Quantum Hall Devices Research Articles

Spatial distribution of nonequilibrium electrons in quantum Hall devices: Imaging via cyclotron emission

Images of the spatial distribution of nonequilibrium electrons are studied in a wide quantum Hall effect (QHE) Hall bar $(\ensuremath{\nu}=2)$ by detecting the local profile of the cyclotron radiation with an improved spatial resolution of $50\ensuremath{\mu}\mathrm{m}$ for the radiation wavelength of $\ensuremath{\lambda}=120\ensuremath{\mu}\mathrm{m}.$ The experiments, along with conventional studies of voltage distribution via voltage probes, reveal the generation of nonequilibrium carriers at the diagonally opposite corners of Hall bars (hot spots) at low current levels (below $80\ensuremath{\mu}\mathrm{A}),$ as well as the occurrence of additional generation of nonequilibrium carriers at the corner opposite to the hot spot on the side of the source contact at higher currents (above $80\ensuremath{\mu}\mathrm{A}).$ The experimental findings are consistently interpreted in terms of earlier models of the electron dynamics around current contacts, providing support to the model of bootstrap-type electron heating for the breakdown of the QHE.

Nonequilibrium Green’s function method for a quantum Hall device in a magnetic field

We have developed a practical approach for the inclusion of magnetic fields in the nonequilibrium Green's function method and we have formulated a general scheme for transport calculations in a multiterminal device with magnetic field. Formulas for the self-energy terms in the presence of magnetic fields have been derived and disorder effects in the potential have been introduced through a model accounting for scattering by impurities. To demonstrate the validity of the model, we have applied it to the quantum Hall effect (QHE), for which a wealth of experimental results and information is readily available. Calculations for a simple structure at zero temperature were first carried out to verify the properties of the solutions over a wide range of conditions. The calculated Green's function results provide the carrier density distribution in the structure, and in order to analyze the QHE results, the resistances ${R}_{\mathrm{xx}}$ and ${R}_{\mathrm{xy}}$ are obtained using B\uttiker's approach. Our results for the integer QHE show a pattern that clearly resembles the edge state picture of transport. To further validate the theoretical model, comparisons have been conducted with experimental results for a realistic quantum Hall device at finite temperature, obtaining good agreement.

Anisotropic Corbino magnetothermopower in a quantum Hall system

A Corbino-geometry contact configuration combined with a scanning laserspot as a heating source, is used for a thermovoltage mapping in a GaAs-AlGaAs quantum Hall device. For an isotropic system, the Corbino thermopower yields the diagonal component ${\ensuremath{\epsilon}}_{\mathrm{xx}}$ of the thermoelectric tensor, which should be zero under the prevailing condition of phonon drag. The experiments reveal that ${\ensuremath{\epsilon}}_{\mathrm{xx}}$ is large and anisotropic with respect to the crystallographic directions. The observations yield conclusive evidence that inhomogeneities are the origin for the existence of ${\ensuremath{\epsilon}}_{\mathrm{xx}}.$

Function principle of a relaxation oscillator based on a bistable quantum Hall device

We present a simple relaxation oscillator based on a quantum Hall device with Corbino geometry near the breakdown of the quantum Hall effect. In the hysteresis region of the breakdown, the quantum Hall device exhibits bistable behavior. If a resistance is connected in series and a capacitor in parallel to the quantum Hall device, the bistable switching leads to subsequent charging and discharging of the capacitor, detectable as relaxation oscillations. We explain the observed oscillations by solving Kirchhoff’s equations and obtain a good quantitative description of the experiment. From this, we deduce some dynamical parameters of the Corbino device and discuss the performance limits of the oscillator.

Coherent control of nuclear-spin system in a quantum-Hall device

Coherent control of local nuclear spins in a solid-state device is demonstrated. By unequally populating spin-resolved quantum-Hall edge channels, nuclear spins in a limited region along the edge channels are strongly polarized via the hyperfine interaction. Pulsed rf magnetic fields, generated by a built-in micrometal strip, cause the nuclear-spin state to evolve coherently. The nuclear-spin state reached during the pulse duration is finally read out via the edge-channel conductance, which shows Rabi oscillation.

Electron–Nuclear Spin Interaction in Edge States of Quantum Hall Systems

We have studied the electron–nuclear spin interaction in integer and fractional quantum-Hall edge channels. By selectively populating edge channels of different spin polarities, nuclear spins along the edge channels are dynamically polarized through the hyperfine interaction. The resultant dynamic nuclear polarization is detected with the edge-channel transport via nuclear magnetic resonance. The technique of controlling and detecting nuclear–spin polarization in quantum-Hall systems opens up new possibilities of developing nuclear–spin solid-state devices as well as shedding new light to spin properties of quantum-Hall systems. We demonstrate local controllability of the nuclear–spin polarization using a built-in micro-metal strip fabricated on a quantum-Hall device. We also demonstrate that the dynamic nuclear polarization can be utilized as a sensitive probe of the spin polarization of fractional quantum-Hall edge channels.

Local control of nuclear-spin system in a quantum-Hall device

We demonstrate coherent control of local nuclear spins in a solid-state device. Nuclear spins in a limited region along spin-resolved quantum-Hall edge channels are strongly polarized through the hyperfine interaction. Quantum states of the nuclear spins evolve coherently during a pulsed-mode application of radio frequency magnetic field generated by a built-in micro-metal strip. The final state reached after the pulsed-mode operation is read out by the edge-channel conductance, which shows Rabi oscillation.

Local control of dynamic nuclear polarization in quantum Hall devices

We manipulate and detect local nuclear spin polarization in integer quantum Hall (IQH) systems using micrometal strips fabricated on top of Al0.3Ga0.7As/GaAs Hall bar devices. The radio-frequency (rf) magnetic fields generated by transmitting rf electrical currents through the micrometal strips causes nuclear magnetic resonance in a limited region along IQH edge channels, and resulting changes in the nuclear spin polarization are detected via Hall resistance of the devices.

Timeconstant of the far-IR response of a quantum Hall device

The characteristic time of the far-infrared response of a quantum Halleffect detector in GaA/AlGaAs has been investigated versus themagnetic field. The response time is shown to increaseexponentially with the field due to the spatial separation ofphotoexcited electrons and holes captured by localized states formed by the disordered potential. The results obtained allow usto estimate the length scale of long-range potentialfluctuations.

Highly sensitive and tunable detection of far-infrared radiation by quantum Hall devices

We studied far-infrared (FIR) response due to cyclotron resonance (CR) of two-dimensional electron gas systems in GaAs/AlGaAs heterostructures by using cyclotron radiation from n-InSb devices as the illumination source. We examined the dependence of the FIR response on different experimental parameters, including the aspect ratio of Hall bars, electron mobility, bias current, illumination intensity, magnetic field, and lattice temperature. A strong photoresponse emerges only in the vicinity of integer quantum Hall effect (IQHE) regimes. Time-resolved measurements show that the recombination lifetime of excited carriers depends largely on the electron mobility, ranging from 5 μs to 1 ms at 4.2 K. The temporal decay of photoresponse is nonexponential in higher-mobility samples, whereas it is exponential with a single time constant in lower-mobility samples. This, together with the relatively large time constants, suggests that the FIR response is induced through multitrapping processes, in which excited carriers in Landau levels are repeatedly captured by localized states and reexcited to delocalized states. This multitrapping process is suggested to be promoted by the CR-induced heating of the electron system. Theoretical calculation based on the electron heating model reasonably reproduces characteristic dependence of the photoresponse on the magnetic field in the vicinity of IQHE plateaus. The IQHE Hall bars serve as a high-sensitive narrow-band FIR detector, where the highest sensitivity reaches ∼108 V/W. Tunability of the detector is demonstrated by varying the electron density. We discuss briefly the design of high-sensitive FIR detectors using the IQHE Hall bars.

Suppression of electron–hole-pair recombination in edge states in quantum Hall regimes

Far-infrared (FIR) photoconductivity induced by cyclotron resonance in edge states of quantum Hall devices are studied by carrying out time-resolved measurements. It is found that the recombination of electron–hole pairs excited via cyclotron resonance in edge states is significantly suppressed, yielding a surprisingly long recombination lifetime (∼10ms). This is in marked contrast to much shorter recombination lifetimes (∼1ms) in bulk states. The experimental results lead us to suggest that the edge-state FIR photoconductivity is induced by an effect of electric polarization. This implies also that edge states can be a promising candidate for application as a FIR detector.

AC QHE-based resistance and capacitance calibrations

AC bridges developed for direct comparison of resistance or capacitance standards with quantum Hall devices are described. Owing to triple-series connection of quantum Hall devices, some of the auxiliary balance conditions are fulfilled automatically and balancing the bridges is simplified.

Measurements of the ac longitudinal resistance of a GaAs-AlGaAs quantum Hall device

The shape of the i=2 minimum of the ac longitudinal resistance R/sub x/ of a quantum Hall device has been obtained at different frequencies from 160 Hz to 16 kHz. The frequency dependence of the resistance and the virtual reactance, measured at the i=2 and i=4 plateau centers with different circuit conditions, have been analyzed. The measurements have been performed with a new system, which includes dedicated electronic units to maintain close to zero the voltage at the current measurement terminal of the device and the current at the voltage terminals. Within the validity of the equivalent circuit adopted to represent the quantum Hall device and the measuring system, R/sub x/ was found to follow an increasing function of frequency, in agreement with previous investigations.

Fabrication of quantum Hall devices for low magnetic fields

The quantized Hall resistance of a two-dimensional electron gas (2DEG) in AlGaAs/GaAs heterostructures is used for the realization of the unit of resistance. This effect is more and more widely used. For possible application even in magnets with magnetic flux densities as low as 6 T, such devices have been produced with carrier concentrations in a range from 2.7/spl times/10/sup 15/ m/sup -2/ to 5.4/spl times/10/sup 15/ m/sup -2/ and their metrological quality has been checked. We find that even in low magnetic fields the quantized Hall resistance can be reproduced with highest accuracy.

Liquid-crystal phases of quantum Hall systems

Mean-field calculations for the two dimensional electron gas (2DEG) in a large magnetic field with a partially filled Landau level with index $N\geq 2$ consistently yield ``stripe-ordered'' charge-density wave ground-states, for much the same reason that frustrated phase separation leads to stripe ordered states in doped Mott insulators. We have studied the effects of quantum and thermal fluctuations about such a state and show that they can lead to a set of electronic liquid crystalline states, particularly a stripe-nematic phase which is stable at $T>0$. Recent measurements of the longitudinal resistivity of a set of quantum Hall devices have revealed that these systems spontaneously develop, at low temepratures, a very large anisotropy. We interpret these experiments as evidence for a stripe nematic phase, and propose a general phase diagram for this system.

26p-YG-15 量子ホール効果デバイスからのサイクロトロン発光 : 空間分解測定II

26p-YG-15 量子ホール効果デバイスからのサイクロトロン発光 : 空間分解測定II

Correlations in one-dimensional quantum impurity problems with an external field

We study response functions of integrable quantum impurity problems with an external field at T = 0 using non-perturbative techniques derived from the Bethe ansatz. We develop the first steps of the theory of excitations over the new, field-dependent ground state, leading to renormalized (or “dressed”) form factors. We obtain exactly the low-frequency behaviour of the dynamical susceptibility χ″ (ω) in the double-well problem of dissipative quantum mechanics (or equivalently the anisotropic Kondo problem), and the low-frequency behaviour of the AC noise S t ( ω) for tunnelling between edges in fractional quantum Hall devices. We also obtain exactly the structure of singularities in χ″ (ω) and S t ( ω). Our results differ significantly from previous perturbative approaches.

Potential barriers in quantum Hall devices.

We investigate numerically the influence of potential barriers on the quantum Hall effect in a six-terminal configuration. The barriers are placed in one of the crossing areas. In agreement with experimental and theoretical results for a simple barrier separating the two crosses, we obtain quantization of the longitudinal resistance ${\mathit{R}}_{\mathit{xx}}$, in addition to the quantization of the Hall resistance ${\mathit{R}}_{\mathit{xy}}$. At a plateau of ${\mathit{R}}_{\mathit{xx}}$, the barrier perfectly separates the edge states into either transmitted states or states deviated along the barrier. For diagonal orientation of the barrier, the two directions of the magnetic field become nonequivalent. In particular, this leads to different plateaus in ${\mathit{R}}_{\mathit{xy}}$ for opposite magnetic fields. \textcopyright{} 1996 The American Physical Society.

Imaging the edge channel structure in a quantum Hall device

In a magnetically quantised two dimensional electron gas (2DEG) of finite dimension, the Landau levels bend up at the boundaries due to the confining potential. Edge channels are formed where these intersect the Fermi level. We have used laser imaging with a spatial resolution of 5 μm to investigate the edge channel structure in a gallium arsenide Hall bar at temperatures between 1.5 K and 150 mK. The beam from an Ar+ laser is focused to a small spot on the top surface of the device and the induced Hall photovoltage is measured as a function of the spot position. The size of the photovoltage depends on the potential profile in the device and, at integer Landau level filling factors, is a maximum at the edges. In our device the edge regions turn out to be very wide compared to the magnetic length.

Application of quantum Hall devices for FIR detection

We propose a novel concept for FIR light detection by means of Hall devices biased at strong currents. The base of the device operation is the effect of photoinduced breakdown of the integer quantum Hall effect (QHE). We demonstrate experimentally that the increase of the bias current from 100 to 300 μA leads to the photoresponse enhancement by over two orders of magnitude. Application of the presented results for designing a tunable high sensitive FIR photodetector is discussed.