What ideas had Kelvin, Matthiessen and Dewar for the resisitivity at low temperatures?
Kelvin - the electrons stop moving at lower temperatures and resistivity increases.
Matthiessen - conductivity reaches a limiting value
Dewar - it goes smoothly to zero
Dewar liquifies hydrogen and measures Au and Ag — finds Matthiessen result - postulates this is due to impurities
This prompts (veranlassen) Onnes to measure Hg and discover superconductivity!
How is an ideal conductor defined?
An ideal conductor is defined as having zero electrical resistance: ρ = 0
Remembering Ohm’s law j = σE and that ρ = 1/σ
We have that for an ideal conductor E = 0
What are the Maxwell’s equations? What does the first equation tell about the magnetic field inside the ideal conductor?
The magnetic field is constant inside the ideal conductor.
What is the Meissner-Ochsenfeld effect? What is the difference between an superconductor and a perfect conductor?
In 1933 Meissner and Ochsenfeld were studying the properties of superconductors when they realized that under TC all magnetic field was expelled from the interior of their superconducting samples.
This means that superconductors are ideal diamagnets.
This is independent of the cooling history as this phenomenon kicks in as soon as T < TC
Zero field cooling: both act the same by expelling the magnetic filed from the interior and they behave as perfect diamagnets
Field cooling: the magnetic field stays the same and continues to cross the sample for the perfect conductor. In contrast, in the superconductor, starting from Tc spontaneous screening currents, also known as LONDON currents, appear and expel the magnetic field from the sample. The magnetic field is “expelled” from the superconductor by screening without induction.
Supercurrent: What can you say about it?
Consider a superconducting slab with an applied field parallel to the surface:
We need to remember that the field inside the superconductor is zero. So we constrain the current induced by the field to the surface.
The supercurrent j_s flows on the surface perpendicular to B_a and screens the interior. The magnitude of j_s depends on B_a.
Notice that the supercurrent needs no electric field to drive it, unlike normal metals!
What are the characteristics of a perfect diamagnet?
How do the H-T and the M-H diagramms look like?
Superconductors are perfect diamagnets:
B=μ0(H + M)=0 M=-H Χ=dM/dH=-1
What is the Ehrenfest’s classification on phase transitions? How is the Gibbs free energy defined?
Ehrenfest’s classification is based on the Gibbs free energy: the order of the derivative which shows a discontinuity is the order of the phase transition.
What are the first derivatives of the Gibbs free energy?
What are the second derivatives of the Gibbs free energy?
Which phase transitions does Helium show?
To put it into context, in Leiden they were looking into the order of the phase transitions in Helium:
The lambda transition shows no latent heat. (Lambda transition = phase transition in superfluid, superconductor and liquid crystal)
How is the relation between the free energies of normal and superconducting states?
We can compare the free energies of normal and superconducting states:
The normal and superconducting phases will coexist at the critical field B_c:
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