Superconducting vortex-charge measurement using cavity electromechanics

As the magnetic field penetrates the surface of a superconductor, it results in the formation of flux-vortices. It has been predicted that the flux-vortices will have a charged vortex core and create a dipolelike electric field. Such a charge trapping in vortices is particularly enhanced in high-T$_c$ superconductors (HTS). Here, we integrate a mechanical resonator made of a thin flake of HTS Bi$_2$Sr$_2$CaCu$_2$O$_{8+\delta}$ into a microwave circuit to realize a cavity-electromechanical device. Due to the exquisite sensitivity of cavity-based devices to the external forces, we directly detect the charges in the flux-vortices by measuring the electromechanical response of the mechanical resonator. Our measurements reveal the strength of surface electric dipole moment due to a single vortex core to be approximately 30~$|e|a_B$, equivalent to a vortex charge per CuO$_2$ layer of $3.7\times 10^{-2}|e|$, where $a_B$ is the Bohr radius and $e$ is the electronic charge.