1. 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 Chen Princeton EE&NHMFL/FSU, now Purdue L. Engel NHMFL/FSU D. C. Tsui, Princeton EE L. N. Pfeiffer and K. W. West Bell Labs, Alcatel-Lucent

2. 2D electron systems Al x Ga 1-x As GaAs 10~50 nm -Late 90’s, 10 m  Integer Quantum Hall Effect  Fractional Quantum Hall Effect  Fractional Quantum Hall Effect of Composite Fermions  Stripes, Bubbles, etc.  Non-Abelian states -1980, 100 k -2005 30 m -2007 45 m -80’-90’, 1 m Electron mobility (cm 2 /Vs)

3. 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-Wigner Crsytal hard easy R_yy R_xx

4. 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...

5. Wigner crystal: Pinning modes B f pk 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

6.  Microwave/rf measuring technique  Stripe phase: anisotropic pinning mode  Stripe phase in In-plane field: Turns resonances on and off Interpretation: pinning energy measured by resonance frequency Outline

7. W =78  m Metal-film coplanar waveguide Microwave/Rf spectroscopy Re(  xx ) =  (1/N  Z 0 )ln(P/ P 0 ) E rf

8. stripe [110], “x”, “hard” [110], “y”, “easy” n = 2.6  10 11 cm -2 μ= 2.9  10 7 cm 2 /Vs T ~ 35 mK Predicted ν range: Shibata& Yoshioka, PRL ’01 Spectra 4<ν<5 bubble

9. [110], “x”, “hard” [110], “y”, “easy” Spectra 4<ν<5 : overview stripe bubble

10. 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 B ip ν =9/2 in B ip DC transport: R_xx R_yy y, [110] x, [110] (Finite thickness) B ip - induced anisotropy energy  CDW picture  Finite layer thickness  Favors stripe  Bip Jungwirth et al. PRB 99’; Stanescu et al. PRL 00’.

11. Rotator Probe for Microwave/Rf spectroscopy SampleFlexible transmission lineCoax cable B ip =0 stripes y, [110] x, [110] Four cases:  _xx or  _yy  B ip || x or y

12. B ip brings up f pk of resonance in  xx B ip =0 stripes x, [11 ̅ 0] y, [110] B ip B ip along y Resonance switches from  xx to  yy around B ip =1 T

13. B ip B ip along x B ip =0 stripes x, [11 ̅ 0] y, [110]

14. Peak Conductivity B ip y, [110] x, [110]

15. B ip Peak Frequency

16. K B Cooper et al.. Solid State Comm 119 89 (2001) 30 nm QW, 2.7  10 11 /cm 2  Native Anisotropy  not understood, weak, sample dependent  Finite thickness B ip - induced anisotropy energy  Calculated from CDW, finite layer thickness,  Favors stripe  B ip Jungwirth et al. PRB 99’; Stanescu et al. PRL 00’  Measured by us: Pinning energy anisotropy  Disorder-carrier interaction,  B ip dependent: increases with B ip  Favors stripe | | B ip What can be determining the stripe orientation Pinning energy is relevant to determining stripe orientation!

17.  Stripe phase resonance  Hard direction 100 MHz, pinning mode interpretation  Apply B ip : switches resonance direction f pk increase with B ip measure of pinning energy B ip along x  xx  yy Summary