Demonstration Some simple theoretical models Materials How to make superconductors Some applications

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Clemence Thomas
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1 Superconductivity Demonstration Some simple theoretical models Materials How to make superconductors Some applications

2 How do we show superconductivity? Superconductors 1. have an electrical resistivity that is exactly zero, (Lab experiment)

3 How do we show superconductivity? Superconductors 1. have an electrical resistivity that is exactly zero, 2. refuse magnetic fields to enter the superconducting volume. (Lab experiment) Let's try!

4 Meissner-Ochsenfeld effect Perfect metal Superconductor Room temperature Room temperature, with magnetic field At low temperature (T<Tc), after cooling in a constant magnetic field

5 "Perfect conductor" effect Perfect metal Superconductor Room temperature Low temperature (T<Tc)without magnetic field After applying a magnetic field at low temperature (T<Tc)

6 How can a magnetic field be expelled? Maxwell's laws are basically valid, so to create zero magnetic field at a superconducting surface we must postulate a very large current just inside the surface: External field Field created by current Current inside plate Just at the superconductor surface, the two fields are equal and cancel each other!

7 "Magnetic mirror" In principle, you can describe this as if the surface was a "mirror" for external magnetic fields: Real magnets outside: "Virtual magnet images" inside:

8 "Magnetic mirror" In principle, you can describe this as if the surface were a "mirror" for external magnetic fields: Real magnets outside: Clearly, no magnetic flux line crosses the boundary, and there is a strong repulsion everywhere! "Virtual magnet images" inside:

9 Why is the levitation stable? When you balance things on soft springs the situation is usually unstable. So why doesn't the magnet simply fall off?

10 Why is the levitation stable? When you balance things on soft springs the situation is usually unstable. So why doesn't the magnet simply fall off? Because the field can penetrate! Take a ceramic:

11 Why is the levitation stable? Although the grains are superconducting, the boundaries are effectively thin "normal" films. Some field lines can find ways to penetrate the ceramic, but then get "locked" in place - they cannot move without crossing grains!

12 A little bit of theory: What clues are there to how superconductivity works? 1. The Meissner-Ochsenfeld effect and zero resistivity both indicate that electrons can move without collisions.

13 A little bit of theory: What clues are there to how superconductivity works? 1. The Meissner-Ochsenfeld effect and zero resistivity both indicate that electrons can move without collisions. 2. Electron tunnelling experiments on superconducting films shows that the quasiparticles coming out of the superconductor always have a charge 2q e.

14 A little bit of theory: What clues are there to how superconductivity works? 1. The Meissner-Ochsenfeld effect and zero resistivity both indicate that electrons can move without collisions. 2. Electron tunnelling experiments on superconducting films shows that the quasiparticles coming out of the superconductor always have a charge 2q e. 3. Spectroscopy shows a "semiconductor-like" behaviour: All photons below a certain energy are reflected.

15 A little bit of theory: What clues are there to how superconductivity works? 1. The Meissner-Ochsenfeld effect and zero resistivity both indicate that electrons can move without collisions. 2. Electron tunnelling experiments on superconducting films shows that the quasiparticles coming out of the superconductor always have a charge 2q e. 3. Spectroscopy shows a "semiconductor-like" behaviour: All photons below a certain energy are reflected. 4. The electronic specific heat has a strong peak at Tc and drops exponentially (not linearly!) with T below this.

16 A little bit of theory: What conclusions follow from this? 2. Electrons travel in pairs ("Cooper pairs"). Two electrons with opposite spins travelling together have a total spin zero. A quasi-particle such as an electron pair is no longer a fermion but a boson!

17 A little bit of theory: What conclusions follow from this? 2. Electrons travel in pairs ("Cooper pairs"). Two electrons with opposite spins travelling together have a total spin zero. A quasi-particle such as an electron pair is no longer a fermion but a boson! 3 & 4. The electrons must be in states with energy E S < E F, and there is an energy gap between E S and E F.

18 A little bit of theory: What conclusions follow from this? 2. Electrons travel in pairs ("Cooper pairs"). Two electrons with opposite spins travelling together have a total spin zero. A quasi-particle such as an electron pair is no longer a fermion but a boson! 3 & 4. The electrons must be in states with energy E S < E F, and there is an energy gap between E S and E F and actually, then it is impossible for the electron pairs to collide with either phonons or impurities at low enough temperature, because that would violate the energy conservation principle!

19 (What do you mean? Impossible??) A superconducting pair has total energy 2 x E S, and we assume the gap energy is 2D, so E F = E S + 2D. We know that all states below E F are filled at low T, so to find empty states after any collision the electrons must have an energy > E F each, i.e. the total energy must be > 2 x E F (which is clearly > 2 x E S, the pair energy!). Elastic scattering (on impurities) can never occur. Inelastic phonon scattering can happen, but only if the phonon has an energy E P > 4D E P + 2 x E S > 2 x E F! (Theory predicts a gap 2D = 3.5 k B Tc, which is reasonable!)

20 A little bit of theory: Superconductors are described by a few parameters: 1. Critical parameters: Tc, Ic, and Bc (critical temperature, current, and magnetic field). If any of these is exceeded, there is no superconductivity.

21 A little bit of theory: Superconductors are described by a few parameters: 1. Critical parameters: Tc, Ic, and Bc (critical temperature, current, and magnetic field). If any of these is exceeded, there is no superconductivity. 2. Magnetic penetration depth, l. How deep does an external magnetic field penetrate? l = (m/m o ne 2 ) 1/2 (SI!)

22 A little bit of theory: Superconductors are described by a few parameters: 1. Critical parameters: Tc, Ic, and Bc (critical temperature, current, and magnetic field). If any of these is exceeded, there is no superconductivity. 2. Magnetic penetration depth, l. How deep does an external magnetic field penetrate? l = (m/m o ne 2 ) 1/2 (SI!) 3. Coherence length x of the order parameter. ( Diameter of a Cooper pair".) x hv F /((2p) 2 k B T c )

23 A little bit of theory: Superconductors are described by a few parameters: 1. Critical parameters: Tc, Ic, and Bc (critical temperature, current, and magnetic field). If any of these is exceeded, there is no superconductivity. 2. Magnetic penetration depth, l. How deep does an external magnetic field penetrate? l = (m/m o ne 2 ) 1/2 (SI!) 3. Coherence length x of the order parameter. ( Diameter of a Cooper pair".) x hv F /((2p) 2 k B T c ) All values are usually given for T = 0; when T Tc, Ic, Bc, and D 0, and l and x. Also, when l/x > 2-1/2 we have type II superconductivity.

24 Two types of superconductors: Types I and II Type I Type II Different behaviours in magnetic fields (red): Weak B-fields are always repelled, by both types; strong fields destroy the superconductivity in type I, but penetrate type II in "vortex tubes" containing one flux quantum each!

25 Two types of superconductors: Types I and II Is it possible to SEE a magnetic field, i.e individual flux quanta? Yes! If you disperse very fine magnetic particles (iron filings) in a thin layer on the surface of a superconductor : This optical micrograph shows (red) magnetic particles on the surface of a superconductor in a strong external magnetic field.

26 Two types of superconductors: Types I and II Most practical applications use type II superconductors, because type I superconductivity is usually destroyed even by very weak external fields.

27 A little bit of theory: Another interesting property is that a closed ring of a superconducting material can only encircle an integer number of magnetic flux quanta, F 0 = h/2e = Wb.

28 A little bit of theory: Another interesting property is that a closed ring of a superconducting material can only encircle an integer number of magnetic flux quanta, F 0 = h/2e = Wb. This property has many consequences. If we make a closed ring with a very thin gap, Cooper pairs can tunnel through this gap showing the Josephson effects: 1. There can exist a tunnelling supercurrent I = Ic sin g without a voltage difference (DC effect) 2. If there is a voltage V, the current will oscillate with frequency f = V/F 0 (or dg/dt = 4peV/h) (AC effect)

Josephson effects The Josephson effects are is the basis for using superconductors in electronics and measurements. DC AC To change the current, I = Ic sin g, we must change g.

29 Josephson effects The Josephson effects are is the basis for using superconductors in electronics and measurements. DC AC To change the current, I = Ic sin g, we must change g. This induces a voltage V since dg/dt = 4peV/h. If we have an AC current oscillating at constant frequency we get a constant DC voltage over the gap, V = f F 0. This is our present practical method of defining the unit for electrical voltage! (f 484 MHz V = 1 mv)

30 Superconducting materials "Classical" superconductors: Metals and alloys! Hg 4.2 K Discovered by Heike Kammerling Onnes in 1911 (Nobel Prize 1913) Pb 7.2 K Nb 9.2 K (0.2 T - type II element!) NbTi 9.8 K 14 T (The "standard" superconductor) NbN 16.1 K 16 T (used in thin film applications) Nb 3 Sn 18 K 24 T (expensive and difficult to use)

31 Superconductivity is actually a common effect! From

32 High Transition Temperature Superconductors (HiTc:s) MgB 2

33 A new star: MgB 2 Superconductivity in MgB 2 was discovered in 2001 with Tc = 39 K, the highest for any "classical" superconductor. The material is cheap, easy to handle, nonpoisonous, and easily formed into wires or films/tapes. Problem: The practical critical field seems to be limited to 3.5 T.

34 An even newer star: iron arsenides In 2008, another type of layered, exotic superconductors, based on iron and arsenic, was discovered. Takahashi et al., Nature 453, 376 (2008)

An even newer star: iron arsenides In 2008, another type of layered, exotic superconductors, based on iron and arsenic, was discovered. Another family is Ba x K y Fe 2 As 2.

35 An even newer star: iron arsenides In 2008, another type of layered, exotic superconductors, based on iron and arsenic, was discovered. Another family is Ba x K y Fe 2 As 2. Critical temperatures up to above 55 K have been reported when changing the La to heavier rare earths. Again, the material is cheap and fairly easy to handle, but As is clearly poisonous!

36 High Transition Temperature Superconductors (HiTc:s) Quite complicated structures! One of the simplest is YBa 2 Cu 3 O x, "Y-1-2-3": The basic structure is tetragonal,

37 High Transition Temperature Superconductors (HiTc:s) Quite complicated structures! One of the simplest is YBa 2 Cu 3 O x, "Y-1-2-3": The basic structure is tetragonal, with copper

38 High Transition Temperature Superconductors (HiTc:s) Quite complicated structures! One of the simplest is YBa 2 Cu 3 O x, "Y-1-2-3": The basic structure is tetragonal, with copper and oxygen forming a framework

39 High Transition Temperature Superconductors (HiTc:s) Quite complicated structures! One of the simplest is YBa 2 Cu 3 O x, "Y-1-2-3": The basic structure is tetragonal, with copper and oxygen forming a framework into which we insert Ba

40 High Transition Temperature Superconductors (HiTc:s) Quite complicated structures! One of the simplest is YBa 2 Cu 3 O x, "Y-1-2-3": The basic structure is tetragonal, with copper and oxygen forming a framework into which we insert Ba and Y. The formula is now YBa 2 Cu 3 O 6, and this material is NOT superconducting!

41 High Transition Temperature Superconductors (HiTc:s) Quite complicated structures! One of the simplest is YBa 2 Cu 3 O x, "Y-1-2-3": The basic structure is tetragonal, with copper and oxygen forming a framework into which we insert Ba and Y. To get a superconducting material we must add more oxygen, to obtain YBa 2 Cu 3 O 7!

42 High Transition Temperature Superconductors (HiTc:s) Quite complicated structures! One of the simplest is YBa 2 Cu 3 O x, "Y-1-2-3": CuO chain Ba spacer CuO plane Y spacer CuO plane Ba spacer CuO chain

43 High Transition Temperature Superconductors (HiTc:s) Quite complicated structures! One of the simplest is YBa 2 Cu 3 O x, "Y-1-2-3": CuO chain These are the metallic, superconducting parts! Ba spacer CuO plane Y spacer CuO plane Ba spacer CuO chain

44 High Transition Temperature Superconductors (HiTc:s) Quite complicated structures! One of the simplest is YBa 2 Cu 3 O x, "Y-1-2-3": CuO chain These are the metallic, superconducting parts! To some extent, more CuO planes mean higher Tc! Ba spacer CuO plane Y spacer CuO plane Ba spacer CuO chain

45 High Transition Temperature Superconductors (HiTc:s) How to make YBa 2 Cu 3 O x, "Y-1-2-3": 1. Mix and grind Y 2 O 3, BaCO 3 and CuO for a long time. 2. Heat in an oven at o C for at least 1 hour. 3. Crush, re-grind, and repeat 2. a few times. 4. Press into a cake, then heat in pure oxygen gas at 450 o C for at least 24 hours. 5. Time to test for superconductivity!

46 But how do you make ceramic "wires"? There are two ways: 1. Thin films on a metal or ceramic substrate 2. "Powder-in-tube" technology

47 But how do you make ceramic "wires"? There are two ways: 1. Thin films on a metal or ceramic substrate 2. "Powder-in-tube" technology Stainless Deposition of Oxygen treatment Storage stell band ceramic film in hot oven

48 But how do you make ceramic "wires"? There are two ways: 1. Thin films on a metal or ceramic substrate 2. "Powder-in-tube" technology Fill a silver tube with superconductor powder, then draw to desired shape, then heat treat ("anneal").

49 But how do you make ceramic "wires"? The "powder-in-tube" method is simlar to what you do to "classical" superconductors: Basic procedure: - Make a Cu cylinder, - make a lot of holes along axis, - fill the holes with superconducting rods, - draw the whole cylinder to wire, as if it were massive Cu! This procedure works well with Nb-Ti, which is soft and ductile like copper!

50 But how do you make ceramic "wires"? All superconductor wires have similar internal "multistrand" structures! NbTi wire High-Tc (BiSSC) wires

51 Applications for superconductors There are basically two types of applications: Power circuits and electronics/measurements. Most practical applications use type II superconductors. Existing and future commercial devices: Power transmission components, power storage devices, electric motors and generators, frictionless bearings, permanent magnets and electromagnets, voltage standards, fast computers and electronics, microwave filters,...

52 Applications for superconductors In electronics, one possible application is in fast computers. Clock pulses must be synchronized in a computer, but at 3 GHz light travels only 10 cm during one clock pulse! Shrinking a computer means more concentrated heating, killing the CPU! The obvious solution is a superconducting computer!

53 Using type II superconductors An obvious application for a superconductor is to transport electric current. What happens to electrons in a B-field?

54 Using type II superconductors An obvious application for a superconductor is to transport electric current. What happens to electrons in a B-field? Current

55 Using type II superconductors An obvious application for a superconductor is to transport electric current. What happens to electrons in a B-field? Current

56 Using type II superconductors An obvious application for a superconductor is to transport electric current. What happens to electrons in a B-field? B-field Current

57 Using type II superconductors An obvious application for a superconductor is to transport electric current. What happens to electrons in a B-field? B-field Let us remember two laws: Current

58 Using type II superconductors An obvious application for a superconductor is to transport electric current. What happens to electrons in a B-field? B-field Let us remember two laws: F m = qv B ("Maxwell") F = 0 ("Newton") Current

59 Using type II superconductors An obvious application for a superconductor is to transport electric current. What happens to electrons in a B-field? B-field Let us remember two laws: F m = qv B ("Maxwell") F = 0 ("Newton") Current

60 Using type II superconductors An obvious application for a superconductor is to transport electric current. What happens to electrons in a B-field? B-field Let us remember two laws: F m = qv B ("Maxwell") F = 0 ("Newton") Current

61 Using type II superconductors An obvious application for a superconductor is to transport electric current. What happens to electrons in a B-field? B-field Let us remember two laws: F m = qv B ("Maxwell") F = 0 ("Newton") Current There will be a force on the magnetic field lines!

62 Using type II superconductors Is this a problem? B-field Current

63 Using type II superconductors Is this a problem? A moving field changing flux; but - df/dt = E! B-field Current

64 Using type II superconductors Is this a problem? A moving field changing flux; but - df/dt = E! B-field This gives two problems: 1. A voltage appears along the current flow; "resistance"! 2. This causes dissipation of heat, since P = U I Current

65 Using type II superconductors Is this a problem? A moving field changing flux; but - df/dt = E! This gives two problems: 1. A voltage appears along the current flow; "resistance"! 2. This causes dissipation of heat, since P = U I

66 Using type II superconductors Or, if we measure voltage as a function of applied current at constant temperature:

67 Using type II superconductors Conclusion: We want to keep the flux lattice fixed in space! How do we do this?

68 Using type II superconductors Conclusion: We want to keep the flux lattice fixed in space! How do we do this? Flux lines prefer to go through non-superconducting regions, because it requires energy to create a vortex tube! So, we should insert impurity particles into the superconductor! This method is called flux pinning.

69 A possible novel application The first practical application for high-tc materials in power circuits is likely to be something that cannot be made without superconductivity. One such example is the superconducting current limiter:

A possible novel application The first practical application for high-tc materials in power circuits is likely to be something that cannot be made without superconductivity.

70 A possible novel application The first practical application for high-tc materials in power circuits is likely to be something that cannot be made without superconductivity. One such example is the superconducting current limiter: Consider a standard transformer (which you can find in any electronic device, at home or here): U 1 /U 2 = N 1 /N 2 = I 2 /I 1, where 1 means "input" side, 2 "output" side, and N is the number of wire turns!

71 A possible novel application The first practical application for high-tc materials in power circuits is likely to be something that cannot be made without superconductivity. One such example is the superconducting current limiter: Suppose we make a transformer with N 2 = 1 (a single turn). If we short-circuit the output, U 2 =0, then U 1 = NU 2 = 0, for all currents! Usually this is just stupid, but what if we make the secondary one turn superconductor wire?

72 A possible novel application Superconducting current limiter: I2 = N I 1 ; Primary current I 1 if the coil superconducts U 1 = U 2 = 0, and P = UI = 0!

73 A possible novel application Superconducting current limiter: I2 = N I 1 ; Primary current I 1 if the coil superconducts U 1 = U 2 = 0, and P = UI = 0! However, whenever I 2 > Ic the secondary turns normal and R 1 = U 1 /I 1 = N 2 U 2 /I 2 = N 2 R 2! Because N can be made large and high-tc materials have very large normal resistivities, this works as a "fuse"!

74 A possible novel application Superconducting current limiter: N 1 = 500 N 2 = 1 Ic 85 A at 77 K (measured!) Tc 110 K (Bi-2223)

Energy Levels Zero energy. From Last Time Molecules. Today. n- and p-type semiconductors. Energy Levels in a Metal. Junctions

Energy Levels Zero energy. From Last Time Molecules. Today. n- and p-type semiconductors. Energy Levels in a Metal. Junctions Today From Last Time Molecules Symmetric and anti-symmetric wave functions Lightly higher and lower energy levels More atoms more energy levels Conductors, insulators and semiconductors Conductors and