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# Superconductivity

Zach Zern and Michael Cohen discuss the basics of Superconductivity
by

## Michael Cohen

on 4 November 2016

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#### Transcript of Superconductivity

Superconductivity By: Zach Zern and Michael Cohen Outline Conduction -A material's ability to conduct electrical current; the reciprocal of resistance.

-We will be focusing on compounds that consist of an atomic lattice structure. Impurities of the compounds and thermal motion of ions are both causes of electron scattering (resistance) Photo Credit: http://www.green-planet-solar-energy.com/images/metal-lattice-2.gif Typically... Resistance, and therefore conductivity, are temperature dependent. In a non-superconducting substance, this relationship looks like... (see graph on blackboard) Resistance as a function of temperature looks like... Notice that even at T=0, there is a residual resistivity from impurity and metal type. Now, on to superconductors. Photo Credit:http://en.wikipedia.org/wiki/Electrical_resistivity_and_conductivity#General_definition Bloch–Grüneisen formula: II. Building the Theory -Heike Onnes: 1911
-Meissner: 1933
-Fritz and Heinz London: 1935
-Bardeen, Cooper, Schreiffer : 1957
-Müller: 1986 Onnes -First to liquify He.

-With new refridgeration techniques, tested resistivity of metals.

-Theories at the time were conflicted. -Resistivity went to zero almost instantaneously. Property I: Superconductors have zero resistance when they reach a critical temperature. Meissner: I.What is Conduction? A Brief Review V. Superconductivity and the Future IV. Applications III. Review of Properties II. Developing the Theory: A Historical Approach -Research on superconductors and their interaction with magnetic fields. EXPERIMENT: Subjected superconductors above their critical temperatures to magnetic fields and then cooled them below critical temperatures. Specific materials used were tin and lead. Results? Results: -Tin and Lead, when they pass Tc, expel internal magnetic fields.

-Measured indirectly by understanding magnetic flux conserved.

-Magnetic flux outside superconductor increased, so internal must have decreased. -Meissner Effect, is proof that superconductivity is more than just a perfect state of conduction. -Differs from perfect conductor because expels internal field upon transition. Fritz and Heinz London THEORY- Postulated that superconducting electrons exhibit a density when in contact with an electric field EXPERIMENT: Cool an extremely pure sample of mercury to 4K and meassure the change in resistivity. Results? Looked for a mathematical representation to describe the Meissiner effect. London Equations Manipulating the equation with Ampere's law we get... Ns = density per unit volume(superconducting electrons) Lambda- London Penetration Depth Important, Why? Property II: Superconductors expel magnetic fields from their interior. John Bardeen John Robert Schrieffer Leon Neil-Cooper Cited Works Wikipedia: Articles
-Meissner Effect
-Superconductivity
-Conductivity and Resistance
-London Equations
-Phonons
-Crystal Lattice "BCS" Theory
http://www.superconductors.org/

http://hep.ph.liv.ac.uk/~hock/Teaching/2010-2011/7-cooper-pair.pdf http://hyperphysics.phy-astr.gsu.edu/hbase/solids/supcon.html#c1 Schrieffer, J. R., and M. Tinkham. "Superconductivity." Reviews of Modern Physics 71.2 (1999): S313-317. Web. The mathematics behind the BCS theory are quite complex; we will present the qualitative understanding, eased by taking a classical particle approach. Lattice-Phonon Interactions
and Cooper Pairs -When cooled below critical temperature, superconductors have 0 resistance. Why?

-Imagine crystal lattice of the conductor is distorted when electrons pass by.

-When this occurs, there is a greater charge density in region of distortion.

-Ultimately, delayed weak attractive force between electrons comes from the interaction with lattice. These interactions between the lattice vibrations, called phonons, and the electrons are responsible for forming Cooper Pairs. See Below. Photo Credit: http://www.abc.net.au/science/basics/img/CooperPair_v2.jpg A bit more technical explanation... -Cooper pairs actually are all co-dependent because of their wave functions entanglement.

-Behave like bosons.

-They are part of a superfluid condensate of such pairs in ground state.

-Since all entangled, collisions need enough energy to change collective wavefunction. Not enough energy below Tc. Müller:
-Contribution to field was testing oxides (a chemical compound containing at least one oxygen) for superconductive behavior
-Results? Eureka! - lanthanum barium copper oxide (LBCO) was found to transition into a superconductive state at the unprecedentedly high temperature of 35K

-The previous record high was 23K, so an about 50% increase

-So, why is this important? Outcome -Sparked a flurry of research into Type II superconductors, the same as LBCO NOTE: Type II superconductors also known as High Tc superconductors, due to their higher critical temperature compared to the classical superconductors, now referred to as Type I Type II Superconductors -BCS can't explain
-More gradual transition to 0 resistance at critical temperature

Includes cuprates, perovskites, and now iron based materials. Properties of Superconductors -Zero resistance below a critical temperature
(demonstrated by Onnes)
-Expulsion of any internal magnetic fields below the critical temperature
(Meissner Effect) -Type I (low Tc) and Type II (high Tc) Critical Surface Superconductor Applications Future of Superconductors Electric Power- Energy transfer with zero energy loss. Isotope Effect Reynolds, Serin, Wright and Nesbitt at Rutgers [University] and Maxwell at the [National] Bureau of Standards: 1950 Isotopes- Same Elements but different masses Photo Credit: http://pdqindustrialelectric.com/High-Temp-Superconductors-(high-Tc,-HTS).html Transportation- Maglev Trains Josephson Junction- superconducting quantum interference device (SQUID) High Temperature Superconductivity The red spheres are X atoms (usually oxygens), the blue spheres are B-atoms (a smaller metal cation, such as Ti4+), and the green spheres are the A-atoms (a larger metal cation, such as Ca2+) Photo and Explanation Credit:
http://en.wikipedia.org/wiki/Perovskite_(structure) Medical Imaging and Diagnostics- MRI Sensors- NMR and Radars -Practicality increases with higher Tc

-Need to explain Type II Superconductors

-Applications to Quantum Computing Photo Credit: http://en.wikipedia.org/wiki/File:EfektMeisnera.svg THE END
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