Superconductivity: The Meissner Effect

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Superconductivity The Meissner Effect

• Alex Mott
• with Andrei Levin
• MIT Junior Lab
• Spring 2007

2
Outline

• Motivation
• BCS theory
• The London Equation
• Perfect conductor versus superconductor
• Experimental Setup
• Demonstration of Meissner Effect
• Measuring Tc
• Error Analysis
• Conclusions

3
Motivation

• 0 electrical resistance
• Can store current indefinitely
• Can create large B-fields
• CMS magnets
• MagLev train

cms.cern.ch
superconductors.org
4
BCS Theory

• Electrons distort lattice
• Bind into Cooper Pairs through lattice distortion
• Cooper pair behaves as a boson
• Stay together as long as thermal vibrations are
  small

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BCS Conductivity

• Cooper Pairs form between electrons
• Near the Fermi Surface
• On opposite sides of Fermi Sphere
• At low energy
• Cooper Pair moves as one unit
• Resists kicks and thus experiences no
  resistance
• At higher energy
• Cooper Pair is broken
• End of superconductivity

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The London Equation

• Initially guessed
• Can be derived from BCS
• The London Equation
• Combining with
• We conclude that
• Which has solution

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Implications of the London Equation

• Valid only for superconductors
• B 0 deep inside
• SC will abruptly expel any magnetic field when
  cooled past Tc

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Perfect Conductors

• Perfect conductors also have 0 resistance
• Not governed by London Equation
• Can show
• The solution gives
• Magnetic fields frozen in

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Perfect Conductors Versus Superconductors

• Both expel changing magnetic fields
• SC expels static magnetic fields
• SC will not form in a strong B-field

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Experimental Setup

• SC sample surrounded by 2 coils
• Apply current to outer coil
• Measure inductance on inner
• Inductance proportional to cross-sectional area
• SC effectively reduces area
• Measure current above and below Tc

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Experimental Setup
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Sample Data
Niobium
13.2K
7.3K
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Demonstration of Meissner Effect
Decreasing Temperature
Increasing Temperature
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SC Transition Niobium
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SC Transition Vanadium
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SC Transition Lead
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Extracting Tc

• Find level of sub-Tc plateau
• Record highest T

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Sources of Error

• Error bars
• Granularity in scope
• Error reading temp
• Something is wrong
• Drifting reduced by averaging
• Temp sensor may be systematically warmer than
  sample

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Applying a B-Field
Niobium
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Systematics

• Temperature Sensor is systematically warmer than
  the sample
• Scale using Niobium (Tc 9.3 K)

For Niobium
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Conclusions

• Shown Meissner Effect
• Seen Tc transition
• Determined Tc for Nb, Pb, Va
• Systematics Correction
• Redo experiment with better temperature
  measurements