What s so super about superconductivity?

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Christine Butler
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What s so super about superconductivity? Mark Rzchowski Physics Department Electrons can flow through the wire when pushed by a battery.

Resistance question Suppose we have a perfect crystal of metal in which we produce an electric current. The electrons in the metal A.

Propagate through the crystal without any electrical resistance If all atoms are perfectly in place, the electron moves though the without any

Electron scatters from these irregularities, -> resistance Temperature-dependent resistance Suppose we cool down the wire that carries

Stay same Resistance As elecron wave propagates through lattice, it faces resistance Resistance: Bumps from vibrating atoms Collisions with

1 What s so super about superconductivity? Mark Rzchowski Physics Department Electrons can flow through the wire when pushed by a battery. Electrical resistance But remember that the wire is made of atoms. Electrons as waves drift through the atomic lattice. Resistance question Suppose we have a perfect crystal of metal in which we produce an electric current. The electrons in the metal A. Collide with the atoms, causing electrical resistance B. Twist between atoms, causing electrical resistance C. Propagate through the crystal without any electrical resistance If all atoms are perfectly in place, the electron moves though the without any resistance! Life is tough In the real world, electrons don t have it so easy Some missing atoms (defects) Vibrating atoms! Electron scatters from these irregularities, -> resistance Temperature-dependent resistance Suppose we cool down the wire that carries electrical current to light bulb. The light will A. Get brighter B. Get dimmer C. Stay same Resistance As elecron wave propagates through lattice, it faces resistance Resistance: Bumps from vibrating atoms Collisions with impurities Repulsion from other electrons Electrons scatter from these atomic vibrations and defects. Vibrations are less at low temperature, so resistance decreases. More current flows through wire Life is tough for electrons, especially on hot days 1

Why does temperature matter? Temperature is related to the energy of a macroscopic object. The energy usually shows up as energy of random motion.

But 0 K means no internal kinetic energy. 0 degrees Kelvin (Absolute Zero) is the coldest temperature possible This is -459.

15 273.15 77.36 4.2 0 comments water boils water freezes liquid nitrogen boils liquid helium boils absolute zero What happens at the lowest temperature?

2 Why does temperature matter? Temperature is related to the energy of a macroscopic object. The energy usually shows up as energy of random motion. There really is a coldest temperature, corresponding to zero motional energy! The Kelvin scale has the same size degree as the Celsius ( C) scale. But 0 K means no internal kinetic energy. 0 degrees Kelvin (Absolute Zero) is the coldest temperature possible This is F Temperature scales Kelvin (K): K = C K = 5/9 F Fahrenheit Celsius Kelvin comments water boils water freezes liquid nitrogen boils liquid helium boils absolute zero What happens at the lowest temperature? Kelvin ( ): electrons freeze and resistance increases Onnes ( ): Resistance continues drop, finally reaching zero at zero temperature Sometimes, something else! Heike Kamerlingh Onnes liquefied helium (~4 K = F ) investigated low temperature resistance of mercury Found resistance dropped abruptly to zero at 4.2 K Nobel Prize in physics Onnes published the finding in November 1911 as On the Sudden Change in the Rate at Which the Resistance of Mercury Disappears. Onnes Superconductivity Superconductors are materials that have exactly zero electrical resistance. But this only occurs at temperatures below a critical temperature, T c In most cases this temperature is far below room temperature. Superconducting Critical Temperature Not superconducting (normal) Hg (mercury) 2

Persistent currents Critical current Critical Current How zero is zero? EXACTLY! Can set up a persistent current in a ring.

Magnetic field Persistent supercurrent If the current is too big, superconductivity is destroyed. Maximum current for zero resistance is called the critical current.

Voltage Superconducting Current Not superconducting (normal) Critical current Superconducting elements Many elements are in fact superconducting In fact, most of them are!

Element Aluminum Mercury Lead Tin Niobium Critical T. (K) 1.75 4.15 7.2 3.72 9.

3 Persistent currents Critical current Critical Current How zero is zero? EXACTLY! Can set up a persistent current in a ring. The magnitude of the current measured by the magnetic field generated. No current decay detected over many years! Magnetic field Persistent supercurrent If the current is too big, superconductivity is destroyed. Maximum current for zero resistance is called the critical current. For larger currents, the voltage is no longer zero, and power is dissipated. Voltage Superconducting Current Not superconducting (normal) Critical current Superconducting elements Many elements are in fact superconducting In fact, most of them are! Critical temperatures If superconductivity is so common, why don t we have superconducting cars, trains, toothbrushes? Many superconducting critical temperatures are low. Element Aluminum Mercury Lead Tin Niobium Critical T. (K) ( C) ( F) Higher transition temperatures Much higher critical temperature alloys have been discovered NbTi 10 K Nb 3 Sn YBa 2 Cu 3 O 7, BiSrCaCuO, 19 K 92 K 120 K High-temperature superconductors 1911: superconductivity discovered: Hg at 4K 1933: Meissner effect A century of superconductivity 1950: Landau- Ginzburg theory 1954: Type II superconductors 1986: high temp supercondu ctivity : BCS microscopic theory 1962: Josephson effect 3

Reaching low temperature Low temperatures obtained with liquid gases.

A liquid gas will remain at its boiling point. Liquid Oxygen: 90.2 K (-297.4 F) Liquid Nitrogen: 77 K (-320.4 F) Liquid Hydrogen: 20.4 K (-423.2 F) Liquid Helium: 4.2 K (-452.

$More subject to fracture. Meissner effect Meissner effect Response to magnetic field For small magnetic fields a superconductor will spontaneously expel all magnetic flux.$

4 Reaching low temperature Low temperatures obtained with liquid gases. To turn a liquid into a gas at fixed temperature requires a certain amount of heat (latent heat) So the liquid warms up to its boiling point, then turns into vapor a little at a time. A liquid gas will remain at its boiling point. Liquid Oxygen: 90.2 K ( F) Liquid Nitrogen: 77 K ( F) Liquid Hydrogen: 20.4 K ( F) Liquid Helium: 4.2 K ( F) Low temperature properties Superconductors become superconducting at low temperature But also, many mechanical properties change at low temperature. Many materials lose their elasticity. More subject to fracture. Meissner effect Meissner effect Response to magnetic field For small magnetic fields a superconductor will spontaneously expel all magnetic flux. Above the critical temperature, this effect is not observed. Apply uniform magnetic field. Superconductor responds with circulating current. Produces own magnetic dipole field that opposite to one produced by magnet Total magnetic field is superposition of field generated by superconductor and applied field Field is zero inside superconductor, enhanced outside Perfect Diamagnet Diamagnetic levitation Many materials are diamagnetic - produce magnetic dipole opposing main field. Causes repulsive force that can oppose gravity. Nijmegen High Fild Magnet Lab 4

Superconducting levitation Superconducting Train Superconductor is a perfect diamagnet Produces strong field that exactly cancels magnet.

Larger fields require larger screening currents. Screening currents cannot be larger than the critical current.

Above this field, superconductivity is destroyed (screening current exceeds critical current) Superconductor phase diagram (Type I) Critical magnetic field Critical fields It

Superconductivity seemed a fragile effect Only observed at low temperature Destroyed by small magnetic fields. DISCOVERY!

5 Superconducting levitation Superconducting Train Superconductor is a perfect diamagnet Produces strong field that exactly cancels magnet. At base of Mount Fuji, close to Tokyo, 18 km long test track constructed 430 km/h = mph Critical magnetic field Magnetic field is screened out by screening current. Larger fields require larger screening currents. Screening currents cannot be larger than the critical current. This says there is a critical magnetic field which can be screened. Above this field, superconductivity is destroyed (screening current exceeds critical current) Superconductor phase diagram (Type I) Critical magnetic field Critical fields It was one of Onnes disappointments that even small magnetic fields destroyed superconductivity. Superconductivity seemed a fragile effect Only observed at low temperature Destroyed by small magnetic fields. DISCOVERY! Some superconductors behave entirely differently in a magnetic field. These are called type II superconductors Vortices in type II superconductors Superconducting vortices Superconductor is normal (not superconducting) at center of vortex Still superconducting between vortices. Uniform flux out here Above the critical field, magnet field penetrates in concentrated vortices of magnetic flux. Each vortex carries one flux quantum of flux. Magnetic flux concentrated here, material driven normal Material still superconducting here 5

Critical Fields: Type II superconductor Upper

type II superconductors, critical fields can be

So large that we generally use a unit of Tesla 1

Tesla, even 60 Tesla Lower critical field vortices

microscopy of vortices Think of vortices as real

through the material by physical force Or pushed by

6 Critical Fields: Type II superconductor Upper critical fields Upper critical field Vortex state In type II superconductors, critical fields can be extremely large. So large that we generally use a unit of Tesla 1 Tesla = 10,000 Gauss Can now easily be 10 Tesla, 20 Tesla, even 60 Tesla Lower critical field vortices Magnetic Field Ranges Field Size Example Field Size Example 850 T 0.4 T Tornado vortex Vortices Bathtub vortex 60 T 33 T 2 T 0.2 T 0.01 T T T 0.5 T 3x10-10 T Superconducting Vortex Lorentz microscopy of vortices Think of vortices as real physical objects Threads of magnetic flux slide through the material by physical force Or pushed by electrical current Magnetic Levitation Defects in the material resist this motion So vortices have to be pushed hard High-temperature superconductor Permanent magnet above a superconductor 6

Superconducting wire Multifilamentary wire Induce strong pinning by incorporation of

Superconducting power cables 2001: Detroit, MI Detroit Edison,Frisbie Substation three

Discovered 1986, work at temperature of liquid notrogen Most applications now use low

htm Superconducting Magnets Coil of wire as in conventional electromagnet But once current

< T c Magnetic Resonance Imaging typically done at 1.

7 Superconducting wire Multifilamentary wire Induce strong pinning by incorporation of defects. Strong pinning leads to zero dissipation even with vortex penetration. Superconducting power cables 2001: Detroit, MI Detroit Edison,Frisbie Substation three 400-foot HTS cables 100 million watts of power Uses high-temperature superconductors Discovered 1986, work at temperature of liquid notrogen Most applications now use low critical temperature alloys. Superconducting Magnets Coil of wire as in conventional electromagnet But once current is injected, power supply turned off, current and magnetic field stays forever as long as T < T c Magnetic Resonance Imaging typically done at 1.5 T Superconducting magnet to provides static magnetic field Spatial resolution of positions of tracer atomic nuclei. Magnets for MRI Large scale applications Superconducting magnet Plasma confinement torus Proposed ITER fusion test reactor Multi-electron effect, interactions with lattice vibrations Correlated ground state Very different from any previous theory. 7

Much more difficult problems than Low-temp. materials.

8 High temperature superconductors Copper and oxygen based materials. Very different from lowtemperature superconductors. Discovered ~ 20 years ago. No theoretical consensus. Much more difficult problems than Low-temp. materials. Another new material Magnesium diboride MgB 2 T c =39K Discovered ~ 3 years ago. Microscopic theory understood, but novel in that it has two independent electron bands. Like two superconductors in the same spatial location. 8

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