Coherence length
Nanophysics in superconductivity • • • • • BCS-theory Flux vortices Josephson junction Coherence length Knut Tyse BCS - theory • • • • The basis for S.C. quantum theory Two and two electrons form cooper pairs Wavevector is or Wavefunction of cooperpair: • Not the only configuration Coherence length A meashure of the spatial variation of the density of superconducting electrons. A small coherence length means that the density changes rapidly. Intrinsic coherence length: Or by using BCS-quantum-theory: is the energy gap needed to destroy superconductivity while the fermi velocity. For alloys and impure superconductor we have For a «dirty» material we have is The coherence length is a meashure of transition-length between normal and superconducting domains. Flux quantization • Magnetic flux vortices are quantized in Figure: http://www.physics.umd.edu/courses/Phys726/The_Quantum_Vortex.htm At saturation • . • Then the normal cores are a distance appart. • This means that the sample becomes normal at . Josephson junctions (JJ) The superconductor (S) is interrupted by a thin barrier (B) (Not to scale in the figure) • The barrier can be - an insulator (oxide layer) , 1-2 nm - a material which is not a S.C. - a point where the S.C material is much thinner. - a grain boundary if is small • The key is to have a weak link between the S.C.s • The thickness of the weak link must be tailored Two theoretical predictions 1: • The tunnel junction will be superconducting up to . 2: • If the junction will radiate EM-waves with high frequency Nobel prize 1973 • Brian David Josephson - theoretical prediction • Leo Esaki and Ivar Giæver - experimental discovery Quantum mechanics explains this Bose condensate: 2 and 2 electrons can form cooperpairs. In a material every cooperpair shares the same wavefunction and energy The cooperpairs in S1 and S2 have equal amplitude in the wavefunction. However they have arbitrary phase. Now: Introduce the weak link • The weak link acts as a perturbation • It does not drastically change the wavefunctions in S1 and S2. • Interference between S1 and S2 creates a new wavefunction across the system. DC effect • Start with wavefunctions: • Write the Schrödinger equation for and • Solving gives a solution for the current through the barrier: AC-effect: Apply a voltage accross the junction BIB IIIII DOS- vacant states Cooper pairs at fermi level Cooper pairs at fermi level DOS filled states http://en.wikipedia.org/wiki/Superconducting_tunnel_junction Result for AC Josephson effect Is an integration constant The current oscillates with frequency Photons with energy Can determine the value of very precisely can be emitted/absorbed Sources http://eu.wiley.com/WileyCDA/WileyTitle/productCd-EHEP000803.html http://books.google.no/books/about/The_Physics_of_Superconductors.h tml?id=8O8svNo_tWoC&redir_esc=y
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