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 mms 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
Comparison

• Semiconductors
• Large overlap of sp 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 df 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

• Frustration (of spin, charge) is a common
  feature of strongly correlated systems

Spinel ACr2X4
AMn,Fe,Co XO
Data from S.-H. Lee, Takagi, Loidl groups
ACd XS
AZn,Cd,Hg XO
Multiferroic
Antiferromagnet
Colossal magnetocapacitance
11
Challenge Correlated Quantum Liquids

• High Tc superconductors

30nm
Superconducting energy gap imaged by STM well
above Tc92K (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

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.
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

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?