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CH 8 _ M A Islam_Superconductors

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CH 8 _ M A Islam_Superconductors

  1. 1. Superconductivity M A Islam EEE, IIUC
  2. 2. 1911: discovery of superconductivity Whilst measuring the resistivity of “pure” Hg he noticed that the electrical resistance dropped to zero at 4.2K Discovered by Kamerlingh Onnes in 1911 during first low temperature measurements to liquefy helium In 1912 he found that the resistive state is restored in a magnetic field or at high transport currents 1913M A Islam, EEE, IIUC
  3. 3. Superconductors Aluminum 1.2K Tin 3.7K Mercury 4.2K Niobium 9.3K Niobium- Tin 17.9K Tl-Ba-Cu- oxide 125K Metal Critical T(K) A superconductor is a metal that allows a current to pass through it with no loss due to heat dissipation. Typical values for the critical temperature range from mK to 100K Using Superconductors we can preserve a wavefunction because the fact that the current wavefunction is not perturbed by its journey through the metal means that it will stay in a given state. The current can be seen as a wavefunction, and is thus A probability distribution of different current values, this implies that clockwise and counter clockwise. It is this view of the current that enables us to create qubits from a simple loop of superconductor. M A Islam, EEE, IIUC
  4. 4. M A Islam, EEE, IIUC
  5. 5. The superconducting elements Li Be 0.026 B C N O F Ne Na Mg Al 1.14 10 Si P S Cl Ar K Ca Sc Ti 0.39 10 V 5.38 142 Cr Mn Fe Co Ni Cu Zn 0.875 5.3 Ga 1.091 5.1 Ge As Se Br Kr Rb Sr Y Zr 0.546 4.7 Nb 9.5 198 Mo 0.92 9.5 Tc 7.77 141 Ru 0.51 7 Rh 0.03 5 Pd Ag Cd 0.56 3 In 3.4 29.3 Sn 3.72 30 Sb Te I Xe Cs Ba La 6.0 110 Hf 0.12 Ta 4.483 83 W 0.012 0.1 Re 1.4 20 Os 0.655 16.5 Ir 0.14 1.9 Pt Au Hg 4.153 41 Tl 2.39 17 Pb 7.19 80 Bi Po At Rn Transition temperatures (K) Critical magnetic fields at absolute zero (mT) Transition temperatures (K) and critical fields are generally low Metals with the highest conductivities are not superconductors The magnetic 3d elements are not superconducting Nb (Niobium) Tc=9K Hc=0.2T Fe (iron) Tc=1K (at 20GPa) ...or so we thought until 2001 M A Islam, EEE, IIUC
  6. 6. Type I Superconductors Type I superconductors are sometimes called "soft" superconductors while the Type II are "hard", maintaining the superconducting state to higher temperatures and magnetic fields. In Type I superconductors transition from normal state to superconducting state occurs instantly i.e. at exactly it's critical/transition temperature Tc: This type of superconductors "repel" magnetic field lines fully, i.e. no magnetic field line could penetrate through in this type of superconductors: As you can see no magnetic field line penetrates though this type of superconductor The pure metals which exhibit zero resistivity at low temperatures and have the property of excluding magnetic fields from the interior of the superconductor (Meissner effect). M A Islam, EEE, IIUC
  7. 7. In Type II superconductors transition from a normal state to a superconducting state occurs "slowly" i.e. as you decrease temperature from it's critical temperature superconducting properties increase: Superconductors made from alloys are called Type II superconductors. Besides being mechanically harder than Type I superconductors, they exhibit much higher critical magnetic fields. Type II superconductors such as niobium-titanium (NbTi) are used in the construction of high field superconducting magnets. As you can see on image, there is small curve which approaches zero resistance after critical temperature Tc. The Common and most popular example of Type II superconductor is YBCO superconductor, which critical temperature is 90K. Also some magnetic field lines can penetrate though in this type of superconductors allowing Flux Pinning which is also know as Quantum Locking . As you can see on image, some magnetic field lines can penetrate though this type of superconductors, thus resulting aforementioned Flux pinning. Using this it is possible to say that this type of superconductors aren't ideal superconductors. Type II Superconductors M A Islam, EEE, IIUC
  8. 8. There are few differences between Type I and Type II superconductors, first of them it transition of superconducting state, second is magnetic field lines. Also there are few more differences between them, for example Type I superconductors always have lower critical temperature than the most of Type II superconductors, also There is theory (BCS Theory) which explains only type I superconductors but can't explain type II superconductors (i.e. High temperature superconductivity) Differences between Type I and Type II M A Islam, EEE, IIUC
  9. 9. The magnetic field strength B just outside the surface of the wire is μ0I / 2a. It follows that if the current flowing in a superconducting wire is increased, eventually the field strength at the surface of the wire will exceed Bc and the sample will revert to its normal state. The maximum current that a wire can carry with zero resistance is known as its critical current, and for a long straight wire the critical current Ic is given by Ic = 2aBc / μ0. A current greater than Ic will cause the wire to revert to its normal state. This critical current is proportional to the radius of the wire.The magnetic field strength B just outside the surface of the wire is μ0I / 2a. It follows that if the current flowing in a superconducting wire is increased, eventually the field strength at the surface of the wire will exceed Bc and the sample will revert to its normal state. The maximum current that a wire can carry with zero resistance is known as its critical current, and for a long straight wire the critical current Ic is given by Ic = 2aBc / μ0. A current greater than Ic will cause the wire to revert to its normal state. This critical current is proportional to the radius of the wire. The critical current density = Ic / a2, the current flows only in a thin surface layer. Critical current density M A Islam, EEE, IIUC
  10. 10. Superconductors II -When a metal is cooled to the critical temperature, electrons in the metal form Cooper Pairs. -Cooper Pairs are electrons which exchange phonons and become bound together. -As long as kT < binding energy, then a current can flow without dissipation. -The BCS theory of Superconductivity states that bound photons have slightly lower energy, which prevents lattice collisions and thus eliminates resistance. -Bound electrons behave like bosons. Their wavefunctions don’t obey Pauli exclusion rule and thus they can all occupy the same quantum state. M A Islam, EEE, IIUC
  11. 11. Cooper Pairs -Cooper pairs can tunnel together through the insulating layer of Josephson Junction. -This process is identical to that of quantum barrier penetration in quantum mechanics. -Because of the superconducting nature (no resistance) and the fact that Cooper pairs can jointly tunnel through an insulator we can maintain a quantum current through the Josephson Junction without an applied voltage. -Thus a Josephson Junction can be used as a very sensitive voltage, current or flux detector. -A changing magnetic field induces a current to flow in a ring of metal, this effect can be used to detect flux quanta. Radio Astronomy uses these devices frequently. M A Islam, EEE, IIUC
  12. 12. Josephson Junction Devices -There are three primary Josephson Junction devices. -The Cooper Pair box is the most basic device. We can envision it as a system with easily split levels, and use the degenerate lowest energy levels as a qubit. -Similarly to the Cooper Pair box we can use inductors to adjust, a Josephson Junction, until the potential represented by the potential well is a degenerate double well. We can then use symmetric and anti- symmetric wavefunctions and their associated eigenvalues as |0> and |1>. M A Islam, EEE, IIUC
  13. 13. Josephson Junction Devices II A current-biased Josephson Junction employs creates a “washboard” shaped potential. Splitting in the wells indicates allows us to use the lowest two levels as qubit states. The higher energy state |1> can be detected because the tunneling probability under a microwave probe will be 500 times as probable to induce a transition. Creates a detectable voltage by “going downhill.” Thus we can know the state. M A Islam, EEE, IIUC
  14. 14. Why Josephson Junctions? • Microscopic implementations: – based on electron spins, nuclei spins, or other microscopic properties – (+)decohere slowly as naturally distinguishable from environment – (+)single ions can be manipulated with high precision – (-)hard to apply to many qubits – (-)difficult to implement with devices • Macroscopic Implementations: Solid State - Semiconductors: quantum dots, single donor systems - Superconductors: Josephson Junctions: - more success so far - Josephson tunnel junction is “the only non-dissipative, strongly non-linear circuit element available at low temperature “ M A Islam, EEE, IIUC
  15. 15. Benefits of Josephson Junctions - Low temperatures of superconductor: - no dissipation of energyno resistanceno electron-electron interactions(due to energy gap of Cooper pairs) - low noise levels - Precise manipulation of qubits possible - Scalable theoretically for large numbers of qubits - Efficient use of resources: circuit implementation using existing integrated circuit fabrication technology - Nonlinear Circuit Element - Needed for quantum signal processing - “easy” to analyze electrodynamics of circuit Current versus flux across Josephson Junction M A Islam, EEE, IIUC
  16. 16. London Theory – 1 • Newton’s law (inertial response) for applied electric field  SJ dt d E  2 en m s        en J dt d meE s S  sv dt d mF  sss evnJ  dt dJ m Een Ss  2 dt Jd m Een Ss      2 dt Jd dt Bd m en Ss     2 0 2        B m en J dt d s S  Supercurrent density is B m en J s S  2  We know B = 0 inside superconductors Faraday’s law Fritz & Heinz London, (1935) M A Islam, EEE, IIUC
  17. 17. London Theory – 2  SJ dt d E  2 en m s  B m en J s S  2  London Equations t E JB      000  JB   0   B m en BB s  2 0 2  B m en B s  2 0 2  Ampere’s law =0; Gauss’s law for electrostatics M A Islam, EEE, IIUC
  18. 18. Conductors in a Magnetic Field Apply field Perfect (metallic) conductor SuperconductorNormal metal Cool Cool Field off Apply field Apply field M A Islam, EEE, IIUC
  19. 19. Meissner-Oschenfeld Effect Superconductor Cool Apply field • B = 0  perfect diamagnetism: cM = -1 • Field expulsion unexpected; not discovered for 20 years. HHM MHB   c  0)(0 B/0 H -M HHc Hc Ideal conductor! Ideal diamagnetic! M A Islam, EEE, IIUC
  20. 20. The Meissner (and Ochsenfeld) Effect superconductors push out magnetic fields - and keep them out with constantly- flowing resistance-less currents this „diamagnetic‟ property is more fundamental than zero resistance T > Tc T < Tc http://www.physics.ubc.ca/~outreach/phys420/p420_96/bruce/ybco.html M A Islam, EEE, IIUC
  21. 21. The dream - “Tomorrow‟s Superconducting World” 350 mph levitated Intercity trains Underground rapid transit: Heathrow to Gatwick in 10 minutes Computing: 1000 times faster supercomputers Cargo- carrying submarines, all-electric US Navy Energy Saving: power lines electric motors transformers Medical Diagnostics: Magnetic Resonance Imaging SQUID: Brain activity Heart function Information Technology: much faster, wider band communications magnetically launched space shuttle M A Islam, EEE, IIUC
  22. 22. Some of these dreams are already reality… Japanese levitating train has superconducting magnets onboard Superconducting power cable installed in Denmark SQUID measure- ment of neuro- magnetic signals (nuclear) magnetic resonance imaging of the brain, in the field from a superconducting magnet www.rtri.or.jp/rd/maglev/html/english/maglev_frame_E.html www.lanl.gov/quarterly/q_spring03/meg_helmet.shtml http://www.bestofjesse.com/projects /indust/project1.html M A Islam, EEE, IIUC
  23. 23. Uses of SC magnets M A Islam, EEE, IIUC
  24. 24. Scientific and industrial NMR facilities 900 MHz superconductive NMR installation. It is used For pharmacological investigations of various bio-macromolecules. Yokohama City University M A Islam, EEE, IIUC
  25. 25. Medical NMR tomography equipment M A Islam, EEE, IIUC
  26. 26. Criogenic high frequency filters for wireless communications M A Islam, EEE, IIUC
  27. 27. Transmission Lines • 15% of generated electricity is dissipated in transmission lines • Potential 100-fold increase in capacity • BNL Prototype: 1000 MW transported in a diameter of 40 cm Pirelli Cables & Systems M A Islam, EEE, IIUC
  28. 28. Telecommunications • Superconductors are used as efficient filters in cellular telephone towers (now 700 worldwide) • Separate signals of individual phone calls. • Because of electrical resistance, conventional interference filters eat away part of the signal. Conductus Clearsite system M A Islam, EEE, IIUC
  29. 29. Other Uses of Superconductivity • Fault current limiters • Electric motors • Electric generators • Petaflop computers (thousand trillion floating point operations per second) M A Islam, EEE, IIUC
  30. 30. Merits & Demerits Trade off between: Cost Saving and Cost Increase Zero resistance, no energy lost, novel uses… Need refrigeration, fabrication costs….
  31. 31. Thank You

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