טכניון מכון טכנולוגי לישראל
הטכניון מכון טכנולוגי לישראל - בית הספר ללימודי מוסמכים  
M.Sc Thesis
M.Sc StudentBlau Nitsan
SubjectMeasuring The Stiffness And Coherence Length Of 2D
Superconductors
DepartmentDepartment of Physics
Supervisors Professor Amit Keren
Professor Amit Kanigel
Full Thesis textFull thesis text - English Version


Abstract

The gauge-invariant London equation Js =- ρs ( A- (h/4?e) φ ) states that the current density in a superconductor (SC) Js is proportional to the vector potential A up to the gradient of the order parameter phase φ . The proportionality constant ρs is called the stiffness which is connected to the penetration depth λ by the relation ρs = 1/μλ2. 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 Js =- ρs A. This relation holds until Js reaches a critical current Jc where φ is forced to change. The coherence length ξ is proportional to 1/ Jc. The standard procedure for measuring ρs 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 Js 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 ρs and Jc 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 ρs and Jc (or the critical SC surface current density Jc 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.