QUANTUM HALL STATES SEEN AS QUANTUM LIQUIDS

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QUANTUM HALL STATES SEEN AS QUANTUM LIQUIDS
Spectroscopy of Electron Fluids in the Quantum
Hall Regimes collective excitation modes
exotic quantum phases of electrons in 2D
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Studies of Quasiparticle Excitations in Quantum
Hall Fluids
OUTLINE
? Introduction
? Inelastic light scattering methods
? Lowest (N0) Landau Level composite
fermions
? First Excited (N1) Landau Level
competing quantum phases
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Quantum Liquids in Condensed Matter
A quantum fluid is a large collection particles
(electrons, atoms, etc) in which interactions
result in a many-particle behavior that is
described as a single quantum entity
Superfluid liquid 4He Superconductors
Atomic condensates Electrons in
two-dimensional structures quantum Hall
fluids
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Energy Levels in the 2D Electron System
Size quantization-QW
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Electron motion in a perpendicular magnetic field
The quantized states of this periodic motion are
Landau levels spaced by ??c
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Occupation of Landau Levels
Landau levels are populated to the extent that
the areas of the orbits (each area is
lo21/B) cover the area of the 2D system
this simple concept is linked to the Landau
level filling factor (?)
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Quantum Hall Effect
Quantum Hall Fluids occur in 2D electron systems
embedded in large magnetic fields
? ?
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Quantum Structures for Optical Experiments
Molecular beam epitaxy by Loren Pfeiffer and Ken
West
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Quantum Liquids in Condensed Matter
A quantum fluid is a large collection particles
(electrons, atoms, etc) in which interactions
result in a many-particle behavior that is
described as a single quantum entity
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Emergent States Superconductivity
a superconductor is a quantum fluid of
electrons current flows without resistance (no
viscosity).
This state could not be predicted nor explained
by microscopic models of metals for almost 50
years
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Normal Liquids
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Superfluid 4He
the fountain effect quantum behavior on a
macroscopic scale
Superfluid 4He
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Superfluid 4He Fountain Effect
quantum behavior on a macroscopic scale
This quantum fluid moves as a single quantum
entity and with no viscosity
Kenji Mizoguchi, (Tokyo)
Superfluid 4He is described as a Bose-Einstein
condensate
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Quantum Hall Effect
at quantum Hall fields ?xx ? 0, ?xy ? 0
? ?

• ?xx ? 0 and ?xx ? 0
• !!!

• ?xx ? 0
• ? emergence of energy gaps

? key roles for spectroscopy!
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Gap Excitations the states at ??1/3
built from quasiparticle-quasihole
excitations above the quantum phase ground state
C. Kallin and B. Halperin, 1984 D. Haldane and E.
Rezayi, 1985 S. Girvin, A. MacDonald, P.
Platzman, 1985
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Activated Transport
R. R. Du, private communication
conceptually activation probes the gap at large
wave vector however
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Activated Transport
In magneto-transport there is impact of edge
states.
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Quantum Hall States Optics
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Inelastic Light Scattering
excitations of electron quantum fluids are seen
directly in inelastic light scattering spectra
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Resonant inelastic light scattering
observations of spectra of dilute electron
systems require large resonant enhancements of
the intensities
cyclotron mode of electrons at energy wc
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Spectroscopy of Quantum Fluids Quantum Hall
Liquid
measured by inelastic light scattering
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Milli-kelvin Light Scattering Spectroscopy
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Long wavelength Mode at ??1/3
The mode at Do is a marker of the macroscopic
quantum fluid.
observation of Do demonstrates that a
macroscopic fluid forms even when electrical
conduction is via edge states
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Excitations at ?1/3 Dispersive Modes
wave vector is changed by changes in ?
The long wavelength mode broadens and splits into
two distinct modes at larger k.
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Dispersive long wavelength modes
Links between long wavelength modes and two-roton
states
C. Hirjibehedin, (2005)
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Resonant inelastic light scattering at
n1/3 observation of large wavevector modes
J. Groshaus (2007)
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Magnetorotons at ??1/3
Upper panel Light scattering spectra Lower
panel Calculated gap mode dispersion
Inelastic light scattering with conservation of
wave vector
Inelastic light scattering that breaks
conservation of wave vector
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Large wavevector modes at ??1/3
Weak residual-disorder causes breakdown of
wavevector conservation
I(?) Sqj F(qj) S(qj, wj)r(qj,wj)
r(qj,wj) DOS (qj,wj) critical points S(qj,
wj) structure factors F(qj) coupling strengths
spectra display the ?R and ?? critical points
in the DOS of the mode dispersion
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A frequently asked question
breakdown of wavevector conservation in
systems of great perfection?
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Light Scattering Matrix Element
add electron collisions
O S q Vq / ( EG hwL )
Weak residual disorder has major impact at
extreme resonance
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Composite Fermions
There is a new quantum number p1,2,3,4,
p CF filling factor
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Electrons vs. Composite Fermions
Integer QHE (integer n)
Fractional QHE (fractional n)
Integer QHE is due fo filling of Landau levels
of electrons
Fractional QHE is due fo filling of Landau
levels of Comp. Fermions
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Composite Fermions Spin Excitations
Two distinct spin modes probe novel fundamental
physics

• Spin Waves
• Only spin orientation changes

• Spin-flip Modes
• Spin orientation and Landau level (CF) change

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Inelastic light scattering methods offer unique
access to spin excitations
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CF Landau levels near ??1/3
a new excitation the spin-flip mode (SF) is
predicted at ngt1/3
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Observation of SF Excitations 2/5 ?? ?1/3
direct evidence of Landau levels of composite
femions
CF levels exist in the full range of filling
factor!
Dujovne et al, PRL (2003) Gallais et at, PRL
(2006)
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Composite Fermion Flavor
A more general view of composite fermions
e- f fluxes fCF
f CF flavor
p CF filling factor
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Crossover in Composite Fermion Flavor
Flavor Crossover
n1/3 is the boundary of a quantum phase
transition in the flavor number
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Spin Excitations at the Flavor Crossover
SW spin-wave SF spin-flip
SF excitations manifest the transition in CF
flavor
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Flavor Transition at ?1/3
SF Excitations on both sides of the ?2 ? ?4
crossover
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Flavor Transition at ?1/3
The discontinuity in the SF energy (?SF) is due
to the abrupt change in CF flavor at the n1/3
crossover
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Spectroscopy of quantum Hall fluids
Excitations of the electron fluid are
observed by inelastic light scattering
Lowest N0 Landau Level

• Long wavelength modes and magnetrotons
• Spin excitations
• Composite fermion levels and flavor

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Quantum Fluids in the N1 Landau Level
odd-denominator states v 2 1/3 7/3 v
2 2/3 8/3 even-denominator states v 2
1/2 5/2 v 3 1/2 7/2 Competition
between quantum phases
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Spectroscopy of quantum phases in the N1 Landau
level
Start at ?3 and move to lower ?

• Inelastic light scattering by spin-waves
• Optical emission (luminescence)
• Rayleigh (elastic) light scattering

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Resonant inelastic Light scatteringSpin-wave of
the polarized state at v 3
Spin wave at the Zeeman energy
1
2
David T. Rhone et al (work in progress)
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Spin-wave away from v3
The sharp spin wave at ?3 collapses into a
continuum spectrum away from ?3
There is coexistence of both spectral features
close to n3
David T. Rhone et al (work in progress)
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Collapse of the spin-wave the N0 Landau level
near ?1
Collapse of the spin wave away from ?1
loss of spin polarization due to spin textures
in the ground state
SW
Y. Gallais et al (2008)
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Collapse of the spin-wave the N0 and
N1Landau levels
Major differences between spin waves in N0 and
N1 Landau levels
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Resonant Rayleigh Scattering
Probing quantum phases of non-uniform 2D electron
fluids
Rayleigh scattering
Incident laser light in resonance with an
optical transition
Resonant Rayleigh scattering probes the spatial
structure (disorder)of the quantum fluid
S. Luin, V. Pellegrini et at (2005), in electron
bilayers at ?1
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Resonant Rayleigh Scattering at ?3
Optical emission (luminescence) detects
populated levels Resonant Rayleigh scattering
peaks at transitions to empty states
David T. Rhone et al (work in progress)
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Resonant Rayleigh Scattering at ?5/2
Resonant Rayleigh scattering has peaks at
transitions to empty states May probe quantum
fluids in the partly populated Landau level
David T. Rhone et al (work in progress)
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Spectroscopy of quantum Hall fluids
N1 Landau Level

• Spin excitations
• well-defined spin-wave at n3
• collapse of spin waves for nlt3
• evidence of coexistence of
• distinct quantum phases

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Spectroscopy of quasiparticle excitations in
quantum Hall fluids
Resonant inelastic light scattering methods
access excitations of quantum fluid phases of
electrons
N0 Landau level composite fermions, skyrmions
N1 Landau level exotic phases of electrons

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SPECTROSCOPY OF QUANTUM HALL LIQUIDS
Inelastic Light Scattering is our Main
Experimental Method collective excitation
modes exotic quantum phases of electrons in 2D