1. Spin Meissner effect in superconductors and the origin of the Meissner effect J.E. Hirsch, UCSD Hvar, 2008  Why the Meissner effect is not understood, and how it can be understood  Spin Meissner effect: spontaneous spin current in the ground state of superconductors  Charge expulsion, charge inhomogeneity in superconducting state  Electrodynamic (London-like) equations for charge and spin  Experiments

2. 3 key pieces of the physics that BCS theory got right: * Cooper pairs * Macroscopic quantum coherence * Electron-phonon-induced attraction between electrons * Energy gap

3. 3 key pieces of the physics that BCS theory got right: * Cooper pairs * Macroscopic quantum coherence * Electron-phonon-induced attraction between electrons * Energy gap (1) Key role of electron-hole asymmetry (2) Key role of kinetic energy lowering as driving force (4) Key role of spin-orbit interaction (5) Key role of mesoscopic orbits 1988-2008 http://physics.ucsd.edu/~jorge/hole.html (3) Macroscopic charge inhomogeneity and internal E-field (6) Spontaneous currents in the absence of applied fields

4. Meissner effect: expulsion of magnetic field from interior of superconductor 1933 The expulsion of magnetic flux from the interior of a superconducting metal when it is cooled in a magnetic field to below the critical temperature, near absolute zero, at which the transition to superconductivity takes place. It was discovered by Walther Meissner in 1933, when he measured the magnetic field surrounding two adjacent long cylindrical single crystals of tin and observed that at ?452.97°F (3.72 K) the Earth's magnetic field was expelled from their interior. This indicated that at the onset of superconductivity they became perfect diamagnets. This discovery showed that the transition to superconductivity is reversible, and that the laws of thermodynamics apply to it. The Meissner effect forms one of the cornerstones in the understanding of superconductivity, and its led F. London and H. London to develop their phenomenological electrodynamics of superconductivity. The magnetic field is actually not completely expelled, but penetrates a very thin surface layer where currents flow, screening the interior from the magnetic field. cool L =London penetration depth

5. same final state E Faraday I I supernormal cool apply B two pathways to Meissner current expel B Faraday electric field points in opposite directions Meissner current I points in the same direction cool super normal apply B B I

6. Why the Meissner effect is a puzzle What is the 'force'pushing the electrons near the surface to start moving all in the same direction, opposite to eE Farad ? How is angular momentum conserved??? Meissner state Current develops 'spontaneously' upon cooling or lowering H opposing E Farad I Lower the temperature... or lower slightly the applied H... B=0 E Farad B

7. The key to the Meissner effect L I vsvs R Angular momentum in Meissner current: (h=cylinder height, n s =superfluid density) r=2 L orbits! B =angular momentum of 1 el =# of electrons in surface layer 2 L bulk some very complicated math..... cylinder

8. Some simple relations: Density of states at the Fermi energy: Normal state: Superconducting state: London penetration depth: Magnetic susceptibility:

9. Larmor diamagnetism r v Apply magnetic field B: magnetic susceptibility per unit volume: n=electrons/unit vol or B vv Orbital magnetic moment:

10. How the transition occurs 2 L orbit expansion: k F -1 r=2 L orbits B r Normal state: Superconducting state: r=k F -1 orbits

11. same final state E Faraday I I supernormal cool apply B two pathways to Meissner current expel B

12. The two pathways to the Meissner current r v Apply magnetic field B: Expand electron orbit in B: Faraday's law pushes e - Lorentz force pushes e - B v r=2 L vv E vv B F r BCS:

13. r=2 L orbits r=k F -1 orbits Why is there macroscopic phase coherence in superconductors? Normal state Non-overlapping orbits Relative phase doesn't matter Superconducting state Highly overlapping orbits Phase coherence necessary to avoid collisions

14. ==>, 137 A little help from a friend...

15. ==>, 137 A little help from a friend... The speed of light must enter into the superconducting wave function!

16. So we learn from the Meissner effect that: transition to superconductivity = expansion of electronic orbit from r=k F -1 to r=2 L What happens when there is no magnetic field? Spin-orbit force deflects electron in expanding orbit!

17. Spin orbit scattering (Goldberger&Watson) scattering center scattering center  v p a moving magnetic moment is equivalent to an electric dipole spin-orbit   v 

18. So we learn from the Meissner effect that: transition to superconductivity = expansion of electronic orbit from r=k F -1 to r=2 L What happens when there is no magnetic field? Spin-orbit force deflects electron in expanding orbit!  v p E  

19. For r=2 L.... E    What's E?

21. The two pathways to the Spin Meissner current r v 'Apply' electric field E: Expand electron orbit in E: Maxwell's law pushes  Lorentz torque pushes   v r=2 L vv E(t) r  B  vv

22. Ground state of a superconductor r=2 L orbits spin down electrons spin up electrons Currents in the interior cancel out, near the surface survive ==> there is a spontaneous spin current in the ground state of superconductors!

23. There is a spontaneous spin current in the ground state of superconductors, flowing within L of the surface For L =400A, v   cm/s # of carriers in the spin current: n s When a magnetic field is applied:   n v0v0 The slowed-down spin component stops when vv B no external fields applied (JEH, EPL81, 67003 (2008))

24. Summary of argument: 1) (Ampere, Faraday, Newton, London) 3) Magnetic moment of electron is Therefore:  Superconductivity is an intrinsically relativistic effect  Electron spin and associated magnetic moment plays a key role  The wavefunction of a superconductor contains c=speed of light 1)+2)+3)+4) ==>1)+2)+3)+4) ==> magnetic field that stops the spin current is H c1 2) Orbits have radius (to explain origin of Meissner current) 4) Background positive charge density is = - superfluid dens.

25. What makes electrons move in the direction needed to create all these currents when T is lowered from above to below T c ? B Intermediate state B I Meissner state I B I Vortex state Back to: cooling a superconductor in the presence of a B-field: A clue from plasma physics

26. www.mpia-hd.mpg.de/homes/fendt/Lehre/Lecture_OUT/lect_jets4.pd f A clue from plasma physics

27. B I Meissner state Intermediate state LeLe B Vortex state B I LeLe veve v FBFB v FBFB v FBFB Electrons have to flow away from the interior of the superconductor, towards the surface and towards the normal regions! But if there is charge flow, it will result in charge inhomogeneity and an electric field in the interior of superconductors.

28. But if there is charge flow, it will result in charge inhomogeneity and an electric field in the interior of superconductors. Can there be an electric field inside superconductors? free acceleration of electrons London says NO. First London equation (1934): (n=density, v=speed, J=current) If E = 0, J increases to infinity, unless Newton’s law is violated? ! can be zero even if E is non-zero!

29. New electrodynamic equations for superconductors (JEH, PRB69, 214515 (2004)) 1) 2) ==> Note: ==>, NOT, continuity equation: ==> integrate in time, 1 integration constant  0,...

30. Electrodynamics Relativistic form: 2 or equivalently 2

31. ; outside supercond. +assume  (r) and its normal derivative are continuous at surface Electrostatics: L Solution for sphere of radius R: No electric field outside sphere

32. Sample size dependence of expelled charge (Q) and E-field    < 0 = charge density near surface    > 0 = charge density in interior Q ~   R 3 ~ -   R 2 L Electrostatic energy cost: U E ~ Q 2 /R ~ (   R 2 L ) 2 /R ~ (      R 3 ~ (      R 5 ~ Volume~R 3 ==>   independent of R,   ~ 1/R sphere of radius R Electric field vs. r: E EmEm r R1R1 R2R2 independent of R how big is  -, E m ? L  

33. How much charge is expelled? elementT c (K)H c (G) L (A) Extra elec- trons/ion E m (Volts/cm) Al1.141055001/17 mill31,500 Sn3.723095101/3.7 mill92,700 Hg4.154124101/2.5 mill123,600 Pb7.198033901/1 mill240,900 Nb9.5019804001/1.3 mill308,400 E max R R 

34. Spin currents in superconductors (JEH, Phys. Rev. B 71, 184521 (2005)) carries a spin current necessarily in the presence of internal E-field Internal electric field (in the absence of applied B) pointing out no charge current ==> no B-field spin current without charge current! E Flows within a London penetration depth of the surface Speed of spin current carriers: ~ 100,000 cm/s Number of spin current carriers: =superfluid density

35. How much charge is expelled? We now have 2 new pieces of physics of superconductors: r=2 L orbits How are they related? L 00  spin current charge expulsion

36. ==> ~ H c1 (JEH)

37.   n v0v0 (Recall ) (charge neutra- lity) E max R

38. Spin current electrodynamics (4d formulation)

39. Energetics Apply a magnetic field: ==> condensation energy per particle: energy lowering per particle in entering sc state: 2  c =  c +  c Coulomb energy cost + condensation energy ~ condensation energy of sc

40. Type I vs type II materials  =distance between orbit centers Type I:  > 2 L Type II:  < 2 L Phase difference:

41. What drives superconductivity? 1) Excess negative charge (CuO 2 ) =, (MgB 2 ) -, (FeAs) - 3) Kinetic energy lowering 2) Almost full bands (hole conduction in normal state) (Kinetic energy is highest when band is almost full) k F -1 is small kFkF too many electrons!

42. How is angular momentum conserved in the Meissner effect?? Electromagnetic field carries angular momentum! =-L e But  - is way too small to give enough L field Spin-orbit interaction transfers counter-L to ions! JEH, J. Phys.: Condens. Matter 20 (2008) 235233 B B LeLe L field L ions

43. Experimental tests? 1) Detect spin current   n v0v0 * polarized light scattering (PRL100, 086603 (08) * inelastic polarized neutron scattering * photoemission * Detect electric fields produced by spin current * Insert a 'spin current rectifier' 2) Detect internal electric field 3) Response of superconductor to applied electric field 4) Detect change in plasmon dispersion relation in sc state..... * positrons, muons, neutrons (Tao effect)

44. To prove this theory wrong, find clear experimental evidence for any of the following: * A superconductor that has no hole carriers in normal state * A superconductor that has no outward-pointing electric field in its interior * A superconductor that has no spontaneous spin current near the surface, with carrier density n s /2 and speed * A superconductor with tunneling asymmetry of intrinsic origin that has opposite sign to the one usually observed * A superconductor with gap function that has no  k dependence * A superconductor that expels magnetic fields without expelling negative charge * A high T c superconductor with no excess negative charge anywhere * A superconductor not driven by kinetic energy lowering IT IS A FALSIFIABLE THEORY!