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This work was also supported, in part, by NSF REU Grant #0452206, and a Cotrell College Science Award from the Research Corporation for Science Advancement

Microwave Superconductivity

Our lab studies the response of superconducting thin films to microwave currents. There are two active, funded research programs. First we are studying ways to modify the nonlinear response of TBCCO thin film superconductors to microwave currents. By re-annealing the thin films in a nitrogen atmosphere we can change the nonlinearity characteristic of the superconductors. Second we are developing a technique to probe the nonlinear generation in patterned superconducting devices. By allowing us to measure both even and odd order distortion in a highly controlled manner, this research is revealing a new understanding of the electrodynics of high temperature superconductors.

Success in this work depends greatly on having the technology. One key in-house technology is the die attachment and wire bonding of superconducting chips. Here is the training video part 1 and part 2 that Andrew Bunnell prepared during Fall 2009 for the indium solder die attach portion of the process. He also prepared a video for an alternate epoxy procedure. Andrew has also worked on other aspects of superconductive device fabrication including wire bonding (yes, we have a wire bonder!) and carrier metallurgy.

A sapphire dielectric resonator is used to measure the surface impedance of high temperature superconductors. dsc00148.jpg

Evan Pease presenting his poster "Time Reversal Symmetry Breaking in the Nonlinear Electrodynamics of TBCCO Superconductors," July, 2009.

Dro Hardaway and Brad Dober removing
a cryostat from liquid nitrogen.
Brad and Dro

The resonator is mounted in a liquid nitrogen cryostat. It is cooled to 77 Kelvin, and then warmed up in a controlled fashion using a heater and a proportional temperature controller.



The resonance peak is measured using a vector network analyzer. The microwave power level is varied using a high power amplifier, giving us a view of the nonlinear electrodynamics inside a superconductor.


The Q values measured from the 3-sample round robin are converted to effective surface resistance, Rs, by solving a linear system of equations (and by using the previously measured loss tangent of the sapphire). As Tc is approached, the film thickness becomes similar to and then less than the c-axis penetration depth, causing the observed Rs to be higher than the intrinsic film Rs. The actual Tc is not directly observed in the Rs curve because the film becomes invisible to the microwaves before Tc is reached.
You will notice that the "effective surface resistance" is shown in the above graph. Because the superconducting films are not thick compared to the penetration depth, it is necessary to make a correction based on the film's thickness and the substrate type. This correction was introduced by Klein in 1990 and we use the film thickness correction here as described in this internal report which research students must consult. It is interesting to note that a number of well funded and heavily cited groups do not bother with this very significant correction.  
15373 Currently under investigation is the effect of oxygen auto-doping on the microwave nonlinearity in the Tl(2)Ba(2)CaCu(2)O(8-x) superconductor. We can control the value of x (e.g. the doping level) by annealing films in a nitrogen atmosphere. The post-anneal Tc, which corresponds to the doping level, is then measured using the microwave sapphire resonator. At the same time, the microwave nonlinearity of the sample can be examined by measuring the intermodulation distortion. The graph indicates the control we have over Tc, with an inset showing the ability of the sapphire resonator to detect the phase transition, which in this case is often called "Tc microwave."

In her research in 2009, freshman Candace Goodson found that, with some experience, she can shift the nonlinearity of samples into different nonlinearity regimes. She is investigating how this can be a powerful method to control the desired nonlinearity for experiments.

Patterned thin film resonators are particularly interesting because of the high current and resulting high nonlinearity. This summer's research includes measurement of intermodulation distortion from a patterned resonator in various resonant modes in order to identify the contribution of stripline bends to the IMD. (Resonator is courtesy of J. Scupin and SSI, Inc.)


Intermodulation distortion is being measured on patterned resonators with resonant mode (frequency and current distribution), IMD order and temperature as variables. Signals are fed into the resonator with magnetic field probes and an electric field probe detects the nonlinear distortion. A third probe (not shown) scans the resonator device with an out-of-band signal, and the resulting distortion then is a measure of the local nonlinearity near the third probe.

2010: To get separate control over the carrier and probing and carrier currents, we began using a third probe to bring these signals in separately.



First measurements using this "3-tone" intermodulation distortion (IMD, or IM as it shows in the figure) technique made by Evan Pease (below) in 2009. Notice the extreme rise in the 3rd order IMD at high temperature, indicating the contribution of the nonlinear Meissner effect to the distortion.


Summer 2011 Construction of a scanning IMD Probe

Because the degree of 2nd and 3rd order nonlinearities varies around the sample, we are building a micromanipulator probe station using an XYZ micrometer arm and a cryogenic feedthrough that was made by LakeShore Cryotronics. The sample under test will sit on the flat horizontal stage seen in the picture on the right. The stage is on the tip of a CTI M22 coldhead. This is in lieu of a grant. The grant would have purchased a completed passively cooled cryogenic microwave probe station for $50,000. We are building an actively cooled station using materials on hand and the new LakeShore parts for a lot less than that.

Micromanipulator Arm PartsM22Cryocooler


1. Develop a process to "engineer" the nonlinearity characteristic of TBCCO thin films.

2. Characterize the generation and understand the origin of even order IMD and find its relation to time-reversal symmetry breaking electrodynamics.

3. Fully develop a scanning 3-tone IMD measurement platform.

Research Students' Reference Literature

Results of Summer 2008.
Results of Summer 2009.
Results of Summer 2010a.
Results of Summer 2010b.

Results of Summer 2011a.
Results of Summer 2011b.

An early paper that details the measurement method:

Wilker, et al., IEEE Transactions on Applied Superconductivity, Vol. 3, No. 1, March 1993, pp. 1457-1460
A paper that ties in the material science that affects microwave superconductivity:
Wang, et al., Physica C: Superconductivity, Vol. 349, No. 3-4, Jan. 15, 2001, pp. 265-270.
Some other papers that have some stuff that we need to do as well:

Han, et al., J. of the Korean Physical Society, Vol. 48, no. 1, Jan. 2006, pp. 113-118.
Gaganidze, et al., Journal of Applied Physics, Vol. 93, no. 7, 1 April 2003, pp. 4049-4054.

Some tutorial reading:
Spectrum analyzer tutorial
Network Analyzer tutorial

Here is a seminar I first gave at Calvin College in 2004 Intermodulation Distortion Seminar

The first paper on the three-tone intermodulation distortion method:

S.K. Remillard, et al., IEEE Trans. Applied Supercond., Vol. 13, no. 3, September 2003, pp. 3797-3802.

The recent Microwave Group paper detailing the three-tone intermodulation distortion method as we use it these days:
Three-tone RSI paper

Some recent papers from the Microwave Group presenting some results obtained by using the three-tone IMD measurements:

(1) PIERS 2010 paper

(2) Annelle M. Eben*, V. Andrew Bunnell*, Candace J. Goodson*, Evan K. Pease*, Sheng-Chiang Lee, and S.K. Remillard, "Even and Odd Order Nonlinearity from a Superconductive Microstrip Line," Accepted for publication in IEEE Trans. on Applied Superconductivity, June, 2011.