1. Free electrons – or simple metals Isolated atom – or good insulator From Isolation to Interaction Rock Salt Sodium Electron (“Bloch”) waves Localised electrons “particle wave duality” in the solid state Interesting stuff happens in between Credits C. Bergmann

2. Energy Orbital OverlapAtomic DistanceBandwidth Atomic energy levels Continuous energy spectrum Bandwidth Interesting stuff happens here: U ~ W

3. Narrow Bands – but where? Organic molecular crystals Transition metal oxides & compounds Heavy fermion compounds

4. Electron Counting Transition metal oxides Ordinary oxide: Al 2 O 3 Ordinary oxide: Al 3+ 2 O 2- 3 Good insulator Transition metal oxide: Sr 2 RuO 4 Al 3+ : [Ne] O 2- : [Ne] Transition metal oxide: Sr 2+ 2 Ru 4+ O 2- 4 Sr 2+ : [Kr] O 2- : [Ne] Ru 4+ : [Kr]4d 4 Leftover d-electrons Correlated metal

5. Electron Counting Transition metal oxides Leftover d-electrons Correlated metal

6. Magnetism and Narrow Bands Magnetism is a narrow band phenomenon that arises from electron correlations MAGNETIC METAL INSULATOR NONMAGNETIC METAL narrower bands Pressure at low-T

7. Electron correlations The way the particles are organised is determined by strong interactions between the particles. Many of these correlations are intimately related to magnetic degrees of freedom of the particles, including collective effects such as ordering, dynamics, and unusual excitations.

8. These new behaviours of the whole system may not have any obvious relationship to the properties of the individual particles, but rather may arise from collective or cooperative behaviour of all the particles. Such phenomena are often referred to as "emergent phenomena" because they emerge as the complexity of a system grows with the addition of more particles.

9. Big questions about the origins of collective behaviour in matter 1. What is the origin of high temperature superconductivity? 2. What is the nature of strange metals? 3. Why don't glasses flow like liquids? 4. What principles govern the organisation of matter away from equilibrium? 5. How do singularities form in collective matter and in space-time? 6. What principles govern the flow of electronically granular materials? When you put a lot of atoms together you get strange, wonderful and sometimes useful new kinds of behaviour: superconductivity, magnetism, superfluidity.

10. Creating Low Temperatures Adiabatic demagnetisation: 50 mK Outer space: 3000 mK Dilution fridge: 5 mK

11. Using basic knowledge to manipulate nature: High Magnetic Fields Superconducting solenoids: up to 21 T Earth’s magnetic field: 0.0001 T NHMFL hybrid: 45 T

12. Creating High Pressures Clamp cell: 30 kbar Ocean floor: 1 kbar Anvil cell: 150 kbar Volume compression of order 10%

15. Suppress Magnetism… Antiferromagnetism in CePd 2 Si 2

16. …and Create Superconductivity! Superconductivity in CePd 2 Si 2 at 28 kbars and 400 mK (Mathur, Julian, Lonzarich et al. 1998)

17. Ferromagnets Too… Superconductivity in UGe 2 at 13 kbars and 600 mK (Saxena, Lonzarich et al. 2000)

18. New Mechanism Superconductivity needs “glue” – attractive inter- action between electrons (see Part III Minor Option in Lent) Conventional theory: phonon

19. New Mechanism Superconductivity needs “glue” – attractive inter- action between electrons (see Part III Minor Option in Lent) Near magnetic phase transition: spin fluctuation usually S = 0

20. New Mechanism Superconductivity needs “glue” – attractive inter- action between electrons (see Part III Minor Option in Lent) Near ferromagnetic phase transition: spin fluctuation possibly S = 1

21. Paradigm Shift Previously, superconductivity and magnetism were thought to be mutually exclusive. Now, we realise that magnetism can promote superconductivity. Magnetism and unconventional superconductivity are natural neighbours in phase diagrams of correlated materials. Does this statement hold for the high-T c superconductors?

22. Doped Magnetic Insulators Cu 2+ : One Electron per Site Antiferromagnetic Insulator Cu O

23. Doped Magnetic Insulators Cu (2+  )+ : Mobile Holes High-T c Superconductor Cu O

24. High-T c Phase Diagram Temperature Holes per CuO 2 Square antiferromagnet super- conductivity Non- metallic metallic