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Superconductivity and Superfluidity PHYS3430 Professor Bob Cywinski

“Superconductivity is perhaps the most remarkable physical property in the Universe” David Pines. Superconductivity and Superfluidity PHYS3430 Professor Bob Cywinski. Superconductivity and Superfluidity PHYS3430 Professor Bob Cywinski.

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Superconductivity and Superfluidity PHYS3430 Professor Bob Cywinski

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  1. “Superconductivity is perhaps the most remarkable physical property in the Universe” David Pines SuperconductivityandSuperfluidityPHYS3430Professor Bob Cywinski

  2. SuperconductivityandSuperfluidityPHYS3430Professor Bob Cywinski “Superconductivity is perhaps the most remarkable physical property in the Universe” David Pines

  3. SuperconductivityandSuperfluidityPHYS3430Professor Bob Cywinski “Superconductivity is perhaps the most remarkable physical property in the Universe” David Pines

  4. SuperconductivityandSuperfluidityPHYS3430Professor Bob Cywinski “Superconductivity is perhaps the most remarkable physical property in the Universe” David Pines

  5. Text Books Introduction to Superconductivity A C Rose-Innes and E H Rhoderick Pergamon Press Good introduction to phenomenology, without too much maths - now quite out of date Superfluidity and Superconductivity Dr Tilley and J Tilley Institute of Physics Publishing Both topics covered well, but it flips between the two topics too much and tries to draw too many analogies Introduction to Superconductivity and High-Tc Materials M Cyrot and D Pavuna World Scientific A good introduction, and cheap, but now hard to get plus appropriate chapters in Solid State Physics books Lecture 1

  6. Syllabus Lectures will focus primarily on superconductivity but the salient features of the phenomenon of superfluidity in liquid helium will be discussed towards the end of the course We shall cover the history of superconductivity and the early phenomenological theories leading to a description of the superconducting state The microscopic quantum mechanical basis of superconductivity will be described, introducing the concepts of electron pairing, leading to the BCS theory Superconductivity as a manifestation of macroscopic quantum mechanics will be presented, together with the implication for superconducting devices, such as SQUIDS An overview of the principal groups of superconducting materials, and their scientific and industrial interest will be given Lecture 1

  7. Discovered by Kamerlingh Onnes in 1911 during first low temperature measurements to liquefy helium Whilst measuring the resistivity of “pure” Hg he noticed that the electrical resistance dropped to zero at 4.2K In 1912 he found that the resistive state is restored in a magnetic field or at high transport currents 1913 Discovery of Superconductivity Lecture 1

  8. Fe (iron) Tc=1K (at 20GPa) Nb (Niobium) Tc=9K Hc=0.2T Transition temperatures (K) and critical fields are generally low Metals with the highest conductivities are not superconductors The magnetic 3d elements are not superconducting ...or so we thought until 2001 The superconducting elements Transition temperatures (K) Critical magnetic fields at absolute zero (mT) Lecture 1

  9. HgBa2Ca2Cu3O9 (under pressure) 160 140 HgBa2Ca2Cu3O9 TlBaCaCuO 120 BiCaSrCuO 100 YBa2Cu3O7 Superconducting transition temperature (K) Liquid Nitrogen temperature (77K) 80 60 40 (LaBa)CuO Nb3Ge Nb3Sn NbN 20 NbC Nb Pb Hg V3Si 1910 1930 1950 1970 1990 Superconductivity in alloys and oxides Lecture 1

  10. Plane waves can travel through a perfectly periodic structure without scattering….. resistivity ….but at finite temperatures phonons destroy the periodicity and cause resistance “impure metal” T Even at T=0, defects such as grain boundaries, vacancies, even surfaces give rise to residual resistivity Residual resistivity T5 “ideal metal” temperature Zero resistance? In a metal a current is carried by free conduction electrons - ie by plane waves Take, eg, pure copper with a resistivity at room temperature of 2cm, and a residual resistivity at 4.2K of 210-5 cm ………….a typical Cu sample would thus have a resistance of only 210-11  at 4.2K Lecture 1

  11. Zero resistance? In a metal a current is carried by free conduction electrons - ie by plane waves Plane waves can travel through a perfectly periodic structure without scattering….. ….but at finite temperatures phonons destroy the periodicity and cause resistance Even at T=0, defects such as grain boundaries, vacancies, even surfaces give rise to residual resistivity Take, eg, pure copper with a resistivity at room temperature of 2cm, and a residual resistivity at 4.2K of 210-5 cm ………….a Cu typical sample would thus have a resistance of only 210-11  at 4.2K Lecture 1

  12. Zero resistance? The resistance of pure copper is so small is there really much difference between it and that of a superconductor? Take an electromagnet consisting of a 20cm diameter coil with 10000 turns of 0.3mmx0.3mm pure copper wire R300K = 1 k R4.2K= 0.01  Pass a typical current of 20 Amps through the coil P300K = 0.4MW P4.2K= 4 Watts At 4.2K this is more than enough to boil off the liquid helium coolant! Lecture 1

  13. This is done by injecting current into a loop of superconductor The current generates a magnetic field, and the magnitude of this field is measured as a function of time i B Measuring zero resistance Can we determine an upper limit for the resistivity of a superconductor? This enables the decay constant of the effective R-L circuit to be measured: Using this technique, no discernable change in current was observed over two years: sc  10-24.cm !! Lecture 1

  14. If the area of the ring is A, the flux threading the loop is Now change BA: by Lenz’s law a current will flow to oppose the change, hence Cool the ring in an applied magnetic field - then decrease the field to zero BA Measuring zero resistance In practice the superconducting ring is cooled in a uniform magnetic field of flux densityBA to below TC Lecture 2

  15. emf i forever So if R=0 the current will persist forever !! Measuring zero resistance In practice the superconducting ring is cooled in a uniform magnetic field of flux densityBA to below TC If the area of the ring is A, the flux threading the loop is Now change BA: by Lenz’s law a current will flow to oppose the change, hence In a “normal” loop, the Ri term quickly kills the current, but if R=0 Currents will flow to maintain the field in the loop…. Therefore Li+ABA = constant (=total flux in loop)

  16. If and Ri = 0 such that Li+ABA = constant (=total flux in loop) The flux in the superconducting loop must remain constant however the field changes …..and the corollary Therefore if a loop is cooled into the superconducting state in zero field and then the magnetic field is applied supercurrents must circulate to maintain the total flux threading the loop at zero. A superconducting cylinder can therefore provide perfect magnetic shielding A Meissner Shield Lecture 2

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