1. Magnets and superconductors: strange bedfellows of the quantum world.
Patrick Lee
MIT
Supported by NSF and DOE over the years.

2. Outline What is condensed matter physics?
Conventional superconductors.
Conventional antiferromagnets (AF).
Emergence of new phenomena at low energies, a theme of modern condensed matter physics.
Unconventional superconductors:
High Tc superconductors, proximity to Mott insulator
Search for unconventional AF, the quantum spin liquid.

3. Condensed matter physics: the study of novel properties of materials.
Material preparation
experiment
theory
Magnetism and superconductivity are two of the most common and important properties. The explanation of both relies on quantum mechanics.

4. Ferromagnetism (FM): known for thousands of years, but explained only in 1930’s after the invention of quantum mechanics.
Electrons carry angular momentum called spin.
Electrons are fermions and obey Pauli’s exclusion Principle, ie 2 electrons with the same spin cannot be at the same place.
A third ingredient is that electrons repel each other by Coulomb repulsion.
This is the main theme of my talk: electrons hate each other!
By having all spins up, the electrons automatically stay away from each other to lower the Coulomb repulsion.
metal
Ferromagnetic metal
FM is relatively rare: Fe, Ni, Co and some rare earths among the elements.

5. Superconductivity was discovered by Kammerling Onnes
in 1911, when he cooled mercury to liquid helium temperature and its resistivity vanishes!
Until 1986, the highest transition temperature (Tc) was 23K. (room temperature is 300K.)
Nobel prize
1913

6. Superconductors are commonplace, but limited to low temperatures.

7. Microscopic theory given by Bardeen, Cooper and Schrieffer (BCS) in 1957. The theory takes 2 steps.
Step 1 : pairing of electrons to form “Cooper pairs,” a molecule of two electrons.
Electrons have an effective attraction due to coupling to lattice vibration.

8. But electrons hate each other! The attraction is short
range in space but retarded in time.

9. But electrons hate each other! The attraction is short
range in space but retarded in time.
Trouble is that the attraction strength is very weak and superconductivity is limited to low temperatures.

10. Step 2. Cooper pairs are bosons
Step 2. Cooper pairs are bosons. They can “Bose-Einstein condense”, ie they behave like waves rather than particles.
Superconductor is described by a “macroscopic wave-function” which is a complex number with a phase angle f.
In short, we associate an angle with every point along a superconducting wire.
The resistance of a superconductor is exactly zero (not just very small!) and persistent current flows around a ring for the life of the universe.
The explanation of this mystery has to do with topology.

11. Conventional Anti-ferromagnet (AF):
Louis Néel (theory 1933)
Cliff Shull 1994 Nobel Prize
1970 Nobel Prize
Anti-ferromagnetic insulators:
When repulsion is strong enough, the electrons are localized on lattice sites and form an insulator (called a Mott insulator.) The spins are aligned opposite.
Common among transition metal oxides.

12. Note that superconductors and magnets are mutually exclusive.

13. Why are superconductors and magnets mutually exclusive?
1. The Cooper pair is formed by opposite spins whereas FM has parallel spins. This explains why it cannot co-exists with FM.
2. Most AF are insulators. The spins are immobile and cannot carry current. This is just the opposite to superconductor.

14. The highest Tc is now about 150K.
High Tc superconductivity began with the discovery of Bednorz and Muller in 1986.
The highest Tc is now about 150K.
J. G. Bednorz
K. A. Mueller
Nobel prize 1987

15. Sm(O1-xFx)FeAs (March, 2008)i t c a l e m p u T ( K )
1920
1940
1960
1980
2000
Year of discovery
1900 50
100
150
LIQUID NITROGEN
Nb3Ge
V3Si Hg
NbC
MgB2
Ba0.6K0.4BiO3
Cs2RbC60
Sm(O1-xFx)FeAs (March, 2008)

16. A key feature of superconductor is that it repels magnetic field
A key feature of superconductor is that it repels magnetic field. (Meissner effect.)
ferromagnet
superconductor

18. 20 years later, large scale applications are beginning to appear.
American Superconductor 2G wires: YBCO based, with Y2O3 nano particles for flux pinning.
Weight reduction of wind turbine:
10 MW generator will weight 120 metric tons instead of 300 using conventional copper wires.

20. Basic features of High-Tc cuprates
I’d like to start from explaining the crystal structure of these materials. Crystal structure: basic element CuO planes. Also, the octahedra. Spin directions. Orthorhombic.
The theorists usually start here, from the simplified 2D version on the right, It is a schematical diagram of a fragment of CuO plane. Blue dotes are Cu, spin, oxygen is black dotes. CuO plane is a 2D spin-1/2 AFM. The combination of spin-1/2 and low dimens creates these very interesting physical phenomena. High-Tc SC is the only, if most famous, phenomenon. Generally believed not the most important.
Spins are immobile and form an anti-ferromagnet. This is called a Mott insulator.
How did they do it? Turn insulator into superconductors.

21. Doped Mott insulator: superconductor!
CuO2 plane with doped holes:
La3+  Sr2+: La2-xSrxCuO4 t
Physicist pair caught doping.
Here is the illustration of the electron transport in the undoped CuO plane first. (Technion: you’ve probably had a more elaborate intro to this subject from Assa Auerbach)
Doping restores the ele conductivity by creating cites at which the holes can jump without paying the cost in Coulomb repuls. The doping is achieved by chemical subitution of La by Sr or by adding additional oxygen into the lattice. As a result of doping, the holed can now move around. However, as you see, doping destroys the AFM order very quickly because this spin after the hole move there wants to be down rather than up. The most famous example of a HTC material is LSCO, which is very similar to the originally discovered LBCO.
So, the 2 basic features which characterize the HTCS materials:
(i) key structural unit shared by all the materials is CuO plane. The interplane correlations are weak, so the behavior is quasi-2D
(ii)HTSC’s are created by doping Mott Insulators
This combination creates the fundamentally different behavior as compared to the “old”, regular superconductors like merculry, Al, NbSe2, etc.
First,CuO plane is a 2D spin-half Heisenberg AFM with very large coupling J, of 1500K. The AFM is due to the superexchange interaction between Cu spins through Oxygen p-orbitals.
Second, there is one hole on every Cu cite, so the conduction band is only half filled. However, hoping between cites is prohibited because the Coulomb energy of double-occupied cite is too large. Therefore, strong el-el correlation plays an important role in this system. This is in contrast to regular Fermi-liquid metals, where el kinetic energy is dominant. Mott Insul is a material, like LaCuO, in which the conductivity vanishes at decreasing T, even though the band theory predicts it to be metallic.
(J=t^2/U)
The combination of the 2-dim and proximity to Mott Insul leads to a new physics. The SC is only one of the welth of new phenomena observed and still poorly understood in HTSC.

22. What is unconventional about high Tc superconductors?
Superconductivity by doping a Mott insulator.
This strongly suggest the origin of pairing comes from electronic repulsion.
Its proximity to anti-ferromagnet indicates the energy scale is set by anti-ferromagnetism and is not necessarily a low temperature phenomenon.

23. In the intervening 20 years, we have discovered many examples of unconventional SC’s.
Organics (Tc=12K)
Heavy fermion superconductors.
Fe based superconductors. (Tc=55K)
In all cases these SC’s are in close proximity to AF.
A marriage of SC and AF?
“Politics does not make strange bedfellows, marriage does,”
Groucho Marx.

24. Why does doping a Mott insulator antiferromaget give rise to a superconductor?
Qualitative picture given by Philip Anderson in 1987.
Anderson’s resonating valence bond (RVB) idea:
spin liquid and its doping.
Unconventional anti-ferromagnetism may be a partner to unconventional superconductors!

25. |  |  Competing visions of the antiferromagnet Lev Landau Quantum
“….To describe antiferromagnetism, Lev landau and Cornelis Gorter suggested quantum fluctuations to mix Neel’s solution with that obtained by reversal of moments…..Using neutron diffraction, Shull confirmed (in 1950) Neel’s model.
……Neel’s difficulties with antiferromagnetism and inconclusive discussions in the Strasbourg international meeting of 1939 fostered his skepticism about the usefulness of quantum mechanics; this was one of the few limitations of this superior mind.”
Jacques Friedel, Obituary of Louis Neel, Physics today, October,1991.
Lev Landau |  | 
Classical
Quantum

26. In 1973 P. W. Anderson proposed a resonating valence bond (RVB) state (Instead of Neel state) for triangular lattice. It is a linear superposition of singlet pairs.
With doping, vacancies becomes mobile in the spin liquid background.
When the vacancies become phase coherent, we have superconductivity.

27. In high Tc superconductors , the physics of spin liquid show up only at finite temperature. Difficult to make precise statements and sharp experimental tests. It will be very useful to have a spin liquid ground state which we can study.
Requirements: insulator, one electron per unit cell, absence of AF order.
After 30 years physicists finally discovered several promising new candidate for spin liquid states, thus ending the drought.

28. The kagome lattice.
The most frustrated 2 dimensional lattice.
One of the few known examples is Iron jarosite, a rare mineral which was studied by Dan Nocera (chemist) and Young Lee (physicist) at MIT.
KFe3(SO4)2OH)6 S=5/2.

29. On April 15,2004, in the outcropping, mission scientists found a hydrated iron sulfate mineral called jarosite, an uncommon mineral on Earth, which forms in dilute sulfuric acid in ground water. Jarosite was first discovered on Earth in 1852 in ravines in the mountainous coast of southeastern Spain.

30. Herbertsmithite : Spin ½ Kagome.
Finally in 2007 Spin liquid was discovered in a S=1/2 Kagome system. (Dan Nocera, Young Lee etc. MIT).
No spin order down to milli Kelvin.
Mineral discovered in Chile in 1972 and named after H. Smith.
Herbertsmithite : Spin ½ Kagome.
Many of us are excited by the discovery of a new state of matter with new emergent properties.

31. Summary:
The hatred of electrons for each other and quantum mechanics are the key ingredients which are responsible for common phenomena such as magnetism and more exotic phenomena such as high temperature superconductors.
These strange bedfellows have opened up new realms of possibilities in condensed matter physics.
Let us see what more surprises Nature has in store for us.