Investigations in Superconductivity

Lulu Liu

Partner: Chris Chronopoulos

8.14 Experiment 4

May 12, 2008

Theory of Superconductivity

Electron-phonon interactions Electron-Electron Attraction

At Low T, overcomes Coulomb Repulsion Coupling of remote electron pairs Boson pairs

Binding Energy ~ kTc Bosons tend to occupy same state: at T < Tc all Cooper pairs condense into single state

Crux of BCS Theory

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

Critical Temperature and Field

Tc measure of binding energy, T > Tc breaking of Cooper Pairs, return to normal conductivity

External magnetic field B similar energetic effect: Critical Field Bc, NC transition for B > Bc

Strongly correlated w/ Tc and Band Gap

Outline

Equipment & Calibration (Probes)

Meisner & Hysteresis Effect (Tc of Vanadium)

Persistent Current (Tc of Lead)

Critical Field Curve (Bc of Lead) High Tc (YBCo) Superconductor Properties:

Evidence of Superconducting Behavior (DC) Non-Zero AC Impedance at high frequency

Errors

Conclusions

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 Tc transition

Voltage drop across Silicon Diode Temperature

Broke on Day 2

Probe 1 Method

Perfect Conductor Vs. Superconductor

Marten Sjostrom

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

Vanadium Data (Probe 1) 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

Hollow Lead Tube – persistent current

CRT calibration for

T(Resistance) -- imprecise

measures B-field

Carbon Resistance Thermometer Calibration (X-axis)

Empirically determined:

R.E. Bedford “Techniques...”

Three points:

LN2 – 77K

LH (?) – 4.2K

RT – 24.6K

Hall Probe Calibration (Y-axis)

Generating a Persistent Current

Phenomenon peculiar to Superconductors

from Feynman

SC transition excludes field (B < Bc) 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)

Results (Lead – Probe 2)

Imperfect Geometry –

marks Tc

Critical Field Measurements Hold Temperature Constant -

increase/decrease external field

increasing external field from zero

Enter SC state w/ zero field

Conclusions

Existence of Superconductors distinct from perfect conductors