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From Isolation to Interaction

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

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From Isolation to Interaction

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

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

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

  4. Electron Counting Correlated metal Transition metal oxides Ordinary oxide: Al2O3 Ordinary oxide: Al3+2 O2-3 Al3+: [Ne] O2-: [Ne] Good insulator Transition metal oxide: Sr2RuO4 Transition metal oxide: Sr2+2Ru4+O2-4 Leftover d-electrons Sr2+: [Kr] O2-: [Ne] Ru4+: [Kr]4d4

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

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

  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 Outer space: 3000 mK Dilution fridge: 5 mK Adiabatic demagnetisation: 50 mK

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

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

  13. Suppress Magnetism… Antiferromagnetism in CePd2Si2

  14. …and Create Superconductivity! Superconductivity in CePd2Si2 at 28 kbars and 400 mK (Mathur, Julian, Lonzarich et al. 1998)

  15. Ferromagnets Too… Superconductivity in UGe2 at 13 kbars and 600 mK (Saxena, Lonzarich et al. 2000)

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

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

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

  19. 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-Tc superconductors?

  20. Doped Magnetic Insulators Cu O Cu2+: One Electron per Site Antiferromagnetic Insulator

  21. Doped Magnetic Insulators Cu O Cu(2+d)+: Mobile HolesHigh-Tc Superconductor

  22. High-TcPhase Diagram Temperature metallic Non-metallic antiferromagnet super-conductivity Holes per CuO2 Square

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