1. Investigations in Superconductivity Lulu Liu Partner: Chris Chronopoulos 8.14 Experiment 4 May 12, 2008

2. Theory of Superconductivity Electron-phonon interactions  Electron-Electron Attraction At Low T, overcomes Coulomb Repulsion  Coupling of remote electron pairs  Boson pairs Binding Energy ~ kT c Bosons tend to occupy same state: at T < T c all Cooper pairs condense into single state Crux of BCS Theory

3. Consequences Zero resistivity:  Resistance: loss of momentum from interactions of charge carriers w/ environment  Superconductor – presence of large energy gap, boson pairs cannot be excited into higher state  flow together Meisner Effect  instead of as perfect conductor  Beyond L, excludes all magnetic field from interior F. & H. London Theory Combined Effect:  Persistent Currents in superconducting state

4. Critical Temperature and Field T c measure of binding energy, T > T c breaking of Cooper Pairs, return to normal conductivity External magnetic field B similar energetic effect:  Critical Field B c, NC transition for B > B c Strongly correlated w/ T c and Band Gap

5. Outline Equipment & Calibration (Probes) Meisner & Hysteresis Effect (T c of Vanadium) Persistent Current (T c of Lead) Critical Field Curve (B c of Lead) High T c (YBCo) Superconductor Properties: Evidence of Superconducting Behavior (DC) Non-Zero AC Impedance at high frequency Errors Conclusions

6. Equipment (Probe 1) Mutual Inductance of Nested Solenoids  pass current through one, measure EMF in other Superconductor (Vanadium) in center Helium (4.2K) Cooled: Oscilloscope shows change in EMF over T c transition Voltage drop across Silicon Diode  Temperature Broke on Day 2

7. Probe 1 Method Perfect Conductor Vs. Superconductor Marten Sjostrom

8. Probe 1 Calibration 10  A current through Diode/ ~30mV AC through outer Solenoid from Lakeshore Spec Sheets EMF = - N d  /dt  reduced when material goes SC  EMF drop  0 imperfect filling Vanadium 27.1  19.3 mV

9. Vanadium Data (Probe 1) Hysteresis Effect evident Data points used in average T c = 5.42 § 0.06 K Established: T c = 5.4 K azom.com

10. Probe 2 Equipment & Setup Hollow Lead Tube – persistent current CRT calibration for T(Resistance) -- imprecise measures B-field

11. Carbon Resistance Thermometer Calibration (X-axis) Empirically determined: R.E. Bedford “Techniques...” Three points: LN2 – 77K LH (?) – 4.2K RT – 24.6K

12. Hall Probe Calibration (Y-axis)

13. Generating a Persistent Current Phenomenon peculiar to Superconductors from Feynman SC transition excludes field (B < B c ) from interior  current on outer and inner surface B-field switched OFF: Outer current disappears, inner persists  detected via Hall Probe (mV) Bring out of SC phase  persistent current dissipates (heat)

14. Results (Lead – Probe 2) Imperfect Geometry – marks T c

15. Critical Field Measurements Hold Temperature Constant - increase/decrease external field increasing external field from zero Enter SC state w/ zero field

17. Conclusions Existence of Superconductors distinct from perfect conductors