Pinning Mode Resonances of 2D Electron Stripe Phases in High Landau Levels
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Transcript of Pinning Mode Resonances of 2D Electron Stripe Phases in High Landau Levels
Pinning Mode Resonances of 2D Electron Stripe Phases in High Landau Levels
Han Zhu (朱涵 )
Physics Department, Princeton UniversityNational High Magnetic Field Laboratory, Florida State University
G. Sambandamurthy, NHMFL/FSU&Princeton EE, now SUNY buffaloPei-Hsun Jiang, NHMFL/FSU&Princeton EER. M. Lewis, NHMFL/FSU, now U MarylandYong Chen Princeton EE&NHMFL/FSU, now Purdue
L. Engel NHMFL/FSUD. C. Tsui, Princeton EE
L. N. Pfeiffer and K. W. West Bell Labs, Alcatel-Lucent
2D electron systemsAlxGa1-xAs
AlxGa1-xAsGaAs 10~50 nm
-Lat
e 90
’s, 1
0 m
Integer Quantum
Hall Effect
Fractional Quantum
Hall Effect
Fractional Quantum
Hall Effect of Composite Fermions
Stripes, Bubbles, etc.
Non-Abelian states
-198
0, 1
00 k
-200
5 30
m
-200
7 45
m
-80’
-90’
, 1 m
Electron mobility(cm2/Vs)
Lilly et al, ’99 ...
CDW in Quantum Hall systems Landau Level filling ν> 4
Fogler et al. ’96,R. Moessner, and J. T. Chalker, 96’
4
IQHE-WignerCrsytal hard
easy
R_yy
R_xx
Different viewpoints on the stripe phase
Stripe crystal smectic nematic
Also, elliptical Fermi surface...Oganesyan, Kivelson, Fradkin’01
A review available by Fogler in cond-mat . . .
Wigner crystal: Pinning modes
B
fpk is a measure of average pinning energy per electron; pinning energy lowers overall energy
In high B, at low filling factors, electrons form a Wigner crystal
Microwave/rf measuring technique
Stripe phase: anisotropic pinning mode
Stripe phase in In-plane field:Turns resonances on and offInterpretation: pinning energy
measured by resonance frequency
Outline
W=78 m
• Metal-film coplanar waveguide
Microwave/Rf spectroscopy
Re(xx) = (1/NZ0)ln(P/P0)
Erf
stripe
[110], “x”, “hard” [110], “y”, “easy”n = 2.61011 cm-2
μ= 2.9107 cm2/VsT ~ 35 mK
Predicted ν range:Shibata&Yoshioka, PRL ’01
Spectra 4<ν<5
bubble
bubble
[110], “x”, “hard” [110], “y”, “easy” Spectra 4<ν<5 : overview
stripe
bubble
bubble
DC experiments:Pan et al., PRL, ‘99 &
PRL,‘00; Lilly et al., PRL,
’99; Zhu et al., PRL, ‘02;Cooper et al., PRL,
‘04 etc.and more...
Lilly et al., PRL, 1999
Bip
Bip
ν =9/2 in Bip DC transport: R_xx
R_yy
y, [110]
x, [110]
(Finite thickness) Bip - induced anisotropy energy CDW picture Finite layer thickness Favors stripe BipJungwirth et al. PRB 99’; Stanescu et al. PRL 00’.
Rotator Probe for Microwave/Rf spectroscopy
Sample Flexible transmission line Coax cable
Bip=0 stripes y, [110]
x, [110]
Four cases:
_xx or _yy Bip || x or y
Bip brings up fpk of resonance in xx
Bip=0 stripes
x, [11 ̅0]
y, [110]
Bip
Bip along y
Resonance switches from xx to yy around Bip=1 T
Bip
Bip along x Bip=0 stripes
x, [11 ̅0]
y, [110]
Peak Conductivity
Bip
Bip
y, [110]
x, [110]
Bip
Bip
Peak Frequency
K B Cooper et al.. Solid State Comm 119 89 (2001)
30 nm QW, 2.7 1011/cm2
Native Anisotropy not understood, weak, sample dependent
Finite thickness Bip - induced anisotropy energy
Calculated from CDW, finite layer thickness, Favors stripe Bip
Jungwirth et al. PRB 99’; Stanescu et al. PRL 00’
Measured by us: Pinning energy anisotropy Disorder-carrier interaction, Bip dependent: increases with Bip
Favors stripe | | Bip
What can be determining the stripe orientation
Pinning energy is relevant to determining stripe orientation!
Stripe phase resonance
Hard direction 100 MHz, pinning mode interpretation
Apply Bip: switches resonance direction fpk increase with Bip
measure of pinning energy
Bip along x
xx
yy
Summary