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Vortex is a topological defect in the superconducting condensate when a magnetic field is applied to a type-II superconductor, as elucidated by the Ginzburg-Landau theory. Due to the confinement of the quasiparticles by a vortex, it exhibits a circular shaped pattern of bound states with discrete energy levels, as predicted by the Caroli-de Gennes-Matricon theory in 1964. Here, however, we report a completely new type of vortex pattern which is necklace-like in an iron-based superconductor KCa2Fe4As4F2. Our theoretical analysis shows that this necklace-like vortex pattern arises from selective off-shell interference between vortex bound states of opposite angular momenta in the presence of rotational symmetry breaking due to disorders. This fascinating effect can be observed in a system with a small Fermi energy and wave vector, conditions fortuitously met in our samples. Our results not only disclose a novel vortex structure but also provide insights into comprehending the physics of the superconducting condensate., Comment: 29 pages total; 16 pages of main text with 5 figures, 13 pages of supplementary materials with 10 figures

We investigate the magnetic-field dependent evolution of the zero-bias conductance peaks (ZBCPs) on the nanoscale bismuth islands grown on the FeTe$_{0.55}$Se$_{0.45}$ substrate. The ZBCPs can be observed throughout the entire region on these islands, and their characteristics align with the signatures of Majorana zero modes. Remarkably, the evolution of ZBCPs on these islands exhibits anomalous behavior under varying magnetic fields: The magnitude of ZBCPs is first enhanced at weak fields lower than 2 T and then suppressed as the fields further increase. We attribute the non-monotonic evolution of the ZBCPs to the magnetic-field-enhanced topological edge states on these Bi islands. Our findings provide valuable insights into the probable origin of the Majorana zero modes in the Bi-island platform and the magnetic-field response of topological edge states., Comment: 6 pages, 4 figures

In cuprate superconductors, the highest superconducting transition temperature $T_c$ is possessed by the HgBa$_2$Ca$_2$Cu$_3$O$_{8+\delta}$ (Hg-1223) system at ambient pressure, but the reason remains elusive. Here we report the scanning tunneling microscope measurements on the Hg-1223 single crystals with $T_c$ = 134 K. The observed superconducting gaps determined from the tunneling spectra can be categorized into two groups: the smaller gap $\Delta_1$ ranges from about 45 to 70 meV, while the larger gap $\Delta_2$ from about 65 to 98 meV. The observed unprecedentedly large gap value gives a straightforward explanation to the highest $T_c$ in the Hg-1223 system. The largest gap observed here is comparable to the magnetic superexchange energy and excludes any possibility of using phonon pictures to interpret the superconductivity. Interestingly, an extremely strong particle-hole asymmetry is observed in associating with a very robust coherence peak at the bias of the larger gap in the hole branch of the Bogoliubov dispersion. We propose that the observed asymmetry results from the interplay of a flat band (van Hove singularity) in the electronic spectrum and the large superconducting gap in the underdoped layer. This could be the main reason for the strong pairing, and significant enhancement of the density of states in the hole branch of the Bogoliubov band yielding strong phase coherence of Cooper pairs. A scenario based on a trilayer model with an interlayer coupling can give a reasonable explanation. Our results provide deep insight into understanding the mechanism of superconductivity in cuprate superconductors., Comment: 24 pages, 4 figures

Using scanning tunnel microscopy (STM), we investigate the superconductivity and vortex properties in topological insulator Bi$_{2}$Te$_{3}$ thin films grown on the iron-based superconductor FeTe$_{0.55}$Se$_{0.45}$. The proximity-induced superconductivity weakens in the Bi$_{2}$Te$_{3}$ film when the thickness of the film increases. Unlike the elongated shape of vortex cores observed in the Bi$_{2}$Te$_{3}$ film with 2-quintuple-layer (QL) thickness, the isolated vortex cores exhibit a star shape with six rays in the 1-QL film, and the rays are along the crystalline axes of the film. This is consistent with the sixfold rotational symmetry of the film lattice, and the proximity-induced superconductivity is still topologically trivial in the 1-QL film. At a high magnetic field, when the direction between the two nearest neighbored vortices deviates from that of any crystalline axes, two cores connect each other by a pair of adjacent rays, forming a new type of electronic structure of vortex cores. On the 3-QL film, the vortex cores elongate along one of the crystalline axes of the Bi$_{2}$Te$_{3}$ film, similar to the results obtained on 2-QL films. The elongated vortex cores indicate a twofold symmetry of the superconducting gap induced by topological superconductivity with odd parity. This observation confirms possible topological superconductivity in heterostructures with a thickness of more than 2 QLs. Our results provide rich information for the vortex cores and vortex-bound states on the heterostructures consisting of the topological insulator and the iron-based superconductor., Comment: 8 pages, 8 figures