Developments in the physics of 2D electron systems during the last decade have revealed a new class of nonequilibrium phenomena in the presence of a moderately strong magnetic field. The hallmark of these phenomena is magnetoresistance oscillations generated by the external forces that drive the electron system out of equilibrium. The rich set of dramatic phenomena of this kind, discovered in high mobility semiconductor nanostructures, includes, in particular, microwave radiation-induced resistance oscillations and zero-resistance states, as well as Hall field-induced resistance oscillations and associated zero-differential resistance states. We review the experimental manifestations of these phenomena and the unified theoretical framework for describing them in terms of a quantum kinetic equation. The survey contains also a thorough discussion of the magnetotransport properties of 2D electrons in the linear response regime, as well as an outlook on future directions, including related nonequilibrium phenomena in other 2D electron systems.

Nonequilibrium phenomena in high Landau levels

The effect of a microwave field in the frequency range from 54 to 140 GHz on the magnetotransport in a GaAs quantum well with AlAs/GaAs superlattice barriers and with an electron mobility no higher than 106 cm2/V s is investigated. In the given two-dimensional system under the effect of microwave radiation, giant resistance oscillations are observed with their positions in the magnetic field being determined by the ratio of the radiation frequency to the cyclotron frequency. Earlier, such oscillations had only been observed in GaAs/AlGaAs heterostructures with much higher mobilities. When the samples under study are irradiated with a 140-GHz microwave field, the resistance corresponding to the main oscillation minimum, which occurs near the cyclotron resonance, appears to be close to zero. The results of the study suggest that a mobility value lower than 106 cm2/V s does not prevent the formation of zero-resistance states in a magnetic field in a two-dimensional system under the effect of microwave radiation.

Giant magnetoresistance oscillations induced by microwave radiation and a zero-resistance state in a 2D electron system with a moderate mobility

Magnetoresistance of two-dimensional electron systems with several occupied subbands oscillates owing to periodic modulation of the probability of intersubband transitions by the quantizing magnetic field. In addition to previous investigations of these magnetointersubband (MIS) oscillations in two-subband systems, we report on both experimental and theoretical studies of such a phenomenon in three-subband systems realized in triple quantum wells. We show that the presence of more than two subbands leads to a qualitatively different MIS oscillation picture, described as a superposition of several oscillating contributions. Under a continuous microwave irradiation, the magnetoresistance of triple-well systems exhibits an interference of MIS oscillations and microwave-induced resistance oscillations. The theory explaining these phenomena is presented in the general form, valid for an arbitrary number of subbands. A comparison of theory and experiment allows us to extract temperature dependence of quantum lifetime of electrons and to confirm the applicability of the inelastic mechanism of microwave photoresistance for the description of magnetotransport in multilayer systems.

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Magnetoresistance oscillations in multilayer systems: Triple quantum wells

Low-temperature dependences of the transport relaxation time (τtr) and quantum lifetime (τq) on the density of the two-dimensional electron gas (n
 e
 ) in GaAs quantum wells with AlAs/GaAs lateral superlattice barriers have been studied. An exponential increase in the quantum lifetime with increasing electron density has been observed. It has been shown that the sharp increase in the quantum lifetime correlates with the appearance of X electrons in the AlAs/GaAs lateral superlattice barriers. It has been established that the ratio of the transport relaxation time to the quantum lifetime in the studied structures nonmonotonically depends on the density: the ratio τtr/τq first increases linearly with n
 e
 and then decreases. This behavior is not described by the existing theories.

Transport relaxation time and quantum lifetime in selectively doped GaAs/AlAs heterostructures

We report the observation of an anomalous magnetoresistance peak in a tilted magnetic field corresponding to filling factor of 2 in several parabolic wells of different width. This phenomenon is due to the unpolarized-ferromagnetic transitions in quantum Hall ferromagnets. The domain formation induced by the random impurity potential is responsible for this magnetoresistance peak. The shift of the peak position with the tilt angle is attributed to the magnetic-field dependence of the exchange-correlation energy across the transition.

http://macbeth.if.usp.br/~gusev/Hall%20ferromagnet.pdf

Quantum Hall ferromagnet in a parabolic well

The effect of millimeter wave radiation on the electronic transport in a GaAs double quantum well at a temperature of 4.2 K in a magnetic field of up to 2 T has been studied. Resistance (conductance) oscillations have been shown to appear in the two-dimensional electronic system under investigation at high filling factors. The magnetic field positions of the oscillation maxima are determined by the condition ΔSAS/ħ = lωc, where ΔSAS = (E2 − E1) is the size quantization sublevel splitting in the quantum well, ωc is the cyclotron frequency, and l is a positive integer. It has been found that the microwave field substantially modifies the oscillations in the double quantum well, which results in alternating two-frequency oscillations of photoresistance with the inverse magnetic field.

Microwave photoresistance of a double quantum well at high filling factors

The low-temperature $(4.2lTl12.5\text{ }\text{K})$ magnetotransport $(Bl2\text{ }\text{T})$ of two-dimensional electrons occupying two subbands (with energy ${E}_{1}$ and ${E}_{2}$) is investigated in GaAs single quantum well with AlAs/GaAs superlattice barriers. Two series of Shubnikov-de Haas oscillations are found to be accompanied by magnetointersubband (MIS) oscillations, periodic in the inverse magnetic field. The period of the MIS oscillations obeys condition ${\ensuremath{\Delta}}_{12}=({E}_{2}\ensuremath{-}{E}_{1})=k\ensuremath{\cdot}\ensuremath{\hbar}{\ensuremath{\omega}}_{c}$, where ${\ensuremath{\Delta}}_{12}$ is the subband energy separation, ${\ensuremath{\omega}}_{c}$ is the cyclotron frequency, and $k$ is the positive integer. At $T=4.2\text{ }\text{K}$ the oscillations manifest themselves up to $k=100$. Strong temperature suppression of the magnetointersubband oscillations is observed. We show that the suppression is a result of electron-electron scattering. Our results are in good agreement with recent experiments, indicating that the sensitivity to electron-electron interaction is the fundamental property of magnetoresistance oscillations, originating from the second-order Dingle factor.

Effect of electron-electron scattering on magnetointersubband resistance oscillations of two-dimensional electrons in GaAs quantum wells

Low-temperature electron magnetotransport in single GaAs quantum wells with two populated subbands is studied at large filling factors. Magneto-intersubband (MIS) and acoustic-phonon-induced oscillations of dissipative resistance are found to be coexisting but interfering substantially with each other. The experiments show that amplitude of the MIS oscillations enhances significantly by phonons, indicating ``constructive interference'' between the electron-phonon scattering and the intersubband electron transitions. Temperature damping of the quantum oscillations is found to be related to broadening of Landau levels caused by considerable electron-electron scattering.

Interference of magneto-intersubband and phonon-induced resistance oscillations in single GaAs quantum wells with two populated subbands

We have studied negative magnetoresistance of a nonplanar two-dimensional electron gas. Effectively due to the curved AlGaAs/GaAs interface, electrons see a uniform in-plane magnetic field B as a random magnetic field (RMF). Small additional perpendicular B leads to a negative magnetoresistance predicted by a semiclassical treatment of the RMF problem beyond the relaxation-time approximation, in accordance with our observations.

Quasiclassical negative magnetoresistance of a two-dimensional electron gas in a random magnetic field

Electron transport in single GaAs quantum wells of widths from 22 to 46 nm with two populated quantum-confinement subbands ES and EAS is investigated at a temperature of T = 4.2 K in tilted magnetic fields B 72° and α > 85°, respectively. The origin of this unexpected behavior of magnetointersubband oscillations in tilted magnetic fields is discussed.

A. V. Goran

Papers

Microwave photoresistance of a double quantum well at high filling factors

Effect of electron-electron scattering on magnetointersubband resistance oscillations of two-dimensional electrons in GaAs quantum wells

Interference of magneto-intersubband and phonon-induced resistance oscillations in single GaAs quantum wells with two populated subbands

Quasiclassical negative magnetoresistance of a two-dimensional electron gas in a random magnetic field

Beats of Quantum Oscillations of the Resistance in Two-Subband Electron Systems in Tilted Magnetic Fields