Breaking electrons apart in condensed matter physics T. Senthil (MIT) Group at MIT Predrag Nikolic...
-
Upload
terence-hampton -
Category
Documents
-
view
214 -
download
0
Transcript of Breaking electrons apart in condensed matter physics T. Senthil (MIT) Group at MIT Predrag Nikolic...
Breaking electrons apart in condensed matter physics
T. Senthil(MIT)
Group at MITPredrag Nikolic Dinesh Raut O. Motrunich (now at KITP)A. Vishwanath
Other main collaboratorsL. Balents (UCSB)Matthew P.A Fisher (KITP)Subir Sachdev (Yale)D. Ivanov (Zurich)
Conventional condensed matter physics: Landau’s 2 great ideas
1. Theory of fermi fluids
(electrons in a metal, liquid He-3, nuclear matter, stellar structure,……..)
2. Notion of ``order parameter’’ to describe phases of matter
- related notion of spontaneously broken symmetry- basis of phase transition theory
Fermi liquid theory
• Electrons in a metal: quantum fluid of fermions
• Inter-electron spacing ~ 1 A Very strong Coulomb repulsion ~ 1-10 eV.
But effects dramatically weakened due to Pauli exclusion.
Important `quasiparticle’ states near Fermi surface scatter only weakly off each other.
Describes conventional metals extremely well.
kx
ky
kz
Fermi surface
Filled states unavailable for scattering
Order parameter
• Example - ferromagnetism
• Spontaneous magnetization: `order parameter’.
• Ordered phase spontaneously breaks spin rotation symmetry.
Ferromagnet: Spins aligned
Paramagnet:Spins disordered
Increase temperature
Notion of order parameter and symmetry breaking
Powerful unifying framework for thinking generally about variety of ordered phases (eg: superfluids, antiferromagnets, crystals, etc).
Determine many universal properties of phases- eg: rigidity of crystals, presence of spin waves in
magnets, vortices in superfluids,…….
Phase transitions -Theoretical paradigm
• Critical singularities: long wavelength fluctuations of order parameter field.
• Landau-Ginzburg-Wilson: Landau ideas + renormalization group
- sophisticated theoretical framework
Modern quantum many-electron physics
• Many complex materials studied in last two decades DEFY understanding within Landau thinking
Examples: 1. One dimensional metals (Carbon nanotubes)2. Quantum Hall effects
3. High temperature superconductors4. Various magnetic ordering transitions in rare-earth alloys
Need new ideas, paradigms!!
Well-developed theory
??!!
High temperature superconductors
2 4La CuO
Cu
O
La
Parent insulator
remove electrons Superconductor at relatively hightemperatures
Complex phase diagram
T
x = number of doped holes
Insulating antiferromagnet
Superconductor
Fermi liquid
Strange non-FermiLiquid metal
Another strangemetal
T = 0 phase transitions in rare earth alloys
• Examples: CePd2Si2, CeCu6-xAux, YbRh2Si2,……
(Quantum) critical point with striking non-fermi liquid physics unexpected in Landau paradigm.
Magnetic metal Fermi liquid
Pressure/B-field/etc
In search of new ideas and paradigms
• Most intriguing – electron breaks apart!!
(Somewhat) more precise: Fractional quantum numbers
Excitations of many body ground state have quantum numbers that are fractions of those of the underlying electrons.
Fractional quantum numbers
• Relatively new theme in condensed matter physics.
• Solidly established in two cases
d = 1 systems (eg: polyacetylene, nanotubes, …..),
d = 2 fractional quantum Hall effect in strong magnetic fields
Broken electrons in d = 1
• Remove an electron from a d = 1 antiferromagnet
Removed chargeSpin domain wall= removed spin
Broken electrons in d = 1
• Remove an electron from a d = 1 antiferromagnet
Removed chargeSpin domain wall= removed spin
Broken electrons in d = 1
• Remove an electron from a d = 1 antiferromagnet
Removed charge Spin domain wall= removed spin
Broken electrons in d = 1
• The charge and spin of the removed electron move separately – the electron has broken!
• ``Spin-charge separation’’ the rule in d = 1 metals
Quantum Hall effect
• Confine electrons to two dimensions
• Turn on very strong magnetic fields
• Make the sample very clean
• Go to low temperature
Extremely rich and weird phenomena
(eg: quantization of Hall conductance)
Fractional charge
• If flux density (in units of flux quantum) is commensurate with electron density, get novel incompressible electron fluid.
• Excitations with fractional charge (and statistics) appear!
(Experiment: Klitzing, Tsui, Stormer, Gossard,……
Theory: Laughlin, Halperin, …………)
Physics Nobel: 1985, 1998.
All important question
Are broken electrons restricted to such exotic situations
(d = 1 or d = 2 in strong magnetic fields)?
Inspiration: Very appealing ideas on cuprate superconductors based on 2d avatars of spin-charge separation (Anderson, Kivelson et al, P.A Lee et al, …..)
All important question
Are broken electrons restricted to such exotic situations
(d = 1 or d = 2 in strong magnetic fields)?
NO!!!
Recent theoretical progress
Electrons can break apart in regular solids with strong interactions in 2 or 3 dimensions and in zero B-fields
1. Novel quantum phases with fractional quantum numbers (spin-charge separation)
(Many people: Anderson, Read, Sachdev, Wen, TS, Fisher, Moessner, Sondhi,
Balents, Girvin, Misguich, Motrunich, Nayak, Freedman, Schtengel,……..)
2. Novel phase transitions described by fractionalized excitations separating two conventional phases.
(TS, Vishwanath, Balents, Sachdev, Fisher ,Science March 04)
Complete demonstrable breakdown of Landau paradigms!!
Some highlights
• Theoretical description of fractionalized phases
(eg: nature of excitation spectrum)
• Concrete (and simple) microscopic models showing fractionalization
• Prototype wavefunctions for fractionalized ground states
• Precise characterization of nature of ordering in the ground state: replace notion of broken symmetry.
Where might it occur?Always a hard question: hints from theory
Frustrated quantum magnets with paramagnetic ground states
``Intermediate’’ correlation regime – neither potential
nor kinetic energy overwhelmingly dominates the other.
(i) Quantum solids near the melting transition
(ii) Mott insulators that are not too deeply into the insulating regime
Possibly in various 3d transition metal oxides
Perhaps even very common but we just haven’t found out!!
One specific simple model – small superconducting islands on a regular lattice (quantum Josephson junction array)
• Competition between Josephson coupling and charging energy:
H = HJ + Hch
• Josephson : Cooper pairs hop between islands to delocalize
• Charging energy: prefer local charge neutrality, i.e localized Cooper pairs.
• Superconductivity if Josephson wins, insulator otherwise.
.
..
Motrunich, T.S, Phys Rev Lett 2002
Phase diagram in d = 2
Jose
phso
n
Charging energy
Fractionalized insulator sandwiched between superfluid and conventional insulator.
Fractionalized phase: excitations with half of Cooper pair charge.
Broken symmetry versus fractionalization
Goldstone modes (spin waves, phonons, etc)
Stiffness (crystal rigidity,
persistent superflow,…)
Topological defects (vortices, dislocations, etc)
Hartree-Fock mean field theory
Coexistence of different broken symmetries (magnetic superconductors, supersolids,etc)
Tools to detect (Bragg scattering, Josephson, etc)
Broken symmetry versus fractionalization
Goldstone modes (spin waves, phonons, etc)
Gauge excitations
Stiffness (crystal rigidity,
persistent superflow,…)
Topological defects (vortices, dislocations, etc)
Hartree-Fock mean field theory
Coexistence of different broken symmetries (magnetic superconductors, supersolids,etc)
Tools to detect (Bragg scattering, Josephson, etc)
Why gauge?
• Relic of glue that confines broken pieces together in conventional phases.
- Analogous to quark confinement.
Conventional phases: Broken pieces (like quarks) are
bound together by a confining gauge field.
Fractionalized phases: Gauge field is deconfined; liberates the fractional particles.
Broken symmetry versus fractionalization
Goldstone modes (spin waves, phonons, etc)
Gauge excitations
Stiffness (crystal rigidity,
persistent superflow,…)
Robustness to all perturbations
Topological defects (vortices, dislocations, etc)
Hartree-Fock mean field theory
Coexistence of different broken symmetries (magnetic superconductors, supersolids,etc)
Tools to detect (Bragg scattering, Josephson, etc)
Robustness to all perturbations(gauge rigidity)
• Gauge excitations preserved for arbitrary local perturbations to the Hamiltonian (including ones that break symmetries)
• Stable to dirt, random noise, coupling to lattice vibrations, etc. (``Topological/quantum order’’ – Wen)
• Protected against decoherence by environment
(Potential application to quantum computing – Kitaev)
Broken symmetry versus fractionalization
Goldstone modes (spin waves, phonons, etc)
Gauge excitations
Stiffness (crystal rigidity,
persistent superflow,…)
Robustness to all local perturbations
Topological defects (vortices, dislocations, etc)
Fractional charge
Hartree-Fock mean field theory
Coexistence of different broken symmetries (magnetic superconductors, supersolids,etc)
Tools to detect (Bragg scattering, Josephson, etc)
Fractional charge: defects in gauge field configuration
• Fractional charges carry the gauge charge that couples to the gauge field - hence defects in the gauge field
(as in ordinary electromagnetism)
Electric charge Electric field lines
Broken symmetry versus fractionalization
Goldstone modes (spin waves, phonons, etc)
Gauge excitations
Stiffness (crystal rigidity,
persistent superflow,…)
Robustness to all local perturbations
Topological defects (vortices, dislocations, etc)
Fractional charge
Hartree-Fock mean field theory Slave particle mean field theory
Coexistence of different broken symmetries (magnetic superconductors, supersolids,etc)
Tools to detect (Bragg scattering, Josephson, etc)
Slave particle mean field theory(Coleman, Read, Kotliar, Lee,….)
• Write electron operator cα = b†fα
Charged spinless boson(``holon’’)
Neutral spinful fermion(``spinon’’)
Replace microscopic Hamiltonian with equivalent non-interacting Hamiltonian for holons and spinons with self-consistently determined parameters.
Broken symmetry versus fractionalization
Goldstone modes (spin waves, phonons, etc)
Gauge excitations
Stiffness (crystal rigidity,
persistent superflow,…)
Robustness to all local perturbations
Topological defects (vortices, dislocations, etc)
Fractional charge
Hartree-Fock mean field theory Slave particle mean field theory
Coexistence of different broken symmetries (magnetic superconductors, supersolids,etc)
Coexistence with conventional broken symmetry
Tools to detect (Bragg scattering, Josephson, etc)
Coexistence(Balents, Fisher, Nayak, TS)
• Fractionalization may coexist with conventional broken symmmetry
(eg: fractionalized magnet, fractionalized superfluid,…)
Important implication: Presence of conventional order may hide more subtle fractionalization physics.
(Is Nickel Sulfide fractionalized?)
Broken symmetry versus fractionalization
Goldstone modes (spin waves, phonons, etc)
Gauge excitations
Stiffness (crystal rigidity,
persistent superflow,…)
Robustness to all local perturbations
Topological defects (vortices, dislocations, etc)
Fractional charge
Hartree-Fock mean field theory Slave particle mean field theory
Coexistence of different broken symmetries (magnetic superconductors, supersolids,etc)
Coexistence with conventional broken symmetry
Tools to detect (Bragg scattering, Josephson, etc)
Flux memory, noise, ??
Detecting the gauge field
• Largely an open problem in general !!
• In some cases can use proximate superconducting states to create and then detect the gauge flux
(TS, Fisher PRL 2001; TS, Lee forthcoming)
Cuprate experiments (Bonn, Moler) find no evidence for Z2 gauge flux
expected for one possible phase with spin-charge separation.
Other possibilities exist and haven’t been checked for yet.
Outlook
• Theoretical progress dramatic (rapid important developments every year)
• But no unambiguous experimental identification yet (though many promising candidates exist)
• Theoretically important answer to 0th order question posed by experiments:
Can Landau paradigm be violated at phases and phase transitions of strongly interacting electrons?
Outlook (cont’d)
• Extreme pessimist:
Why bother? Might not be seen in any material.
Extreme optimist: Might be happening everywhere without us knowing (eg: in Nickel Sulfide,…..)
Outlook (cont’d)
• Strong need for probes to tell if fractionalized (completely new experimental toolbox).
Ferromagnetism (relatively rare)– known for centuries
Antiferromagnetism (much more common) – known only
for < 70 years
Had to await development of new probes like neutron scattering
Questions for the future
Will these ideas ``solve’’ existing mysteries like the
cuprates?
Will they have deep implications for other branches of physics (much like ideas of broken symmetry did)?
See X.-G. Wen, Origin of Light for some suggestions.
Will they form the basis of quantum computing technology?