G. Nachtwei

Breakdown of the quantum Hall effect

Abstract The quantum Hall effect (QHE) is one of the most prominent effects in modern solid state physics. Since its discovery, the effect has been attracting interest by a steadily increasing community of researchers. The research activities have been focussed on both application aspects and the basic physics of the effect. The limits of the QHE, in particular its persistence at higher currents, are of crucial importance for the application of the effect as a resistance standard. The observation of the current-induced breakdown of the QHE initiated a variety of experimental and also theoretical work. In this article, the experiments related to the breakdown of the QHE are reviewed. Some current theories are discussed in conjunction with the experiments. Although no comprehensive theory of the breakdown is available yet, an at least qualitatively conclusive picture can be provided on the basis of the present knowledge.

Spatial evolution of the generation and relaxation of excited carriers near the breakdown of the quantum Hall effect

Abstract We have measured the generation and relaxation of excited carriers along their drift direction near the breakdown of the quantum Hall effect (QHE). The dissipative resistivity ρ xx ( x ) at current densities close to the critical value for the QHE breakdown was measured as a function of the distance x from the electron injection at x =0. By injecting “cold” electrons into constrictions at supercritical current levels, the evolution of the breakdown along the drift direction was monitored. After a smooth increase of the resistivity with the drifting distance, an avalanche-like rise towards a saturation value occurs. Drastic changes of the resistivity profiles with the applied current were found in a narrow range around the critical current. The observed behavior is attributed to impurity-assisted tunneling between Landau levels. By injecting hot electrons (excited in a periodic set of constrictions) into a region with subcritical current density, the relaxation process was analyzed. Inelastic relaxation lengths with typical values in the range from 0.3 to 4 μm were found, which agree within 10% with the elastic mean free path determined from the Hall mobility at zero magnetic field. We conclude that the energy relaxation process is triggered by scattering at impurity potentials.

Dynamics of nonequilibrium electrons at the breakdown of the quantum Hall effect

Abstract We have analysed the energy excitation and relaxation of hot electrons close to the breakdown of the quantum Hall effect. Hot electrons were generated by a periodic set of constrictions (parallel microscopic trenches or antidot arrays). For the relaxation experiments, hot electrons are injected into two-dimensional electron systems (2DES) of various mobilities, with Hall fields below the breakdown value. The resistivity of the 2DES is measured as a function of the distance from the injection front. The characteristic decay length of the resistivity was found to strongly increase with current in a rather narrow range of currents until the dissipation persists over the entire sample at the breakdown. The results are compared with calculations on the basis of a nonequilibrium between the excitation and relaxation of hot electrons. Energy relaxation lengths from 0.3 to 3 μm were deduced, which are comparable to the mean free path. Thus, the inelastic scattering, which is responsible for the breakdown of the QHE, is strongly related to elastic Coulomb scattering. Spatially resolved measurements of the electron heating were performed in samples with antidot and wire arrays, and with macroscopic constrictions. An avalanche-like heating of electrons could be observed in the antidot array, but the data have not yet been reconciled with a quantitative picture.

Nonequilibrium Quantum Transport in Antidot Arrays

We have studied the onset of dissipation in the quantum Hall effect (QHE) in different antidot arrays (periodic or aperiodic antidot arrays, and single lines of antidots), patterned on a two-dimensional electron system. In periodic arrays, the breakdown current is systematically reduced with increasing antidot density. In comparable aperiodic arrays, the breakdown current is markedly lower, and the electron temperature starts rising at lower currents than in periodic arrays. Single lines of antidots across the current channel cause only a small reduction of the breakdown current, indicating the relevance of avalanche electron heating. In arrays of very small antidots, a suppression of the electron heating due to additional scattering and a complete absence of hot-electron-induced hysteresis in the current–voltage characteristics were observed.

Time-resolved far-infrared spectroscopy of quantum Hall systems

Abstract We have performed time-resolved measurements of the far-infrared photoconductivity of the two-dimensional electron system in GaAs/AlGaAs heterostructures in the integer quantum Hall regime (near filling factor ν=2) by the application of a p–Ge laser radiation. We have found, that the photoresponse (PR) signal has two components, a bolometric component with a decay time not longer than 1– 2 μs , and a cyclotron resonance-related component of opposite polarity with a decay time of about 4– 5 μs . We have observed a strong dependence of the PR signal on the filling factor, sample current and laser intensity. Surprisingly, no pronounced dependence of the PR decay times on these parameters and on the electron mobility was found. Accordingly, we have found a decreasing influence of the mobility on the critical drift length of the quantum Hall effect breakdown with increasing amplitude when applying short electric pulses.

Spatially resolved measurements of hot-electron generation and relaxation at the breakdown of the quantum Hall effect

Abstract We have measured the dissipative resistivity of quantum Hall conductors as a function of the distance from the electron injection. The injection of electrons into constrictions at supercritical current levels allowed to monitor the evolution of the breakdown along the drift direction. After a smooth increase, an avalanche-like growth of the resistivity occurs. Drastic changes of the resistivity profiles with the applied current near the breakdown value were observed and are attributed to tunneling between Landau levels. By injecting hot electrons from constrictions into a sample region at subcritical currents, the relaxation process was analyzed. The inelastic relaxation lengths agreed with the elastic mean free path within 10%, indicating the importance of scattering at impurity potentials.

Evidence for Coulomb staircase in tunneling through an antidot island in the quantum Hall regime

We studied the I–V characteristics of tunneling devices, defined by two trench fingers and an antidot island patterned on Corbino rings in the quantum Hall plateau regime. Well-developed current steps were observed at filling factors near ν=2, which we interpret as a Coulomb staircase phenomenon due to charging of compressible strips around the antidot. The evolution of the current steps with filling factor is explained in the quasi-elastic inter landau level scattering model.

Cyclotron resonance in a two-dimensional electron system with self-organized antidots

Experimental data are reported on studying cyclotron resonance in a two-dimensional electron system with an artificial random scattering potential generated by an array of self-organized AlInAs quantum islands formed in the plane of an AlGaAs/GaAs heterojunction. A sharp narrowing of the cyclotron resonance line is observed as the magnetic field increases, which is explained by the specific features of carrier scattering in this potential. The results obtained point to the formation of a strongly correlated electron state in strong magnetic fields at carrier concentrations smaller than the concentration of antidots.

Tunnelling via an artificial impurity in a narrow quantum Hall conductor controlled by mesoscopic gates

In the quantum Hall regime, we observed current steps in the I-V characteristics of Corbino-like devices with a narrow constriction, containing an artificial impurity. The constriction is defined by metallic gates. We investigated the features of the current steps as a function of the Landau level filling factor and the gate voltages at the constriction. A dominant role of the electrostatic boundary confinement near the side of electron injection (emitter of the electrons) was found. The observed effects can be explained conclusively by including the quasi-elastic inter-Landau-level tunnelling and the limitation of tunnelling current due to charging of the nonequilibrium electron states around the artificial impurity.

QHE breakdown induced by a single antidot: Coulomb staircase in the breakdown current

We have studied the breakdown of the quantum Hall effect in a constriction defined by two trench fingers and an antidot, patterned on a Corbino ring. At filling factors near ν=2, the I–V characteristics show well developed current steps, which we interpret as a Coulomb staircase phenomenon due to charging of compressible strips around the antidot. The evolution of the current steps with filling factor is explained in terms of quasi-elastic inter Landau level scattering.