Phase Diagram of 2D Electron System on the Surface of Liquid Helium

1
Phase Diagram of 2D Electron System on the
Surface of Liquid Helium

• Ph.D. Defense of I.Skachko
• Under the Supervision of Prof. E. Andrei

2
2D Electron Systems

• In Si-MOS inversion layers
• In GaAs/AlxGa1-xAs heterostructures
• On cryogenic surfaces
• Liquid 4He
• Liquid 4He, 3He mixtures
• Solid Hydrogen
• Solid Inert Elements (Neon, etc.)

3
Basic Properties of 2DES
2D Electrons on Helium

• Nondegenerate for T gt 50mK
• High Mobility

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2DES on Helium
n 107 109 cm-2
4He
5
Interaction in 2DES
1 1000
n 107 109 cm-2
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Normal Modes of Circular 2DES
Ve(z h,d) 0
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? 0, ? 1
? 1, ? 1
? 2, ? 1
? 1, ? 1
? 2, ? 1
? 1, ? 2
? 3, ? 1
? 3, ? 1
? 1, ? 2
? 4, ? 1
? 0, ? 2
? 2, ? 2
? 4, ? 1
? 5, ? 1
? 5, ? 1
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Helium Surface Excitations - Ripplons


d
4He
4He kc  (gr/s)1/2 20 cm-1



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2D Electron Mobility (liquid phase)

• Scattering from helium vapor atoms.

b out-of-plane extension of the wavefunction
(Saitoh 1977)
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Phase Diagram
Experiment
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2D Lattice
(Bonsall and Maradudin 1977)
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Coupled Phonon-Ripplon (CPR) Modes
Uncoupled Modes wp(q), wr(Gp)
Fisher, Halperin, Platzman(1979)
q 1/R 1cm-1 ltlt G1 1mm-1
wd
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Guard Ring
Top Plate
Dielectric Substrate
Transmission Line






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Excitation of 2DES Normal Modes
1. c gtgt vp 108 cm/s



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Circuit
Filament
Top Plate
Guard Ring
RF amplifier
Meander Line
Splitter
Mixer
Low-pass Filter
50W
Lock-in Detector
Compensating Line
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Direct vs. Modulated Transmission
Density Modulation Center Frequency Modulation
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2DES Spectrum
T 100mK P -38dBm n 4.5 107 cm-2
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T 100mK
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Why Use Log Frequency Scale?
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ncm-2
T 100mK
7.6 107
9 107
1 108
1.5 108
2.3 108
3 108
3.8 108
4.6 108
5.3 108
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Identification of 2D Plasma Modes
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Manifestation of Melting Transition in the
Spectrum
Why Optical Plasmons?
Evolution is gradual

• Measure
• Melting temperature Tm
• Dimple frequency wd

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n 9 107 cm-2
P - 44 dBm

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Temperature Shift
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2DES Heating

• Absorbed power Pabs Nm eE2
• Scattering is quasielastic

Pabs k (Te-T), k 10 pW/K (Glattli, Andrei et
al. 1984)
Te-T 100mK Pincident -44dBm , N 108, m
107cm2/Vs, E? 75 V/cm
2DES is melted by power
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Electron Crystal Helium Decoupling (Sliding
Transition)

• At resonance for f 100 MHz, P -44dBm
• ve m Erf 500 cm/s

Ripplon Phase Velocity wr /kr 200 cm/s for kr
G1 (8n/30.5)0.5 G1 2D crystal reciprocal
vector for n 108 cm-2
2DES remains in a crystal state
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Melting with Power
-50dBm(melted)
T 90mK
Tm 460mK
n 4.5 108 cm-2
-56dBm (solid)
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Melting Temperature Measurement

• For a fixed T take sequence of spectra with
  varying power
• If a shift is observed, 2DES is solid
• Otherwise, 2DES is liquid

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Phase Diagram
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Mobility
Electron Liquid
muncpl solid gt mliquid gt mcpl solid
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Mobility vs. Pressing Field
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Spectra in Magnetic Field
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Magnetoplasmon
fc(2.8 m 0.1) B
m me
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Summary

• Technique for excitation of 2DES normal modes was
  developed
• Identification of the spectrum with that of 2D
  plasma
• Measure the phase diagram of 2DES
• 2DES displays non-linear behavior
• Melting with power - dominates at low E?
• Sliding transition dominates at high E?

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2D Electron System
z
x
y
Electrons are confined to xy plane by potential
V(z)
2D when E2-E1ltlt kBT
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Binding to Helium
Electron









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Confining Potential
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Energy Diagram
1eV
z
4He
a0 76 Å E1  0.65 meV  7.5 K
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Energy Diagram
a0 76 Å Ry  0.65 meV  7.5 K
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He Surface is Smooth
Effective Bohr radius a076Å

• Fluctuations at T lt 1K ltzgtrms 2Å (Cole 1970)

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Screening
2DES
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2D Plasmons
Top Plate
h
2DES
d
Bottom Plate
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Surface of Liquid Helium
If ltzgt gtgt z , the Hamiltonian is separable gt the
system is 2-dimensional.
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Helium Surface Excitations - Ripplons
Vapor

z

z

x

d

Liquid

Substrate


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Ripplon Dispersion
kc  (gr/s)1/2 20 cm-1
Long wavelength (gravity waves) k ltlt kc, 1/d
wr k
Short wavelength k gtgt kc, wr  k1.5
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Mobility (Liquid Phase)
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Wigner Solid Modes

• Longitudinal

Impossible to observe without magnetic field
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Experimental Limitations
EHD Instability n lt 2.2 109 cm-2

• Thermal Escape from 2D layer
• Excessive Dissipation
• T lt 1.5 K

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Phase Diagram on Thin Film Above Dielectric
Substrate
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Phase Diagram on Thin Film Above Metallic
Substrate
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Cell
Top Plate

Filling Line

Filament
Guard Ring

Transmission Line


Dielectric Substrate


Level Capacitor


LEGEND
Leads


Liquid Helium

Stainless Steel

Solder Joints


Coaxes


MacorTM



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Identification of Resonances
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Resonance Splitting
n5 108 cm-2
Tm 0.5K
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Derivative Spectra
Modulating Resonance Frequency
Modulating Linewidth
Hybrid Modulation
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fr vs. T
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Mobility (Melting)
Low freq. Transport Wigner transition (Mehrotra,
Guenin et al. 1982)
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2DES Reflections
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2DES Transmission
Vin
Vout
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Ripplon Dispersion for Charged Surface
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EHD Instability
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Ripplon Bragg Diffraction
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Why Optical Plasmons?

• Evolution is gradual

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2D Plasma in Magnetic Field
(Glattli, Andrei et al. 1985)
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2D Electron Solid in Magnetic Field
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2DES Confinement
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Direct vs. Modulated
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Helium Filling Curves
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Meander Line

Slow velocity
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Other Slow-Wave Structures
Coplanar Meander Line
Interdigital Capacitor
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Power Sequence