Emergence of Collective Phenomena: Strongly Correlated Multiparticle Systems

1. Emergence of Collective Phenomena: Strongly Correlated Multiparticle Systems Leon Balents, UCSB Julia Phillips, Sandia National Lab

2. Correlations and Emergence • 1 cm3 of matter = 1023 atoms, electrons • Motion of one influences another Correlations: jammed Controlled correlations: Fast and efficient Uncorrelated: Light traffic = “ideal gas” AHS, San Diego 1997

3. Scientific Setting • Emergence and correlations are everywhere • e.g. Every solid and molecule • Other types of correlations are more subtle and still waiting to be uncovered. Correlated particles include: • electrons, atoms, molecules, grains, biological structures, cars… • In a single crystal, two atoms’ relative positions are determined within small fraction of an Angstrom even when microns or mm’s apart! diamond

4. Challenge: Understand and Harness… • Electronic correlations  unique materials and device properties • Superconductivity • All magnetism • Spin-charge coupling, e.g. multiferroics • Large thermopower • Controlled many-electron coherence in nanostructures • Atomic correlations • Quantum: ultra-cold atoms • Classical: amorphous solids, glasses, self-assembly, non-equilibrium processes • Biological correlations

5. Electronic Materials • Semiconductors: a success story • Multi-billion dollar industry • Science: Hall effect, nanostructures, and at least 4 Nobel prizes • Accurate understanding and modeling • Major energy applications: • Photovoltaic solar cells: clean, unlimited energy • Light emitting diodes: efficient, durable lighting • A Major Challenge: • Can we go beyond semiconductors, i.e. Achieve semiconductor-level fabrication with correlated electron materials? • Potential gain: new multifunctional materials and devices, which do more and do it better than semiconductors do. • Challenges: Understanding phenomena, controlling materials and interfaces

6. Semiconductors Large overlap of s+p orbitals gives very extended wavefunctions High quality and flexible fabrication Sensitivity due to weak donor/acceptor binding No intrinsic magnetism or other correlations Intrinsic length scale = large effective Bohr radius a0 Weak correlation and large a0 enable simple and accurate modeling Correlated Electron Materials Localization of d+f orbitals enhances Coulomb interaction Materials chemistry challenging! Sensitivity due to competing ordered states Diverse magnetic and other correlations Intrinsic length scales as short as atomic size Strong correlations very challenging to existing theoretical tools Comparison

7. The Beyond – what could we do? • Combine magnetic and electric functionality • Build dissipationless wires and devices from high (room?) temperature superconductors • Make better thermoelectrics • Make smaller, faster, more efficient electronics Device with 4 states stored in magnetic and electric polarization made from multiferroic manganites (CMR materials)

8. Challenge: Correlated Interfaces • Quality materials and interfaces needed for heterostructures: some exciting progress • Si-SiO2 interface • Metallic interfaces have been observed with mobility of 105 cm2V-1s-1 , comparable to high quality GaAs. • LaTiO3-SrTiO3 interface

9. Correlated Interfaces are Different • With strong correlations, there is a possibility of new emergent phenomena at the interface itself SrTiO3-LaAlO3 junction appears to be a ferromagnetic metal, even though both materials are paramagnet insulators! A single unit cell layer of SrTi0.8Nb0.2O3 embedded in SrTiO3 shows 5-fold enhanced thermopower H. Ota et al, Nat. Mat. 2007 A. Brinkman et al, Nat. Mat. 2007

10. Cr: d3 Challenge: Harness Competing Orders • Frustrated materials, which have competing interactions, exhibit tunable ordered states • Frustration (of spin, charge…) is a common feature of strongly correlated systems Spinel: ACr2X4 Data from S.-H. Lee, Takagi, Loidl groups A=Mn,Fe,Co X=O A=Cd X=S A=Zn,Cd,Hg X=O Multiferroic Antiferromagnet Colossal magnetocapacitance

11. Challenge: Correlated Quantum Liquids • High Tc superconductors 30nm Superconducting energy gap imaged by STM well above Tc=92K (Gomes et al, Nature, 2007) • What is the mechanism? • Need to understand the “normal” state first! ? • Quantum criticality • NaxCoO2 Strongly correlated “Curie-Weiss Metal” state shows very large thermopower below 100K – a missing ingredient for thermoelectric applications in this temperature range Many interesting correlated liquids occur near quantum critical points, which control their properties – here leading to anomalous resistivity in YbRh2Si2.

12. Challenge: Nanoscale Quantum Correlations • Electrons confined to small structures experience enhanced Coulomb forces • Nanowires, nanotubes, quantum dots • We want to control the full quantum state! Long-term prospects: nanoscale spintronics, quantum computing? A two electron quantum dot in which the spin state has been fully measured and controlled (J. Petta et al, 2007), taking advantage of Coulomb and Pauli blockade effects The spin coherence time is enhanced from nanoseconds to microseconds by controlling the correlations between the electronic and nuclear spins of the GaAs

13. Challenge: Atomic/Molecular Correlations • Correlations between atoms and molecules are usually very strong in solids or dense liquids, but can be described classically Stress fields of compressed amorphous “solid” mixtures of photoelastic polymer disks. The obvious strong correlations in the stress must be understood to fathom the limits of strength and failure mechanisms of amorphous materials and glasses. Schematic illustration of “raft” of actin filaments which forms due to a short-range attraction, despite the fact that all actin filaments have the same (negative) charge and would be naively expected to repel. The attraction is due to strong correlations of counterions in the solution.

14. The human heart is developmentally programmed to occur in the same position again and again. Correlations in Biology • Biological systems involve correlations of large numbers of designed, active elements operating highly out of equilibrium, on many length scales simultaneously Synthesizing this complexity in general mechanisms of emergence used by biology is a truly major Challenge, probably necessary to put it to work for us

15. Summary: Needs • Experiment: New and improved tools must be developed to probe “hidden” correlations • c.f. Historical discovery of antiferromagnetism only occurred in 1949 with the advent of neutron scattering! • e.g. High Tc superconductivity drove vast improvements in photoemission and low-temperature STM. • Materials synthesis: high quality, single crystal samples are needed for many experiments. • e.g. Inelastic neutron scattering gives maximum information for single crystals. • Flexible fabrication is a key for passage to technology. • Theory: a combination of first-principles and phenomenological approaches is needed to encompass the broad range of length scales in strongly correlated systems. • Theory should uncover general mechanisms of emergence which apply across families of materials, organisms etc. • e.g. Is there a unifying framework to understand “competing orders”?