acoustic study of wigner crystal near integer and fractional … · 2018. 2. 8. · pphmf-8...

PPHMF-8 ACOUSTIC STUDY OF WIGNER CRYSTAL NEAR INTEGER AND FRACTIONAL FILLING FACTORS IN HIGH-MOBILITY N-GAAS/ALGAAS HETEROSTRUCTURE I. L. Drichko 1 , I. Yu. Smirnov 1 , A. V. Suslov 2 , L. N. Pfeiffer 3 , K. W. West 3 , and Y. M. Galperin 4,1 1 A. F. Ioffe Physico-Technical Institute of Russian Academy of Sciences, 194021 St.Petersburg, Russia 2 National High Magnetic Field Laboratory, Tallahassee, FL 32310, USA 3 Department of Electrical Engineering, Princeton University, Princeton, NJ 08544, USA 4 Department of Physics, University of Oslo, 0316 Oslo, Norway We measured magnetic field dependences of the attenuation and velocity of surface acoustic wave (SAW) in a high-mobility n-GaAs/AlGaAs structure with a wide GaAs quantum well of 65 nm. The density of 2D electron gas was n=5·10 10 cm -2 and the mobility was 8·10 6 cm 2 /V·s. Measurements were performed versus perpendicular magnetic field of up to 18 T, in the frequency, f, range from 28.5 MHz to 306 MHz, and at temperatures between 40 mK and 380 mK. It allowed us finding the complex ac conductivity, σ = σ 1 - i·σ 2 , showing integer and fractional quantum Hall effect (see Fig. 1). At integer filling factors ν=1 and 2 the ac conductivity behaves as that of a 2D system of localized electrons. Namely, both real and imaginary parts of the complex ac conductance at low temperature agree with the predictions for the two-site model for a 2D hopping system under condition 2πf >> τ 0 -1 , where τ 0 is the minimal relaxation time describing the two-site model. At the same time sharp cusps observed on the conductivity in the vicinity of ν=1 and 2 (and in vicinity of ν=1/5) indicate that the state of the 2D systems drastically changes at small deviation of ν from these values. Analysis of temperature (see Fig. 2) and frequency dependences of σ 1 and σ 2 shows formation of pinned Wigner crystals (WC) in the vicinity of ν=1, 2 and 1/5 at low temperature. The WC is melted when the temperature (or SAW intensity) rises. The crossover from the electronic state at an integer ν to a pinned mode of the WC was studied in detail. The characteristic temperature of this crossover depends on the deviation of the filing factor from the integer: Δν=|j-ν|, where j=1 or 2 (see Fig. 2). Fig. 1. Magnetic field dependence of σ 1 (see text) at 40 mK and 28.5 MHz. Insets: σ 1 in the vicinity of ν=1 and ν=1/5 at various temeperatures: 1 - 45 mK, 2 - 80 mK, 3 - 100 mK, 4 - 110 mK, 5 - 150 mK, 6 - 350 mK. Fig. 2. Temperature dependences of σ 1 , the real part of the conductivity, at 28.5 MHz for different values of 1.0≤ν≤1.1 shown near the curves. The lines are guides to the eye. Inset: Similar dependences for 0.9≤ν≤1.0. I.L.D. is grateful for support from Russian Foundation for Basic Research grant 14-02-00232. The authors are thankful to E. Palm, T. Murphy, J.-H. Park, and G. Jones for technical assistance. NHMFL is supported by NSF Cooperative Agreement No. DMR-1157490 and the State of Florida. The work at Princeton was partially funded by the Gordon and Betty Moore Foundation Grant GBMF2719, and by the NSF MRSEC-DMR-0819860 at the Princeton Center for Complex Materials.

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PPHMF-8

ACOUSTIC STUDY OF WIGNER CRYSTAL NEAR INTEGER AND FRACTIONAL FILLING FACTORS IN HIGH-MOBILITY N-GAAS/ALGAAS HETEROSTRUCTURE

I. L. Drichko1, I. Yu. Smirnov1, A. V. Suslov2, L. N. Pfeiffer3, K. W. West3, and Y. M. Galperin4,1

1A. F. Ioffe Physico-Technical Institute of Russian Academy of Sciences, 194021 St.Petersburg, Russia

2National High Magnetic Field Laboratory, Tallahassee, FL 32310, USA 3Department of Electrical Engineering, Princeton University, Princeton, NJ 08544, USA

4Department of Physics, University of Oslo, 0316 Oslo, Norway

We measured magnetic field dependences of the attenuation and velocity of surface acoustic wave (SAW) in a high-mobility n-GaAs/AlGaAs structure with a wide GaAs quantum well of 65 nm. The density of 2D electron gas was n=5·1010 cm-2 and the mobility was 8·106 cm2/V·s. Measurements were performed versus perpendicular magnetic field of up to 18 T, in the frequency, f, range from 28.5 MHz to 306 MHz, and at temperatures between 40 mK and 380 mK. It allowed us finding the complex ac conductivity, σ = σ1 - i·σ2, showing integer and fractional quantum Hall effect (see Fig. 1). At integer filling factors ν=1 and 2 the ac conductivity behaves as that of a 2D system of localized electrons. Namely, both real and imaginary parts of the complex ac conductance at low temperature agree with the predictions for the two-site model for a 2D hopping system under condition 2πf >> τ0

-1, where τ0 is the minimal relaxation time describing the two-site model. At the same time sharp cusps observed on the conductivity in the vicinity of ν=1 and 2 (and in vicinity of ν=1/5) indicate that the state of the 2D systems drastically changes at small deviation of ν from these values. Analysis of temperature (see Fig. 2) and frequency dependences of σ1 and σ2 shows formation of pinned Wigner crystals (WC) in the vicinity of ν=1, 2 and 1/5 at low temperature. The WC is melted when the temperature (or SAW intensity) rises. The crossover from the electronic state at an integer ν to a pinned mode of the WC was studied in detail. The characteristic temperature of this crossover depends on the deviation of the filing factor from the integer: Δν=|j-ν|, where j=1 or 2 (see Fig. 2).

Fig. 1. Magnetic field dependence of σ1 (see text) at 40 mK and 28.5 MHz. Insets: σ1 in the vicinity of ν=1 and ν=1/5 at various temeperatures: 1 - 45 mK, 2 - 80 mK, 3 - 100 mK, 4 - 110 mK, 5 - 150 mK, 6 - 350 mK.

Fig. 2. Temperature dependences of σ1, the real part of the conductivity, at 28.5 MHz for different values of 1.0≤ν≤1.1 shown near the curves. The lines are guides to the eye. Inset: Similar dependences for 0.9≤ν≤1.0.

I.L.D. is grateful for support from Russian Foundation for Basic Research grant 14-02-00232. The authors are thankful to E. Palm, T. Murphy, J.-H. Park, and G. Jones for technical assistance. NHMFL is supported by NSF Cooperative Agreement No. DMR-1157490 and the State of Florida. The work at Princeton was partially funded by the Gordon and Betty Moore Foundation Grant GBMF2719, and by the NSF MRSEC-DMR-0819860 at the Princeton Center for Complex Materials.