2. 20 th century physics Relativity Quantum mechanics Brownian motion Particle physics Study of fields 21 st 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. Towards the electronic analogue: Metal - Ammonia solutions 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. Metal concentration (mole per cent metal) Temperature (K) 100 200 48 Phase separation Non metallic solution Metallic solution Solid ammonia Solid two-phase mixture 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

5. Materials at the border between being Metals – Insulators – SC’s 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 changes dramatically the properties of the material. Concurrently, activated transitions between electronic structures lead to very slow dynamics … 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) 30 -135 K Temperature (K) Quantum control parameter: Carrier concentration (%) 30 0 350-400 AF SC Non- metallic metallic Transition Metal Oxides displaying a zoology of phases with: Insulating, Delocalised, Metallic, High-T c Superconducting properties using charge carrier doping as the Quantum Tuning Parameter ?

8. Temperature (K) Carrier concentration (%) 300 350-400 AF SC Non- metallic metallic 0.11 10 250 300 Temperature (K) Moles percent metal Non metal solvated electrons Metal free electrons Non-metal to metal transition J. Thompson Rev. Mod. Phys. 40, 704 (1968) 200 The tendency for electronic phase separation reminds us of amphiphile & (water+oil), or metal- ammonia solutions or even structural glass Behaviour may generic among the many SC’s on the border of magnetism Metal-Ammonia solution Phase separation

9. Ordered crystalline, checkerboard and striped electronic glasses emerge as candidate forms of correlated electronic matter J.C. Davis group Cornell University Could be mistaken for phase separated Amphiphile & (water+oil) Temperature (K) Carrier concentration (%) 300 350-400 AF SC Non- metallic metallic