Pinning Mode Resonances of 2D Electron Stripe Phases in High Landau Levels
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Pinning Mode Resonances of 2D Electron Stripe Phases in High Landau Levels. Han Zhu ( 朱涵 ) Physics Department, Princeton University National High Magnetic Field Laboratory, Florida State University G. Sambandamurthy, NHMFL/FSU&Princeton EE, now SUNY buffalo

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Pinning Mode Resonances of 2D Electron Stripe Phases in High Landau Levels

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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 University

National High Magnetic Field Laboratory, Florida State University

G. Sambandamurthy,NHMFL/FSU&Princeton EE, now SUNY buffalo

Pei-Hsun Jiang,NHMFL/FSU&Princeton EE

R. M. Lewis,NHMFL/FSU, now U Maryland

Yong ChenPrinceton EE&NHMFL/FSU, now Purdue

L. EngelNHMFL/FSU

D. C. Tsui,Princeton EE

L. N. Pfeiffer and K. W. WestBell Labs, Alcatel-Lucent


Pinning mode resonances of 2d electron stripe phases in high landau levels

AlxGa1-xAs

2D electron systems

GaAs 10~50 nm

AlxGa1-xAs

Electron mobility

(cm2/Vs)

-2007 45 m

-2005 30 m

-Late 90’s, 10 m

-80’-90’, 1 m

-1980, 100 k

  • Fractional Quantum

  • Hall Effect of Composite Fermions

  • Stripes, Bubbles, etc.

  • Non-Abelian states

  • Fractional Quantum

  • Hall Effect

  • Integer Quantum

  • Hall Effect


Pinning mode resonances of 2d electron stripe phases in high landau levels

CDW in Quantum Hall systems

Landau Level filling ν> 4

easy

IQHE-Wigner

Crsytal

hard

R_yy

4

9/2

R_xx



Fogler et al. ’96,

R. Moessner, and J. T. Chalker, 96’

Lilly et al, ’99 ...


Pinning mode resonances of 2d electron stripe phases in high landau levels

Different viewpoints on the stripe phase

nematic

Stripe crystal

smectic

Also, elliptical Fermi surface...

Oganesyan, Kivelson, Fradkin’01

A review available by Fogler in cond-mat . . .


Pinning mode resonances of 2d electron stripe phases in high landau levels

Wigner crystal: Pinning modes

B

In high B, at low filling factors,

electrons form a Wigner crystal

fpk is a measure of average pinning energy per electron; pinning energy lowers overall energy


Pinning mode resonances of 2d electron stripe phases in high landau levels

Outline

  • Microwave/rf measuring technique

  • Stripephase: anisotropic pinning mode

  • Stripephase in In-plane field:

    Turns resonances on and off

    Interpretation: pinning energy measured by resonance frequency


Pinning mode resonances of 2d electron stripe phases in high landau levels

Microwave/Rf spectroscopy

W=78 mm

  • Metal-film coplanar waveguide

Erf

Re(xx) = (1/NZ0)ln(P/P0)


Pinning mode resonances of 2d electron stripe phases in high landau levels

n = 2.61011 cm-2

μ= 2.9107 cm2/Vs

T ~ 35 mK

[110],“x”, “hard” [110], “y”, “easy”

bubble

Spectra

4<ν<5

stripe

bubble

Predicted ν range:

Shibata&

Yoshioka, PRL ’01


Pinning mode resonances of 2d electron stripe phases in high landau levels

Spectra 4<ν<5 : overview

[110], “y”, “easy”

[110], “x”, “hard”

bubble

stripe

bubble


Pinning mode resonances of 2d electron stripe phases in high landau levels

ν =9/2 in BipDC transport:

y, [110]

Lilly et al., PRL, 1999

x, [110]

R_yy

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...

Bip

R_xx

  • (Finite thickness) Bip - induced anisotropy energy

  • CDW picture

  • Finite layer thickness

  • Favors stripe Bip

  • Jungwirth et al. PRB 99’; Stanescu et al. PRL 00’.

Bip


Pinning mode resonances of 2d electron stripe phases in high landau levels

Sample

Flexible transmission line

Coax cable

Rotator Probe for Microwave/Rf spectroscopy

Bip=0 stripes

Four cases:

y, [110]

_xxor _yy

Bip || x or y

x, [110]


Pinning mode resonances of 2d electron stripe phases in high landau levels

Bip=0 stripes

y, [110]

x, [11̅0]

Bip along y

Bip

Resonance switches from xx to yy around Bip=1 T

Bip brings up fpk of resonance in xx


Pinning mode resonances of 2d electron stripe phases in high landau levels

Bip=0 stripes

y, [110]

x, [11̅0]

Bip alongx

Bip


Pinning mode resonances of 2d electron stripe phases in high landau levels

Peak Conductivity

y, [110]

x, [110]

Bip

Bip


Pinning mode resonances of 2d electron stripe phases in high landau levels

Peak Frequency

Bip

Bip


Pinning mode resonances of 2d electron stripe phases in high landau levels

What can be determining the stripe orientation

  • 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

K B Cooper et al..

Solid State Comm 119 89 (2001)

30 nm QW, 2.7 1011/cm2

Pinning energy is relevant to determining stripe orientation!


Pinning mode resonances of 2d electron stripe phases in high landau levels

Bip along x

Summary

yy

  • Stripe phase resonance

  • Hard direction 100 MHz,

    pinning mode interpretation

  • Apply Bip:

  • switches resonance direction

  • fpk increase with Bip

  • measure of pinning energy

xx


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