Breakdown Of Quantum Hall Effect Research Articles

Electrically induced breakdown of the quantum Hall effect at different Hall bar widths: Visualizing the edge- and bulk-dominated regimes within a quantum Hall plateau

We present systematic investigations of the electrically induced breakdown of the integer quantum Hall effect (QHE) in (Al,Ga)As-based Hall bars of different widths ranging from 7 to 70 $\ensuremath{\mu}\mathrm{m}$. It is striking that, for the narrow Hall bars, the threshold values for the applied voltage that induces the breakdown of the longitudinal zero-resistance state differ appreciably between the upper and lower sides of a quantum Hall (QH) plateau. When moving from the low magnetic field side of the QH plateau to higher magnetic fields, the threshold rises in a strongly superlinear manner until---at the expected integer value for the Landau level (LL) filling factor in the bulk of the two-dimensional electron system (2DES)---the threshold value abruptly drops to low values for the rest of the plateau. With increasing widths of the Hall bars, the zero-resistance state extends slightly further to higher magnetic field values. The threshold values on the low-magnetic field side are almost independent of the Hall bar width, whereas the threshold values on the high magnetic field side scale linearly with the Hall bar width. These observations correspond perfectly with the microscope picture of the QHE where the biased current flows in a dissipationless manner in electrically incompressible regions of the 2DES of locally the same LL filling factor, driven by the respective drop of the Hall voltage over the width of these incompressible regions. Owing to the self-consistent evolution of the electrically incompressible/compressible landscape within the 2DES as a function of magnetic field, a transition from an edge- to a bulk-dominated QH regime is described within a QH plateau. This microscopic picture was derived from sophisticated, long-lasting scanning probe experiments measuring Hall potential profiles on typically 15-$\ensuremath{\mu}$m-wide Hall bars. Conversely, performing systematic electrically induced breakdown measurements like those presented here would allow us to identify the presence of edge- and bulk-dominated regimes of the QHE in a wider variety of samples.

High-frequency breakdown of the integer quantum Hall effect in GaAs/AlGaAs heterojunctions

The integer quantum Hall effect is a well-studied phenomenon at frequencies below about 100 Hz. The plateaus in high-frequency Hall conductivity were experimentally proven to retain up to 33 GHz, but the behavior at higher frequencies has remained largely unexplored. Using continuous wave THz spectroscopy, the complex Hall conductivity of GaAs/AlGaAs heterojunctions was studied in the range of 69-1100 GHz. Above 100 GHz, the quantum plateaus are strongly smeared out and replaced by weak quantum oscillations in the real part of the conductivity. The amplitude of the oscillations decreases with increasing frequency. Near 1 THz, the Hall conductivity does not reveal any features related to the filling of Landau levels. Similar oscillations are observed in the imaginary part as well, this effect has no analogy at zero frequency. This experimental picture is in disagreement with existing theoretical considerations of the high-frequency quantum Hall effect.

Nonlinear transport of graphene in the quantum Hall regime

We have studied the breakdown of the integer quantum Hall (QH) effect with fully broken symmetry, in an ultra-high mobility graphene device sandwiched between two single crystal hexagonal boron nitride substrates. The evolution and stabilities of the QH states are studied quantitatively through the nonlinear transport with dc Hall voltage bias. The mechanism of the QH breakdown in graphene and the movement of the Fermi energy with the electrical Hall field are discussed. This is the first study in which the stabilities of fully symmetry broken QH states are probed all together. Our results raise the possibility that the ν = ±6 states might be a better target for the quantum resistance standard.

Electron transport in suspended semiconductor structures with two-dimensional electron gas

We study electron transport in suspended semiconductor microstructures fabricated from AlAs/GaAs membranes containing a high mobility two-dimensional electron gas. In quantizing magnetic fields, a reflection of edge current channels from the border of suspended area is observed resulting in the absence of vanishing magnetoresistance in the quantum Hall effect (QHE) regime. Relocation of this border out of the Hall bar revives the QHE. We have also found that the critical current of the breakdown of QHE in suspended samples is three times lower than in non-suspended samples due to the peculiarity of heat transport in the membranes.

Dynamic nuclear polarization induced by the breakdown of fractional quantum Hall effect

Dynamic polarization of nuclear spins has been studied in the breakdown regime of fractional quantum Hall effect using a Corbino-disk device. We find that nuclear spins are polarized in the Corbino disk in the breakdown regime of fractional quantum Hall effect. Since edge channel is completely absent in the Corbino disk, the demonstration of dynamic nuclear polarization in the Corbino disk shows that nuclear spins are polarized and detected in the bulk channel of the quantum Hall conductor.

Strain-induced enhancement of electric quadrupole splitting in resistively detected nuclear magnetic resonance spectrum in quantum Hall systems

We show electrical coherent manipulation of quadrupole-split nuclear spin states in a GaAs/AlGaAs heterostructure on the basis of the breakdown of quantum Hall effect. The electric quadrupole splitting in nuclear spin energy levels is intentionally enhanced by applying an external stress to the heterostructure. Nuclear magnetic resonance spectra with clearly separated triple peaks are obtained, and Rabi oscillations are observed between the nuclear spin energy levels. The decay of the spin-echo signal is compared between the cases before and after the enhancement of quadrupole splitting.

Dynamic nuclear polarization induced by breakdown of fractional quantum Hall effect

We study dynamic nuclear polarization (DNP) induced by breakdown of the fractional quantum Hall (FQH) effect. We find that voltage-current characteristics depend on current sweep rates at the quantum Hall states of Landau-level filling factors $\ensuremath{\nu}=1$, 2/3, and 1/3. The sweep-rate dependence is attributed to DNP occurring in the breakdown regime of FQH states. Results of a pump and probe experiment show that the polarity of the DNP induced in the breakdown regimes of the FQH states is opposite to that of the DNP induced in the breakdown regimes of odd-integer quantum Hall states.

Electrical coherent control of nuclear spins in a breakdown regime of quantum Hall effect

Using a conventional Hall-bar geometry with a micrometal strip on top of the surface, the authors demonstrate an electrical coherent control of nuclear spins in an AlGaAs∕GaAs semiconductor heterostructure. A breakdown of integer quantum Hall (QH) effect is utilized to dynamically polarize nuclear spins. By applying a pulse rf magnetic field with the metal strip, the quantum state of the nuclear spins shows Rabi oscillations, which is detected by measuring longitudinal voltage of the QH conductor.

HIGH-CURRENT BREAKDOWN OF THE QUANTUM HALL EFFECT

We have recently developed a model for the high-current breakdown of the integer quantum Hall effect, as measured in contactless experiments using a highly-sensitive torsion balance magnetometer. The model predicted that, for low-mobility samples, the critical current for breakdown should decrease linearly with temperature. This prediction was verified experimentally with the addition of a low-temperature (≲ 300 mK) saturation of the critical current. This saturation is consistent with quasi-elastic inter-Landau-level scattering when the maximum electric field in the sample reaches a large enough value. In this paper we extend this model to nearly integer filling factors to show how the model may account for the shape of the magnetisation signal.

Temperature dependence of the breakdown of the quantum Hall effect studied by induced currents

We have developed a model of the high-current breakdown of the integer quantum Hall effect, as measured in contactless experiments using a highly-sensitive torsion balance magnetometer. The model predicts that, for empirically ``low-mobility'' samples $(\ensuremath{\mu}<75\phantom{\rule{0.3em}{0ex}}{\mathrm{m}}^{2}\phantom{\rule{0.3em}{0ex}}{\mathrm{V}}^{\ensuremath{-}1}\phantom{\rule{0.3em}{0ex}}{\mathrm{s}}^{\ensuremath{-}1})$, the critical current for breakdown should decrease with, and have a linear dependence on, temperature. This prediction is verified experimentally with the addition of a low-temperature saturation of the critical current at a temperature that depends on both sample number density and filling factor. It is shown that this saturation is consistent with quasielastic inter-Landau-level scattering when the maximum electric field in the sample reaches a large enough value. In addition we show how this model can be extended to give qualitative agreement with experiments on high-mobility samples.

Temperature-dependent high-current breakdown of the quantum Hall effect

We have developed a model of the high-current breakdown of the integer quantum Hall effect, as measured in contactless experiments using a highly-sensitive torsion balance magnetometer. The model predicts that, for low-mobility samples, the critical current for breakdown should decrease linearly with temperature. This prediction is verified experimentally with the addition of a low-temperature (<∼300 mK) saturation of the critical current. It is shown that this saturation is consistent with quasi-elastic inter-Landau-level scattering when the maximum electric field in the sample reaches a large enough value.

Model for breakdown of laminar flow of a quantum Hall fluid around a charged impurity: comparison with experiment

In samples used to maintain the US resistance standard the breakdown of the dissipationless integer quantum Hall effect occurs as a series of dissipative voltage steps. A mechanism for this type of breakdown is proposed, based on the generation of magneto-excitons when the quantum Hall fluid flows past an ionised impurity above a critical velocity. The calculated generation rate gives a voltage step height in good agreement with measurements. We also compare this model to a hydrodynamic description of breakdown.

Model for the Voltage Steps in the Breakdown of the Integer Quantum Hall Effect

In samples used to maintain the U.S. resistance standard the breakdown of the dissipationless integer quantum Hall effect occurs as a series of dissipative voltage steps. A mechanism for this type of breakdown is proposed, based on the generation of magnetoexcitons when the quantum Hall fluid flows past an ionized impurity above a critical velocity. The calculated generation rate gives a voltage step height in good agreement with measurements on both electron and hole gases. We also compare this model to a hydrodynamic description of breakdown.

Diagonal Conductivity due to Tunneling in Quantum Hall Systems in the High Electron-Temperature Regime

The diagonal conductivity of two-dimensional electron systems in strong magnetic fields is derived in an analytical form by considering tunneling processes through a saddle point of the slowly-fluctuating potential in the high electron-temperature regime where the breakdown of the integer quantum Hall effect occurs. The calculation is made for a two-dimensional periodic potential modulation with a fixed amplitude equal to the Landau level separation. The electron-temperature dependence of the conductivity is mainly determined by the presence of an activation energy. It is found that an estimated value of the conductivity in the present model at even-integer filling factors is smaller by an order of magnitude than the experimental value in the integer quantum Hall effect breakdown regime.

Two types of breakdown of quantum Hall effect depending on the electron density fluctuation

We investigate different types of the breakdown of the quantum Hall effect (QHE), which are characterized by the sample width dependence of the critical current for the breakdown. The distinction of two different types of breakdown is thought to be the properties of the two-dimensional electron gas (2DEG) wafers, but it is not related directly to the 2DEG mobility and electron density determined by Hall measurement at low magnetic field. We observe the switching between linear and sublinear dependence of the QHE breakdown by varying temperature, gate voltage, and by illumination condition. The type of QHE breakdown is determined by the extent of potential fluctuations in the 2DEG, which are characterized by the random potential from ionized donors and by screening effects, comparing with those resulting from the thermal broadening of the electron distribution. The result of magnetocapacitance between 2DEG and Schottky gate also suggests that the 2DEG homogeneity play an important role in the breakdown of the QHE.

Quantum Hall effect breakdown: can the bootstrap heating and inter-Landau-level scattering models be reconciled?

We study the breakdown of the integer quantum Hall effect in a series of n-type GaAs/AlGaAs heterostructures in which the current flows through a short and narrow constriction. The critical mean current density is strongly dependent on the constriction width and is ∼10 A m −1 for the narrowest (1 μm) constriction, in qualitative agreement with earlier work by Bliek et al. We compare our data with other breakdown measurements and with the bootstrap-electron-heating and inter-Landau-level-scattering models.

Current-polarity characteristics in breakdown of the integer quantum Hall effect in GaAs/AlGaAs heterostructures

Current-polarity dependence has been examined on the quantum Hall effect breakdown in two types of Hall bars with voltage probes asymmetrically located to the source and the drain-electrode. Polarity-dependent asymmetry observed in the critical breakdown currents is not larger than 1.3.

Quantum Hall effect breakdown steps: evidence for an instability induced by inter-Landau level scattering

The breakdown of the integer quantum Hall effect at high currents sometimes occurs as a series of regular steps in the dissipative voltage drop measured along the Hall bar. The steps were first seen clearly in two Hall bars used to maintain the US Resistance Standard, but have also been reported in other devices. This paper discusses the origin of the steps in terms of an instability in the dissipationless flow induced by inter-Landau level tunnelling processes due to charged impurities in local microscopic regions of the Hall bar. It is proposed that electron–hole pairs are generated in the quantum Hall fluid in these regions at high flow rates and that the electronic motion can be envisaged as a quantum analogue of the von Karman vortex street which forms when a classical fluid flows past an obstacle.

Quantum hall effect in an antidot lattice: Macroscopic limit

The quantum Hall effect in a 2D system with antidots is studied. The antidots are assumed to be large compared with the quantum and relaxation lengths. In this approximation the electric field in the system can be described by the continuity equation. It is found that the electric field in a system without conducting boundaries can be expressed in terms of the same system without a magnetic field. Specific problems of the electric field and current in structures containing one or two antidots and in a circular disk with point contacts are solved. The effective Hall and longitudinal conductivities in a sample containing a large number of randomly distributed antidots are found. In the limit of zero local longitudinal conductivity, the effective longitudinal conductivity also vanishes, and the Hall conductivity is equal to the local conductivity. The corrections to the conductivity tensor which are due to the finiteness of the local conductivity are obtained. Breakdown of the quantum Hall effect in a lattice of antidots is studied on the basis of the assumption that a high current density in narrow locations of the system results in overheating of the electrons. Local and nonlocal models of over-heating are studied. The high-frequency effective conductivity of a system with antidots and the shift of the cyclotron resonance frequency are found.

A phase diagram for the breakdown of the odd integer quantum Hall effect

The breakdown of the dissipationless conductance in the integer quantum Hall effect regime has been investigated for odd filling factors. The temperature dependence of the critical current and of the critical magnetic field at breakdown is presented and the scaling between filling factors discussed.