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Edit Comment Close Premium member Presentation Transcript Slide1: “… at each new level of complexity, entirely new properties appear, and the understanding of this behavior requires research which I think is as fundamental in its nature as any other” Philip W. Anderson 1972 From last lecture ….Slide2: Where could we find superfluidity? n p p He - 3 He - 4 Helium Helium - 4 atoms are bosons particles with integer spin. Helium - 3 atoms are fermions particles with half integer spin. Slide3: 1938 Kapitza and Allen discover superfluidity in He-4Slide4: For T < 2.4Κ – gravity ... If the bottle containing helium rotates for a while and then stops, helium will continue to rotate for ever – there is no internal friction (for as long as He is at T = -269 C or lowerSlide5: 1938 Pyotr L. Kapitsa discovered the superfluidity of liquid Helium 4 Nobel Prize in 1978 1941-47 Lev Landau formulated the theory of quantum Bose liquid - 4He superfluid liquid. 1956-58 he further formulated the theory of quantum Fermi liquid. Nobel Prize in 1962 Early 1970s David M. Lee, Douglas D. Osheroff, and Robert C. Richardson discovered the superfluidity of liquid Helium 3. Nobel Prize in 1996 Anthony Leggett first formulated the theory of superfluidity in liquid 3He in 1965. Nobel Prize in 2003Slide6: Διάστημα: 3000 χιλιοστά από το απόλυτο μηδέν (-273.15 C) 5 χιλιοστά από το απόλυτο μηδέν Χαμηλές θερμοκρασίεςLOW-TC Superconductors: LOW-TC Superconductors Lead (Pb) Mercury (Hg) Aluminum (Al) Gallium (Ga) Molybdenum (Mo) Zinc (Zn) Zirconium (Zr) Americium (Am) Cadmium (Cd) Ruthenium (Ru) Titanium (Ti) Uranium (U) Hafnium (Hf) Iridium (Ir) Beryllium (Be) Tungsten (W) Platinum (Pt)* Rhodium (Rh) 7.196 K 4.15 K 1.175 K 1.083 K 0.915 K 0.85 K 0.61 K 0.60 K 0.517 K 0.49 K 0.40 K 0.20 K 0.128 K 0.1125 K 0.023 K 0.0154 K 0.0019 K 0.000325 K Conductors vs. Insulators: Conductors vs. Insulators No free electrons to carry the current FREE ELECTRONSSlide9: The foam balls (containing small magnets) organise themselves based on the laws of minimum energy. This arrangement mimics the crystal lattice of a solid material. What is Resistance?: What is Resistance? Electrical Resistance: Electrical Resistance Thermal vibrations (phonons) of the ionic lattice Lattice defects Impurities RESISTANCE is caused by electrons colliding with: Cations ElectronsSlide12: V I Vs copper Liquid helium 4.2K (-269 ºC) Slide13: R T 77K 273K = 0ºC Ro ImpuritiesSlide14: V I Vs Hg Liquid helium 4.2K (-269 ºC) Onnes (1911)Low -Tc Superconductivity: Low -Tc Superconductivity Heike Kamerlingh Onnes (1911)LOW-TC Superconductors: LOW-TC Superconductors Lead (Pb) Mercury (Hg) Aluminum (Al) Gallium (Ga) Molybdenum (Mo) Zinc (Zn) Zirconium (Zr) Americium (Am) Cadmium (Cd) Ruthenium (Ru) Titanium (Ti) Uranium (U) Hafnium (Hf) Iridium (Ir) Beryllium (Be) Tungsten (W) Platinum (Pt)* Rhodium (Rh) 7.196 K 4.15 K 1.175 K 1.083 K 0.915 K 0.85 K 0.61 K 0.60 K 0.517 K 0.49 K 0.40 K 0.20 K 0.128 K 0.1125 K 0.023 K 0.0154 K 0.0019 K 0.000325 K BCS Theory: BCS Theory John Bardeen Leon Cooper John Schrieffer (1957) No collisions Zero resistance Meissner Effect : Meissner Effect 1933 – Walther Meissner and Robert Ochsenfeld T<Tc: external magnetic field is perfectly expelled from the interior of a superconductor The energy gap and Bardeen-Cooper-Schrieffer theory: The energy gap and Bardeen-Cooper-Schrieffer theory The key point is the existence of energy gap between ground state and quasi-particle excitations of the system. 1. Existence of condensate. 2. Weak attractive electron-phonon interaction leads to the formation of bound pairs of electrons, occupying states with equal and opposite momentum and spin. 3. Pairs have spatial extension of order . Slide23: The electron-electron attraction of the Cooper pairs caused the electrons near the Fermi level to be redistributed above or below the Fermi level. Because the number of electrons remains constant, the energy densities increase around the Fermi level resulting in the formation of an energy gap. Slide36: Type I Type II In summary … Characteristic lengths in SC: In summary … Characteristic lengths in SC London equation: The Pippard coherence length: Penetration depth is the characteristic length of the fall off of a magnetic field due to surface currents. Ginzburg-Landau parameter: for pure SC far from Tc temperature- dependent Ginzburg-Landau coherence length is approximately equal to Pippard coherence length Coherence length is a measure of the shortest distance over which superconductivity may be established The London equation shows that the magnetic field exponentially decays to zero inside a SC (Meissner effect) Magnetic properties: Magnetic properties Dependences of critical fields on temperature. Phase boundaries between superconducting, mixed and normal states of type I and II SC.Intermediate state (SC of type I) (Type I SC show a reversible 1st order phase transition with a latent heat when the applied field reached Bc. At this particular field relatively thick Normal and SC domains running parallel to the field can coexist, in what is known as the intermediate state): Intermediate state (SC of type I) (Type I SC show a reversible 1st order phase transition with a latent heat when the applied field reached Bc. At this particular field relatively thick Normal and SC domains running parallel to the field can coexist, in what is known as the intermediate state) Intermediate state of a mono-crystalline tin foil of 29 mm thickness in perpendicular magnetic field (normal regions are dark) A distribution of superconducting and normal states in tin sphere (superconducting regions are shaded)Mixed state (SC of type II) (In type II SC finely divided quantized flux vortices or flux lines enter the material over a range of applied fields below Bc, and remain stable over a range of applied fields, in what became known as the mixed state. If these flux lines are pinned by lattice defects or other agencies, type II SC can carry a large super-current: see development of useful high-field SC magnets.): Mixed state (SC of type II) (In type II SC finely divided quantized flux vortices or flux lines enter the material over a range of applied fields below Bc, and remain stable over a range of applied fields, in what became known as the mixed state. If these flux lines are pinned by lattice defects or other agencies, type II SC can carry a large super-current: see development of useful high-field SC magnets.) Abrikosov: [1957] One vortex carries one quantum of the flux: Triangular lattice of vortex lines going out to the surface of SC Pb0.98In0.02 foil in perpendicular to the surface magnetic field Supercurrent Normal core Normal regions are approximately 300nm Closer packing of normal regions occurs at higher temperatures or higher external magnetic fields Vortex characteristics: Vortex characteristics Magnetic field of a vortex Vortex state of type II superconductors: Vortex state of type II superconductors Type II Phase of GL pseudo-wave function changes by 2 when going around spatial lines where is zero Vortex state of type II superconductors: Vortex state of type II superconductors Type II In type-II SC field penetrates to the bulk of material in the form of vortices (or magnetic flux lines, or fluxons) Phase of GL pseudo-wave function changes for 2 when going around spatial lines where is zero Each vortex represents magnetic flux quantum Critical current density: Critical current density Critical current is the maximum current SC materials can carry, above which they stop being SCs. If too much current is pushed through a SC, the latter will become normal, even though it may be below its Tc. The colder you keep the SC the higher the current it can carry. Three critical parameters Tc, Hc and Jc define the boundaries of the environment within which a SC can operate. Fig. demonstrates relationship between Tc, Hc and Jc (a critical surface). The highest values for Hc and Jc occur at 0K, while the highest value for Tc occurs when H and J are zero. Josephson effect (see also hand-out): Josephson effect (see also hand-out) Electrical current flows between two SC materials - even when they are separated by a non-SC or insulator. Electrons "tunnel" through this non-SC region, and SC current flows. The Meissner-Ochsenfeld Effect: The Meissner-Ochsenfeld Effect Walter Meissner Robert Ochsenfeld (1933) Superconductor Magnet DIAMAGNETISM ? You do not have the permission to view this presentation. In order to view it, please contact the author of the presentation.
Lecture 2 Danielle Download Post to : URL : Related Presentations : Share Add to Flag Embed Email Send to Blogs and Networks Add to Channel Uploaded from authorPOINTLite Insert YouTube videos in PowerPont slides with aS Desktop Copy embed code: (To copy code, click on the text box) Embed: URL: Thumbnail: WordPress Embed Customize Embed The presentation is successfully added In Your Favorites. Views: 672 Category: Entertainment License: All Rights Reserved Like it (0) Dislike it (0) Added: October 13, 2007 This Presentation is Public Favorites: 0 Presentation Description No description available. Comments Posting comment... By: shalinpeg (14 month(s) ago) sir plz send me this ppt its argent plz sir.. Saving..... Post Reply Close Saving..... Edit Comment Close By: zainraza52 (19 month(s) ago) sir plz send me this ppt its argent plz sir... Saving..... Post Reply Close Saving..... Edit Comment Close Premium member Presentation Transcript Slide1: “… at each new level of complexity, entirely new properties appear, and the understanding of this behavior requires research which I think is as fundamental in its nature as any other” Philip W. Anderson 1972 From last lecture ….Slide2: Where could we find superfluidity? n p p He - 3 He - 4 Helium Helium - 4 atoms are bosons particles with integer spin. Helium - 3 atoms are fermions particles with half integer spin. Slide3: 1938 Kapitza and Allen discover superfluidity in He-4Slide4: For T < 2.4Κ – gravity ... If the bottle containing helium rotates for a while and then stops, helium will continue to rotate for ever – there is no internal friction (for as long as He is at T = -269 C or lowerSlide5: 1938 Pyotr L. Kapitsa discovered the superfluidity of liquid Helium 4 Nobel Prize in 1978 1941-47 Lev Landau formulated the theory of quantum Bose liquid - 4He superfluid liquid. 1956-58 he further formulated the theory of quantum Fermi liquid. Nobel Prize in 1962 Early 1970s David M. Lee, Douglas D. Osheroff, and Robert C. Richardson discovered the superfluidity of liquid Helium 3. Nobel Prize in 1996 Anthony Leggett first formulated the theory of superfluidity in liquid 3He in 1965. Nobel Prize in 2003Slide6: Διάστημα: 3000 χιλιοστά από το απόλυτο μηδέν (-273.15 C) 5 χιλιοστά από το απόλυτο μηδέν Χαμηλές θερμοκρασίεςLOW-TC Superconductors: LOW-TC Superconductors Lead (Pb) Mercury (Hg) Aluminum (Al) Gallium (Ga) Molybdenum (Mo) Zinc (Zn) Zirconium (Zr) Americium (Am) Cadmium (Cd) Ruthenium (Ru) Titanium (Ti) Uranium (U) Hafnium (Hf) Iridium (Ir) Beryllium (Be) Tungsten (W) Platinum (Pt)* Rhodium (Rh) 7.196 K 4.15 K 1.175 K 1.083 K 0.915 K 0.85 K 0.61 K 0.60 K 0.517 K 0.49 K 0.40 K 0.20 K 0.128 K 0.1125 K 0.023 K 0.0154 K 0.0019 K 0.000325 K Conductors vs. Insulators: Conductors vs. Insulators No free electrons to carry the current FREE ELECTRONSSlide9: The foam balls (containing small magnets) organise themselves based on the laws of minimum energy. This arrangement mimics the crystal lattice of a solid material. What is Resistance?: What is Resistance? Electrical Resistance: Electrical Resistance Thermal vibrations (phonons) of the ionic lattice Lattice defects Impurities RESISTANCE is caused by electrons colliding with: Cations ElectronsSlide12: V I Vs copper Liquid helium 4.2K (-269 ºC) Slide13: R T 77K 273K = 0ºC Ro ImpuritiesSlide14: V I Vs Hg Liquid helium 4.2K (-269 ºC) Onnes (1911)Low -Tc Superconductivity: Low -Tc Superconductivity Heike Kamerlingh Onnes (1911)LOW-TC Superconductors: LOW-TC Superconductors Lead (Pb) Mercury (Hg) Aluminum (Al) Gallium (Ga) Molybdenum (Mo) Zinc (Zn) Zirconium (Zr) Americium (Am) Cadmium (Cd) Ruthenium (Ru) Titanium (Ti) Uranium (U) Hafnium (Hf) Iridium (Ir) Beryllium (Be) Tungsten (W) Platinum (Pt)* Rhodium (Rh) 7.196 K 4.15 K 1.175 K 1.083 K 0.915 K 0.85 K 0.61 K 0.60 K 0.517 K 0.49 K 0.40 K 0.20 K 0.128 K 0.1125 K 0.023 K 0.0154 K 0.0019 K 0.000325 K BCS Theory: BCS Theory John Bardeen Leon Cooper John Schrieffer (1957) No collisions Zero resistance Meissner Effect : Meissner Effect 1933 – Walther Meissner and Robert Ochsenfeld T<Tc: external magnetic field is perfectly expelled from the interior of a superconductor The energy gap and Bardeen-Cooper-Schrieffer theory: The energy gap and Bardeen-Cooper-Schrieffer theory The key point is the existence of energy gap between ground state and quasi-particle excitations of the system. 1. Existence of condensate. 2. Weak attractive electron-phonon interaction leads to the formation of bound pairs of electrons, occupying states with equal and opposite momentum and spin. 3. Pairs have spatial extension of order . Slide23: The electron-electron attraction of the Cooper pairs caused the electrons near the Fermi level to be redistributed above or below the Fermi level. Because the number of electrons remains constant, the energy densities increase around the Fermi level resulting in the formation of an energy gap. Slide36: Type I Type II In summary … Characteristic lengths in SC: In summary … Characteristic lengths in SC London equation: The Pippard coherence length: Penetration depth is the characteristic length of the fall off of a magnetic field due to surface currents. Ginzburg-Landau parameter: for pure SC far from Tc temperature- dependent Ginzburg-Landau coherence length is approximately equal to Pippard coherence length Coherence length is a measure of the shortest distance over which superconductivity may be established The London equation shows that the magnetic field exponentially decays to zero inside a SC (Meissner effect) Magnetic properties: Magnetic properties Dependences of critical fields on temperature. Phase boundaries between superconducting, mixed and normal states of type I and II SC.Intermediate state (SC of type I) (Type I SC show a reversible 1st order phase transition with a latent heat when the applied field reached Bc. At this particular field relatively thick Normal and SC domains running parallel to the field can coexist, in what is known as the intermediate state): Intermediate state (SC of type I) (Type I SC show a reversible 1st order phase transition with a latent heat when the applied field reached Bc. At this particular field relatively thick Normal and SC domains running parallel to the field can coexist, in what is known as the intermediate state) Intermediate state of a mono-crystalline tin foil of 29 mm thickness in perpendicular magnetic field (normal regions are dark) A distribution of superconducting and normal states in tin sphere (superconducting regions are shaded)Mixed state (SC of type II) (In type II SC finely divided quantized flux vortices or flux lines enter the material over a range of applied fields below Bc, and remain stable over a range of applied fields, in what became known as the mixed state. If these flux lines are pinned by lattice defects or other agencies, type II SC can carry a large super-current: see development of useful high-field SC magnets.): Mixed state (SC of type II) (In type II SC finely divided quantized flux vortices or flux lines enter the material over a range of applied fields below Bc, and remain stable over a range of applied fields, in what became known as the mixed state. If these flux lines are pinned by lattice defects or other agencies, type II SC can carry a large super-current: see development of useful high-field SC magnets.) Abrikosov: [1957] One vortex carries one quantum of the flux: Triangular lattice of vortex lines going out to the surface of SC Pb0.98In0.02 foil in perpendicular to the surface magnetic field Supercurrent Normal core Normal regions are approximately 300nm Closer packing of normal regions occurs at higher temperatures or higher external magnetic fields Vortex characteristics: Vortex characteristics Magnetic field of a vortex Vortex state of type II superconductors: Vortex state of type II superconductors Type II Phase of GL pseudo-wave function changes by 2 when going around spatial lines where is zero Vortex state of type II superconductors: Vortex state of type II superconductors Type II In type-II SC field penetrates to the bulk of material in the form of vortices (or magnetic flux lines, or fluxons) Phase of GL pseudo-wave function changes for 2 when going around spatial lines where is zero Each vortex represents magnetic flux quantum Critical current density: Critical current density Critical current is the maximum current SC materials can carry, above which they stop being SCs. If too much current is pushed through a SC, the latter will become normal, even though it may be below its Tc. The colder you keep the SC the higher the current it can carry. Three critical parameters Tc, Hc and Jc define the boundaries of the environment within which a SC can operate. Fig. demonstrates relationship between Tc, Hc and Jc (a critical surface). The highest values for Hc and Jc occur at 0K, while the highest value for Tc occurs when H and J are zero. Josephson effect (see also hand-out): Josephson effect (see also hand-out) Electrical current flows between two SC materials - even when they are separated by a non-SC or insulator. Electrons "tunnel" through this non-SC region, and SC current flows. The Meissner-Ochsenfeld Effect: The Meissner-Ochsenfeld Effect Walter Meissner Robert Ochsenfeld (1933) Superconductor Magnet DIAMAGNETISM ?