between the $d_{xz}$and $p_z$bands. Furthermore, we propose a renormalization scheme for the band structure under the framework of a tight-binding model preserving crystal symmetry. Our results highlight the significant influence of correlation on modifying the band structure and make a strong case for the existence of topological band structure in this unconventional superconductor. Published by the American Physical Society2024 

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