Investigations in Superconductivity Lulu Liu Partner Chris Chronopoulos

Investigations in Superconductivity Lulu Liu Partner: Chris Chronopoulos 8. 14 Experiment 4 May 12, 2008

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

Consequences n Zero resistivity: ¡ ¡ n 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 n Combined Effect: ¡ Persistent Currents in superconducting state

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

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

Equipment (Probe 1) n Mutual Inductance of Nested Solenoids pass current through one, measure EMF in other n Superconductor (Vanadium) in center n Voltage drop across Silicon Diode Temperature n Helium (4. 2 K) Cooled: Oscilloscope shows change in EMF over Tc transition n Broke on Day 2

Probe 1 Method n Perfect Conductor Vs. Superconductor Marten Sjostrom

Probe 1 Calibration n 10 A current through Diode/ ~30 m. V AC through outer Solenoid EMF = - N d /dt reduced when material goes SC EMF drop 0 imperfect filling Vanadium 27. 1 19. 3 m. V from Lakeshore Spec Sheets

Vanadium Data (Probe 1) n Hysteresis Effect evident Data points used in average Tc = 5. 42 § 0. 06 K Established: Tc = 5. 4 K azom. com

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

Carbon Resistance Thermometer Calibration (X-axis) Empirically determined: R. E. Bedford “Techniques. . . ” Three points: LN 2 – 77 K LH (? ) – 4. 2 K RT – 24. 6 K

Hall Probe Calibration (Y-axis)

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

Results (Lead – Probe 2) Imperfect Geometry – marks Tc

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

Conclusions n Existence of Superconductors distinct from perfect conductors