The coexistence of multiple types of orders is a common thread in condensed matter physics and unconventional superconductors. The nature of superconducting orders may be unveiled by analyzing local perturbations such as vortices. For thin films, the vortex magnetic profile is characterized by the Pearl-length \(\Lambda\) , which is inversely proportional to the 2D superfluid density; hence, normally, also inversely proportional to the film thickness, \(d\) . Here we employ the scanning SQUID-on-tip microscopy to measure \(\Lambda\) in NbSe2 flakes with thicknesses ranging from \(N=3\) to \(53\) layers. For \(N\, > \,10\) , we find the expected dependence \(\Lambda \propto 1/d\) . However, six-layer films show a sharp increase of \(\Lambda\) deviating by a factor of three from the expected value. This value remains fixed for \(N=3\) to \(6\) . This unexpected behavior suggests the competition between two orders; one residing only on the first and last layers of the film while the other prevails in all layers.
