The
gauge-invariant London equation *J*_{s} =- ρ_{s} ( A- (h/4?*e)**∇ φ )* states that the
current density in a superconductor (SC) *J*_{s} is proportional
to the vector potential *A* up to the gradient of the order parameter
phase *φ* . The proportionality constant *ρ*_{s} is called
the stiffness which is connected to the penetration depth *λ* by the
relation *ρ*_{s} = 1/μλ^{2}. When cooling a SC at zero *A*,
*φ* will be uniform to minimize the kinetic energy. In cases where *φ*
is quantized, it remains uniform upon slightly increasing *A*, leading to
the familiar London equation *J*_{s} =- ρ_{s} A. This
relation holds until* J*_{s} reaches a critical current *J*_{c}
where *φ* is forced to change. The coherence length *ξ* is proportional
to *1/ J*_{c}. The standard procedure for measuring *ρ*_{s}
in a bulk SC is to apply a magnetic field and measure its penetration depth *λ*
into the interior of the SC. However, in ultra-thin SC films, the penetration
depth is not well defined since there is no interior although surface current *J*_{s}
and *A* do exist. A new way of measuring the superconducting stiffness and
coherence length using a Stiffnessometer was developed in our group. This
method measures *ρ*_{s} and *J*_{c} directly, based
on the London equation with a rotor free vector potential. The method,
applicable to 3D and 2D SC, is based on long and narrow excitation coil which
pierces a ring-shaped SC and produces a current in the ring. The ring?s
magnetic moment *m* is then measured by a superconducting quantum interference
device (SQUID) to extract *ρ*_{s} and *J*_{c} (or the
critical SC surface current density *J*_{c} in the 2D case). In
this work, I will present stiffness and coherence length measurements of a 2D, ultra-thin
δ -NbN and thin Granular Al SC films. The thinnest film that was measured is a
3[nm] thick NbN film. A surplus of signal to noise ratio (SNR) in this
measurement shows that a reduction of factor 10 in the thickness of the samples
is possible, a fact that will allow in the future to apply this method on a true
2D systems with a single atomic layer. The analysis of the measured signals
with the Pearl equation shows that our new method works appropriately and gives
similar stiffness values found in the literature. Using full analysis of the
two coupled Ginzburg-Landau (GL) equations we extract the coherence lengths
which are similar to those available in the literature. Finally, this work
demonstrates for the first time that the Stiffnessometer agrees with other
techniques while it opens new measurement regimes.