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

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. EngelNHMFL/FSU D. C. Tsui, Princeton EE L. N. Pfeiffer and K. W. WestBell Labs, Alcatel-Lucent

2. 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

3. 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 ...

4. 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 . . .

5. 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

6. 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

7. Microwave/Rf spectroscopy W=78 mm • Metal-film coplanar waveguide Erf Re(xx) = (1/NZ0)ln(P/P0)

8. 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

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

10. 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

11. 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]

12. 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

13. Bip=0 stripes y, [110] x, [11̅0] Bip alongx Bip

14. Peak Conductivity y, [110] x, [110] Bip Bip

15. Peak Frequency Bip Bip

16. 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!

17. 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