Vortex state in a doped Mott insulator

We analyze the recent vortex core spectroscopy data on cuprate superconductors and discuss what can be learned from them about the nature of the ground state in these compounds. We argue that the data are inconsistent with the assumption of a simple metallic ground state and exhibit characteristics of a doped Mott insulator. A theory of the vortex core in such a doped Mott insulator is developed based on the $U\left(1\right)\mathrm{}$ gauge-field slave boson model. In the limit of vanishing gauge-field stiffness such a theory predicts two types of singly quantized vortices: an insulating “holon” vortex in the underdoped and a metallic “spinon” vortex in the overdoped region of the phase diagram. We argue that the holon vortex exhibits a pseudogap excitation spectrum in its core qualitatively consistent with the existing experimental data on ${\mathrm{Bi}}_2{\mathrm{Sr}}_2{\mathrm{CaCu}}_2{\mathrm{O}}_8.$ As a test of this theory we propose that the spinon vortex with a metallic core might be observable in the heavily overdoped samples.