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Register a new userAnisotropy of Vortex-Liquid and Vortex-Solid Phases in Single Crystals of Bi$_2$Sr$_2$CaCu$_2$O$_{8+delta}$: Violation of the Scaling Law
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The vortex-liquid and vortex-solid phases in single crystals of Bi$_2$Sr$_2$CaCu$_2$O$_{8+delta}$ placed in tilted magnetic fields are studied by in-plane resistivity measurements using the Corbino geometry to avoid spurious surface barrier effects. It was found that the anisotropy of the vortex-solid phase increases with temperature and exhibits a maximum at $Tapprox 0.97 T_c$. In contrast, the anisotropy of the vortex-liquid rises monotonically across the whole measured temperature range. The observed behavior is discussed in the context of dimensional crossover and thermal fluctuations of vortices in the strongly layered system.
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A magnetic field applied to type-II superconductors introduces quantized vortices that locally quench superconductivity, providing a unique opportunity to investigate electronic orders that may compete with superconductivity. This is especially true in cuprate superconductors in which mutual relationships among superconductivity, pseudogap, and broken-spatial-symmetry states have attracted much attention. Here we observe energy and momentum dependent bipartite electronic superstructures in the vortex core of Bi$_2$Sr$_2$CaCu$_2$O$_{8+delta}$ using spectroscopic-imaging scanning tunneling microscopy (SI-STM). In the low-energy range where the nodal Bogoliubov quasiparticles are well-defined, we show that the quasiparticle scattering off vortices generates the electronic superstructure known as vortex checkerboard. In the high-energy region where the pseudogap develops, vortices amplify the broken-spatial-symmetry patterns that preexist in zero field. These data reveal canonical d-wave superconductivity near the node, yet competition between superconductivity and broken-spatial-symmetry states near the antinode.
Competition with magnetism is at the heart of high temperature superconductivity, most intensely felt near a vortex core. To investigate vortex magnetism we have developed a spatially resolved probe using nuclear magnetic resonance. Our spin-lattice-relaxation spectroscopy is spatially resolved both within a conduction plane as well as from one plane to another. With this approach we have found a spin-density wave associated with the vortex core in Bi$_2$Sr$_2$CaCu$_2$O$_{8+delta}$, which is expected from scanning tunneling microscope observations of checkerboard patterns in the local density of electronic states.[1] We determine both the spin-modulation amplitude and decay length from the vortex core in fields up to H=30 T.
Low magnetic field scanning tunneling spectroscopy of individual Abrikosov vortices in heavily overdoped Bi$_2$Sr$_2$CaCu$_2$O$_{8+delta}$ unveils a clear d-wave electronic structure of the vortex core, with a zero-bias conductance peak at the vortex center that splits with increasing distance from the core. We show that previously reported unconventional electronic structures, including the low energy checkerboard charge order in the vortex halo and the absence of a zero-bias conductance peak at the vortex center, are direct consequences of short inter-vortex distance and consequent vortex-vortex interactions prevailing in earlier experiments.
We present a scanning tunneling spectroscopy study on quasiparticle states in vortex cores in Bi$_2$Sr$_2$CaCu$_2$O$_{8+delta}$. The energy of the observed vortex core states shows an approximately linear scaling with the superconducting gap in the region just outside the core. This clearly distinguishes them from conventional localized core states, and is a signature of the mechanism responsible for their discrete appearance in high-temperature superconductors. The energy scaling of the vortex core states also suggests a common nature of vortex cores in Bi$_2$Sr$_2$CaCu$_2$O$_{8+delta}$ and YBa$_2$Cu$_3$O$_{7-delta}$. Finally, the observed vortex core states do not show any dependence on the applied magnetic field in the range from 1 to 6 T.
Fluctuating superconductivity - vestigial Cooper pairing in the resistive state of a material - is usually associated with low dimensionality, strong disorder or low carrier density. Here, we report single particle spectroscopic, thermodynamic and magnetic evidence for persistent superconducting fluctuations in heavily hole-doped cuprate superconductor Bi$_2$Sr$_2$CaCu$_2$O$_{8+delta}$ ($T_c$ = 66~K) despite the high carrier density. With a sign-problem free quantum Monte Carlo calculation, we show how a partially flat band at ($pi$,0) can help enhance superconducting phase fluctuations. Finally, we discuss the implications of an anisotropic band structure on the phase-coherence-limited superconductivity in overdoped cuprates and other superconductors.
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