Abstract
We present a detailed study of vortex-core spectroscopy in slightly overdoped ${\mathrm{Bi}}_{2}{\mathrm{Sr}}_{2}{\mathrm{CaCu}}_{2}{\mathrm{O}}_{8+\ensuremath{\delta}}$ using a low-temperature scanning tunneling microscope. Inside the vortex core, we observe a fourfold symmetric modulation of the local density of states with an energy-independent period of ($4.3\ifmmode\pm\else\textpm\fi{}0.3){a}_{0}$. Furthermore, we demonstrate that this square modulation is related to the vortex-core states which are located at $\ifmmode\pm\else\textpm\fi{}6\text{ }\text{ }\mathrm{meV}$. Since the core-state energy is proportional to the superconducting gap magnitude ${\ensuremath{\Delta}}_{p}$, our results strongly suggest the existence of a direct relation between the superconducting state and the local electronic modulations in the vortex core.
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