Atom chips made of superconducting material can generate
magnetic traps with significantly reduced noise. Recently, several
designs for superconducting chips have been theoretically analyzed and
experimentally tested for cases with many vortices considered as an
average vortex density. Here we show theoretically how the magnetic
field of a single vortex, pinned by a superconducting nanodisk of
radius ∼100 nm and combined with an external bias field parallel to the
disk surface, yields a closed three-dimensional trap for cold atoms.
The size of the trap and its height above the superconductor surface are
typically tens or hundreds of nanometers. We estimate the average
lifetime τ of