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