20 th century physics

2. RelativityQuantum mechanicsBrownian motion Particle physics Study of fields 20th century physics • 21st century Condensed Matter Physics electronically complex functional materials

3. Soft matter: Amphiphile + [water & oil] (Molecule of both hydrophilic and hydrophobic nature. It has an oily tail chemically bonded to a water soluble head group) The mixture causes frustration and oil & water molecules associated with the amphiphile are near each other Leads to mesoscopic phase separation occurring dynamically with many equilibrium phases due to competition between oil and water for the two parts of the amphiphile

4. Regions of high density free e-’s, owing to the Pauli principle, avoid the e- rich ammonia However, the ammonia phase attempts to retain the +ve charged metal ions, which can then be solvated. Towards the electronic analogue:Metal - Ammonia solutions Non metallic solution Temperature (K) Metallic solution • In the drive to local electrical neutrality, the +ve metal ions act much like amphiphiles in microemulsions: Here the metal ions separate the high and low density e- phases Phase separation 200 Solid ammonia 100 Solid two-phase mixture 4 8 Metal concentration (mole per cent metal)

5. With the help of little, but inevitable, lattice disorder we have several bona fide phase transitions Close to a phase transition, materials exhibit large responses to small external signals driving the system from one phase to the other. This changesdramatically the properties of the material. Concurrently, activated transitions between electronic structures lead to very slow dynamics … Materials at the border between being Metals – Insulators – SC’s • We anticipate the electronic degrees of freedom to become pre-organised on intermediate length scales and then fluctuate collectively on longer scales, much like the systems we encounter in colloids

6. Modern complex electronic systems: Spin, charge & Orbital • Intrinsic complexity The many degrees of freedom interact in a nonlinear & synergic manner, and with charge & spin as fundamental order we can imagine equilibrium phase degrees at least as complex as oil-water-amphiphile • Hard & Soft Condensed matter In such systems in addition to periodically ordered phases, we may also have long lived aperiodically inhomogeneous systems, like gel or glass • Electron liquid crystals The resulting electronically complex systems may be intermediate between electron liquid and electron crystal.

7. Materials needed to study e- - complexity: Possessing the widest range of a tuneable ground state at T=0 (quantum comes in) Transition Metal Oxides displaying a zoology of phases with: Insulating, Delocalised, Metallic, High-Tc Superconducting properties using charge carrier doping as the Quantum Tuning Parameter 350-400 metallic Non-metallic AF Temperature (K) 30 -135 K ? SC 0 30 Quantum control parameter: Carrier concentration (%)

8. 350-400 The tendency for electronic phase separation reminds us of amphiphile & (water+oil), or metal-ammonia solutions or even structural glass metallic Non-metallic Temperature (K) AF Metal-Ammonia solution Non-metal to metal transition SC 300 0 30 Metal free electrons Carrier concentration (%) Non metal solvated electrons Temperature (K) 250 Behaviour may generic among the many SC’s on the border of magnetism Phase separation 200 0.1 1 10 Moles percent metal J. Thompson Rev. Mod. Phys.40, 704 (1968)

9. J.C. Davis group Cornell University 350-400 Could be mistaken for phase separated Amphiphile & (water+oil) metallic Non-metallic Temperature (K) AF SC 0 30 Carrier concentration (%) Ordered crystalline, checkerboard and striped electronic glasses emerge as candidate forms of correlated electronic matter