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Register a new userWigner crystal in a two-dimensional electron system in the vicinity of filling factor 1/5: Acoustic studies
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By simultaneous measurements of the attenuation and velocity of surface acoustic waves propagating in proximity to a high-quality GaAs quantum well we study the complex AC conductance of the two-dimensional electron system. Focusing on the vicinity of the filling factor $ u=1/5$ we confirm that the insulating states formed closely to this value of $ u$ are pinned Wigner crystals.
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Using acoustic method we study dependences of transverse AC conductance, $sigma (omega)$, on magnetic field, temperature and the amplitude of AC electric field in a wide (75 nm) quantum well (QW) structure focusing on the vicinity of the filling factor $ u =1/2$. Measurements are performed in the frequency domain 30-307 MHz and in the temperature domain 20-500 mK. Usually, in wide QW structures closely to $ u =1/2$ the fractional quantum Hall effect (FQHE) regime is realized at some parameters of the sample. However, in our structure, at $ u =1/2$ it is a compressible state corresponding to gas of composite fermions which is observed. This is confirmed by apparent frequency independence and weakly decreasing temperature dependence of $mathrm{Re}, sigma(omega)$. Comparing the dependences of this quantity on temperature and power of the acoustic wave we conclude that the observed nonlinear behavior of the conductance is compatible with heating of the composite fermions by the acoustic wave. For comparison, we also study the vicinity of $ u = 3/2$ where the FQHE regime is clearly observed.
Using acoustic methods the complex high-frequency conductance of high-mobility $n$-GaAs/AlGaAs heterostructures was determined in magnetic fields 12$div$18~T. Based on the observed frequency and temperature dependences we conclude that in the investigated magnetic field range and at sufficiently low temperatures, $T lesssim 200$~mK, the electron system forms a Wigner crystal deformed due to pinning by disorder. At some temperature, which depends on the electron filling factor, the temperature dependences of both components of the complex conductance get substantially changed. We have ascribed this rapid change of the conduction mechanism to melting of the Wigner crystal and study the dependence of the so-defined melting temperature on the electron filling factor.
One of the most fascinating ground states of an interacting electron system is the so-called Wigner crystal where the electrons, in order to minimize their repulsive Coulomb energy, form an ordered array. Here we report measurements of the critical filling factor ($ u_{C}$) below which a magnetic-field-induced, quantum Wigner crystal forms in a dilute, two-dimensional electron layer when a second, high-density electron layer is present in close proximity. The data reveal that the Wigner crystal forms at a significantly smaller $ u_{C}$ compared to the $ u_{C}$ ($simeq 0.20$) in single-layer two-dimensional electron systems. The measured $ u_{C}$ exhibits a strong dependence on the interlayer distance, reflecting the interaction and screening from the adjacent, high-density layer.
The Wigner-crystal phase of two-dimensional electrons interacting via the Coulomb repulsion and subject to a strong Rashba spin-orbit coupling is investigated. For low enough electronic densities the spin-orbit band splitting can be larger than the zero-point energy of the lattice vibrations. Then the degeneracy of the lower subband results in a spontaneous symmetry breaking of the vibrational ground state. The $60^{circ}-$rotational symmetry of the triangular (spin-orbit coupling free) structure is lost, and the unit cell of the new lattice contains two electrons. Breaking the rotational symmetry also leads to a (slight) squeezing of the underlying triangular lattice.
We have measured magnetic field dependences of the attenuation and velocity of surface acoustic waves in a high-mobility $n$-GaAs/AlGaAs structure with a wide quantum well. The results allowed us to find the complex conductance, $sigma(omega)$, of the heterostructure for different frequencies, temperatures and magnetic fields near filling factors $ u=1, 2$. Observed behavior of $sigma(omega)$ versus magnetic field outside close vicinities of integer fillings reveals an oscillation pattern indicative of the rich fractional quantum Hall effect. Our result is that in very close vicinities of integer filling factors the AC response of a high-mobility two-dimensional structures behaves as that of a two-dimensional system of localized electrons. Namely, both real and imaginary parts of the complex AC conductance at low temperatures agree with the predictions for the two-site model for a two-dimensional hopping system. Another result is the specific temperature dependences of $sigma(omega)$, which are extremely sensitive to the filling factor value. These dependences indicate a sharp crossover between the localized modes and a pinned Wigner crystal.
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