Past Project: TDO/Pulsed Field
Related publication: C.C. Agosta, L. Bishop-Van Horn, M. Newman. The Signature of Inhomogeneous Superconductivity. Submitted to The Journal of Low Temperature Physics, May 2016.
Related poster presentations: Searching for the FFLO state in quasi 2D superconductors. Clark University Academic Spree Day, April 2016.
Related page: Frequency demodulation.
Background:
Since the summer of 2014 I have been involved in research involving the properties of high-Tc and organic superconductors in high magnetic fields. We use tunnel diode oscillators (TDOs) as a contactless probe of the rf penetration depth of superconducting samples. A TDO is a tank circuit driven by a tunnel diode biased into its negative resistance region.
My first foray into high field studies of superconductivity involved a small pulsed field system at Clark. This system, consisting of a capacitor bank and small resistive magnet, nitrogen bath, heterodyne detection setup, and LabView data acquisition and control station, allowed for fast, cheap studies of high-Tc superconductors up to 15 tesla. More recently I have traveled to the National High Magnetic Field Lab's Pulsed Field Facility at Los Alamos National Lab (January 2016) and DC Field Facility at Florida State University (July 2016).
During the trip to LANL, we measured the organic superconductor λ-(BETS)2GaCl4 ("BETS") at temperatures below 1K and fields up to 60T. At very high fields, BETS exhibits Shubnikov-de Haas oscillations, oscillations in resistivity as a function of external field, which serve as a powerful probe of the Fermi surface. During the trip to the DC facility we studies a few organic superconductors in the very cold, low noise environment of an 18T superconducting magnet with dilution refrigerator.
Measurement:
TDO rf penetration depth measurements are performed at Clark by placing the sample in the inductor of the tank circuit. The gist of the experiment is that when the superconducting state is altered, either through a temperature sweep or a field pulse, the changing penetration depth of the sample changes the inductance of the coil, thereby shifting the frequency of the TDO signal. The TDO, along with a platinum thermometer and heater resistor, is placed in the center of the probe (yellow cylinder below), which is placed in the bore of the magnet (small blue cylinder below). Incredibly, this magnet has been operating without incident since the early '90s. The wooden box on the left contains the bank of eight capacitors. There are three cables leaving the aluminum box on top of the probe: thermometer excitation current and voltage measurement (left), TDO bias and output signal (back of box), and heater current (right). In addition to these connections, there is a connection to a pickup coil wound around the probe to record field data.
We use a LabVIEW program for slow monitoring of the system (temperature and frequency), and rely on an oscilloscope for fast data aquisition and digitization (TDO signal and pickup voltage). From the probe, the TDO signal (10s to 100s of MHz) is sent through a super-heterodyne frequency discrimination process consisting of, in total, four stages of amplification, two heterodyne stages, and three filter stages. The final signal, increased in amplitude and decreased in frequency to ~1MHz, is split and sent to a frequency counter and the oscilloscope. We can then grab the data with LabVIEW and analyze.
Analysis:
Data from pulsed field TDO experiments is analyzed as follows:
- We start with two voltage vs. time signals: the pickup voltage (voltage induced in a pickup coil during the field pulse) and heterodyned TDO signal (mixed down to approx. 1MHz).
- The pickup voltage is integrated with respect to time and multiplied by a constant geometric factor according to Faraday's Law to obtain the field as a function of time.
- The TDO signal is demodulated to obtain frequency as a function of time. This is typically done using a sliding FFT, but good results can also be achieved using peak-counting methods. Several periods are used to approximate the frequency at a single instant, but this does not cause any problems because the frequency is high compared to the rate of change of frequency. (See my frequency demodulation page for more information on this step.)
- The relationship we are interested in is frequency as a function of field. We now have both frequenecy and field as a function of time, but the timebase for these quantities is different. To remedy this, we generate a new evenly spaced timebase and calculate a cubic spline for both the frequency signal and field signal, then evaluate these splines at the new time points.
- We can now examine the TDO frequency as a function of field, so we can look for changes in London Penetration Depth as a result of phase transitions, quantum oscillations, and other interesting effects.