  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, for the first time, how the magnetic field of a $\it single$
vortex, pinned by a superconducting nano-disc of radius $\sim$100 nm and
combined with an external bias field parallel to the disc surface, yields a
closed 3D 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 $\tau$ of $^{87}$Rb (rubidium) atoms (subject to
thermal escape and Majorana spin flips) in the range 0.05-1.0 ms. Next, we
model the trap in a quantum adiabatic approximation and apply Fermi's rule to
estimate the lifetime of $^{87}$Rb atoms in the ground state of this trap. We
obtain similar lifetimes $\tau$ as in the semiclassical estimate, in the range
0.05-3.5 ms. We find that $\tau$ depends on the gradient $B_0$ of the vortex's
magnetic field according to $\tau \sim(B_0)^{-2/3}$.
