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Emergence of Collective Phenomena: Strongly Correlated Multiparticle Systems

Leon Balents, UCSB

Julia Phillips, Sandia National Lab

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Correlations and Emergence

• 1 cm3 of matter = 1023 atoms, electrons

– Motion of one influences another

Uncorrelated:Light traffic = “ideal gas”

Correlations:jammed

Controlled correlations:Fast and efficient

AHS, San Diego 1997

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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…

diamond

• In a single crystal, two atoms’ relative positions are determined within small fraction of an Angstrom even when microns or mm’s apart!

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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

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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

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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

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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)

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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

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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

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Cr: d3Spinel: ACr2X4

A=Zn,Cd,HgX=O

Antiferromagnet Multiferroic

A=Mn,Fe,CoX=O

A=CdX=S

Colossal magnetocapacitance

Data from S.-H. Lee, Takagi, Loidl groups

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

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Challenge: Correlated Quantum Liquids

• High Tc superconductors

What is the mechanism?• Need to understand the “normal” state first! ?

Superconducting energy gap imaged by STM well above Tc=92K (Gomes et al, Nature, 2007)

30nm

• 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.

• Quantum criticality

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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!

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

Long-term prospects: nanoscale spintronics, quantum computing?

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Challenge: Atomic/Molecular Correlations

• Correlations between atoms and molecules are usually very strong in solids or dense liquids, but can be described classically

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.

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.

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Correlations in Biology

• Biological systems involve correlations of large numbers of designed, active elements operating highly out of equilibrium, on many length scales simultaneously

Permission needed Mark Sussman, Ph.D.

Wouter-Jan Rappel

John Collins MBI

Correlated excitation of muscle cells lead to spiral waves which can lead to either healthy beating or arrhythmia.

Individual muscle cells contract in a polarized manner along their aligned myofibrils

Individual myosin fibrils composed of repeating units of mysoin interact with another repeating polymer, actin, to create organized contraction.

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

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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”?