1. Leon Balents, UCSB Julia Phillips, Sandia National Lab
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 Photovoltaic solar cells: clean, unlimited energy
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. Comparison 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

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
A. Brinkman et al, Nat. Mat. 2007
H. Ota et al, Nat. Mat. 2007

10. Challenge: Harness Competing Orders
Frustrated materials, which have competing interactions, exhibit tunable ordered states
Cr: d3
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. Correlations in Biology
Biological systems involve correlations of large numbers of designed, active elements operating highly out of equilibrium, on many length scales simultaneously
The human heart is developmentally programmed to occur in the same position again and again.
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”?