Simclair- Intro to Superconductivity Flashcards
What is a superconductor?
An element or material that will conduct electricity without resistance below a certain critical temperature Tc.
Difference between conduction in metals and superconductors
For metals the electrons collide with the atoms in the material causing electrical resistance. For superconductors under Tc, electrons travel in pairs (Cooper pairs) through the solid. Once set in motion an electrical current will flow forever in a closed loop
Zero heat loss current carrying applications
Large scale power transmission (100% efficient)
Micro-electronic circuits (reduced heat losses)
Meissner effect
Superconductors show strong diamagnetism below Tc with a magnetic susceptibility χ of about -1. It sets up a surface current to oppose the magnetic field. Means that the SC will be repelled from either the North or South poles of a magnet
Applications of the Meissner effect
Magnetic levitation
Magnetic shielding
Three ways of destroying the superconducting state
Increase temperature above Tc
Increase current density above Jc
Increase the magnetic field above Hc
Superconducting elements
Early and late transition metals and heavy p-block metals.
Tc below 10K for all elements.
Tc=9.5K for Nb which is best superconducting element
Superconducting intermetallics
Tc below 23K and many based on A3B crystal structure type. A and B both metals. Example is Nb3Ge
What level of magnetic flux density comes from a high field magnet?
14-21T
Features of cuprate superconductors
Most based on the perovskite structure and contain mixed valent Cu2+ and Cu3+ ions. Ideal average charge on Cu ions is +2.15. They are brittle ceramics. Can dramatically change the SC properties of cuprates by small changes in chemical composition. Tc can be greater than 77K (liquid nitrogen)
What is Tc*?
The maximum Tc possible in the system
How do fullerenes work as superconductors?
Alkali doped C60. The C60 balls packed in a fcc arrangement with alkali metals filling all oct and tet sites. Record Tc is 38K for Cs3C60 under 7kBar (bcc in this case). Electrons can’t move freely between C60 molecules and are immobilised on the molecules because adjacent C60s are far apart under normal pressure (Mott insulator). Electrons with opposite spin immobilised on adjacent molecules. Greater pressure shortens intermolecular distance between C60s. Strong attractive force simultaneously acts between electrons producing Cooper pairs and causing a transition to a SC state. Tc controlled by size of alkali metal ion and packing arrangement of C60.
Type 1 superconductors
Soft SC. Obey the Bardeen-Cooper-Schrieffer (BSC) theory to explain SC in metals and alloys using Cooper pairs so Tc<23K. Low Hc and Jc. 1st order transition. Simple metals (except Nb, V) and elemental metalloids (except Te) only
H vs T graph for type 1 SC
Curve down from Hco to Tc. The line is Hc(T). Region bound by curve is B=0 Meissner state and superconducting. Region outside is normal behaviour. Equation of curve roughly
Hc(T)=Hco(1-(T/Tc)^2)
Where H sub c0 is critical field at 0K
-4πM ca applied field B graph for type 1
y=x line up to (Hc, Hc) then vertical line down
Type 2 superconductors
Hard SC. No established theory for oxides. Tc>77K and max about 138K. Large Hc and Jc. 2nd order transition. Mainly alloys and oxides. Can have stripes/flux vortices that are not allowed to move for SC to exist?
H vs T graph for type 2 superconductors
Two curves. Lower one from Hc1o shallow curve down to Tc on x axis. Area bound by this has B=0 Meissner state. Curve represents Hc1(T). Higher curve from Hc2o steeper curve down to Tc on x axis. Curve represents Hc2(T). Area between this and Hc1(T) curve has B not 0 vortex or mixed state and shows SC and normal behaviour. Outside all curves is normal behaviour. Hc2>100T at 4K.
Hc would be between Hc1 and Hc2
-4πM ca applied field B graph for type 2
y=x until Hc1 on x axis. Then sharp corner and curve down (getting less steep) to Hc2. Hc is between Hc1 and Hc2. SC state is under graph between 0 and Hc1 applied field. Vortex state is under graph between Hc1 and Hc2. Right of Hc2 is normal state.
What are phonons?
Quanta of lattice vibrations
What is a cooper pair?
A pair of two separate conduction electrons that are weakly bound by some form of coulombic attraction i.e p+e(1) then p+e(2)
How do cooper pairs travel together?
e(1) distorts the lattice and therefore e(2) has a lower energy if it travels in that region. Net effect is that they travel as a pair. Under an applied electric field, each pair is locked to the motion of all others and none can be individually scattered by the lattice so R=0 (in dc). Generally form at low temperatures
Ground state of a superconductor
A collective state which describes the ordered motion of a large number of cooper pairs
Distance between electrons in a Cooper pair
Behaviour of superconductors suggests electron pairs are coupling over distances significantly greater (up to 3 orders of magnitude) than the lattice spacing (100nm compared to 0.1-4nm). The pair binding energy is a few meV which is enough to keep them paired at low temperatures. This is basics of BSC theory.
Proof that cooper pairs involve lattice vibrations in their mechanism
Phonons act as the glue. Proved by isotope effect. If electrical conduction was purely electronic there would be no dependence of Tc on nuclear masses. However dependence of Tc on isotopic mass of Hg was observed. Tc proportional to A^-1/2. This was first evidence for interaction between electrons and the lattice. Support BCS theory of lattice coupling of electron pairs
How can electrons have the same energy?
Become bosons from fermions which can have the same energy and a spin of 0 or 1
