Optical spectroscopy in the fractional quantum hall effect and wigner solid regimes

Physica B 169 North-Holland

OPTICAL

(1991)

557-558

SPECTROSCOPY

A. S. PLAUT”, II. BUHMANNb, V. B. TIMOFEEV” (a) (b) (c) (d)

IN THE FRACTIONAL

W. JOSS*,

QUANTUM

Ii. v. KLITZING”,

HALL

EFFECT

AND WIGNER

I. V. KUKUSIIKINa~C,

SOLID

G. MARTINEZd,

REGIMES

K. PLOOG”

and

Max-Planck-Institut. fiir Festkijrperforschung, D-7000 Stuttga.rt 80. Federal Republic of Germany Max-Planck-Institut fiir Festk6rperforschung, HML, BP 166X, F-35042 Grenoble, CEDEX, France Institute for Solid State Physics? Academy of Sciences of the IJSSR, 142432, Chernogolovka, USSR SNCI/CNRS, BP lGGX> 38042 Grenoble, CEDE?;, France

Discontinuities have been observed in the spectral position of the magnet,o-luminescence from GaAs-Al,Gal_,As heterojunctions at fractional filling factors (u) down to l/9. Below a critical temperature and ~~0.28 an additional luminescence line appears and the integrated intensity decreases drastically indicating formation of a Wigner solid.

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Figure 1: The dependence of the luminescence position on magnetic field for sample 1.

line peak

The ground state of a two-dimensional electron system at fractional filling factors (u) is an incompressible Fermi liquid [l]. At very small v a liquid to solid transition is predicted theorectically [l]. This paper reports on magneto-optical experiments in just this extreme quantum limit, from which we are able to determine the fractional quantum Hall effect (FQW gapsdown to v=1/9 and also to detect various Y and temperature dependent phenomena which we ascribe to a liquid-solid phase transition. In fig.1 we have plotted the spectral position of the 2D luminescence as a function of magnetic field. At low field we observe numerous transitions associated with the electrons from various 2D Landau levels recombining with photoexcited holes bound to acceptors in a &layer located in the GaAs at 25nm from the hetero-interface. (The experimental details have been described previously [2]). At high magnetic fields, however, the energy dependence is no longer linear: showing, in particular, discontinuities at fractional filling factors. In fig.2 AE, the energy shift from the low-field slope (depicted in fig.1 by a dashed line), is plotted for clarity. The energy jump at ~=l is mainly due to g-factor enhancement [3]. The broad feature around v=l/2 is much less sensitive to temperature than those anomalies at odd fractions. In another sample with a higher mobility and smaller electron concentration (n,), discontinuities down to v=l/S are observed but not at ~=l/ll. On raising

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Figure 2: (a) AE(H) measured for samples 1 and 2 at different n,: (i) 0.59x10”cm-2, (ii) 0.7s10’~cm-2, (iii) 0.54x10”cm-2. And (b) AE(H) measured for sample 2 at different temperatures. The dashed line depicts the actual position of the 1.2K data. the temperature to 1.2K (fig.2b) the features at the lowest fractions disappear and by 6K the line returns to the slope expected from the low-field data.

A.S. Plaut et al. / Fractional quantum Hall effect and Wigner solid regimes

558

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for

From the size of the steps in fig.2a we have determined the FQHE gap values (A[,,, = qAc) and the values obtained (fig.3) are in good agreement with transport data on similar quality samples [4]. Below a critical v (vc) an extraline appears. 1.4meV to lower energy than the original line, which grows in intensity with ma.gnetic field relative to the latter (fig.4): except at magnetic fields around the fractional I/ where its relative intensity sharply decrea.ses (fig.5b). At the same magnetic field (11~) as the first, appearance of the new line, t,hc total integrated intensity starts to decrease sharply (fig.,%). IIc has been found to depend linearly on n, and we thereby have evaluated vc to be 0.28~0.02 [5]. The new line also disappears suddenly when the temperature is raised; at 267 (i/=0.09) it has completely vanished above 1 :lIi.

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MAGNETIC FIELD ( T) magnetic field depcndcnce of (a) the iritr:. grated luminescence intensity and (b) the irrtensity ratio at O.GI< for two different IL,. I 2 /I 1, measured Figure 5: The

We would like to propose the existence of tire new line as indicative of the onset of Wigner crystallisation [I]. The decrease in integrated intensity we believe to he due to a. decrease of the electron-hole wavefunction overlap in the plane parallel to the interface as a result of localisation of the electron. This localisation is not just solely due to the magnetic length reduction, since on raising the temperature the in tegrated intensity recovers. It is unlikely that localisation on random potential fluctuations is the cause for this drastic reduction in integrated intensity since I/C appears to bc independent of the value of the Landau level width at I,= 1 (vvhich gives a measure of the disorder in the sample). Finally the relative drop in the intensity of the new line at fractional 11, results vve believe from the cluant,um fluid bccoming the energetically favoured ground state again at csactly these V.

[II It. 121I.

B. Laughlin;

I’hys.

Rev. Lett.

50 (1983)

1395

V. I
[31A.

S. Plant, Ploog, Phys.

I. V. Kukushkin, Rev. B .12 (1990)

li. v. Iilitzing 57-14

and

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and

Ii.

Nl G.

ENERGY Figure 1: Luminescence netic fields

spectra

S. Boebinger, 11. L. Stormer, 1). c’. Tsui, A. hl. Chang, J. C. hl. IIwang, A. Y. Cho, C. WT. Tu and G. M’eimann, Phys. Rev. B 36 (1987) 7919; R. I,. \Villett; H. L. Stormer, D. C. Tsui, A. C. Gossartl and J. 11. English, Phys. Rev. B 37 (1988) 8476; J. R. Mall&t, It. G. Clark. R. J. Nicholas. R. \Villett,, J. .I. Ilarris and (‘. T. Foxon; Plrys. Rev. B 38 (1988) 2200; R. G. Clark, J. R. Mall&t, S. R. Hayues, J. J. 1Iarris and C. T. Foson. Pbys. Rev. T&t. 60 (19%) 17.47

(eV) measured

at various

mag-

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C. 1.. Andrei, G. Deville, 1). C. Glatti, 1:. I. B. \Yillianrs. E. Paris and B. Etienne. Phys. Rev. Lett. 60 (I!%%) 2765