Breakdown of the quantum hall effect in regularly inhomogeneous 2D electron systems

A breakdown mechanism is discussed for the current-voltage characteristic of the system of integer Hall channels in a 2D sample with a regularly inhomogeneous 2D electron density. It has been shown that the appearance of an external potential V on the “edges” of such strips leads to two alternatives: as V increases, the strip width decreases to zero or increases geometrically but “deteriorates qualitatively.” In both cases with their (different) thresholds, integer strips lose their properties inherent in them in the quantum Hall effect regime. These thresholds are attributed here to the asymmetric breakdown of the quantum Hall effect for the system of integer channels.     

The quantum Hall＇s effect： A quantum electrodynamic phenomenon

<正>We have applied Maxwell’s equations to study the physics of quantum Hall’s effect.The electromagnetic properties of this system are obtained.The Hall’s voltage,V_H = 2πh²n_s/em,where n_s is the electron number density,for a 2- dimensional system,and h = 2πh is the Planck’s constant,is found to coincide with the voltage drop across the quantum capacitor.Consideration of the cyclotronic motion of electrons is found to give rise to Hall’s resistance. Ohmic resistances in the horizontal and vertical directions have been found to exist before equilibrium state is reached. At a fundamental level,the Hall’s effect is found to be equivalent to a resonant LCR circuit with L_H = 2πm/e²n_s and C_H = me²/2πh²n_s satisfying the resonance condition with resonant frequency equal to the inverse of the scattering （relaxation） time,τ_s.The Hall’s resistance is found to be R_H =（（L_H）/C_H）^1/2.The Hall’s resistance may be connected with the impedance that the electron wave experiences when it propagates in the 2-dimensional gas.     

Nonstationary phenomena in Si MOSFETs in the quantum hall effects regime

We report the observation of nonstationary hysteresis phenomena in charging of Si MOSFET at a quantizing magnetic field. In these experiments (Pudalovet al 1984; Pudalov and Semenchinsky 1985) the charging currentJ _g of the capacitance gate-2D-layer was measured while sweeping of the magnetic fieldH or a gate voltageV _g at a constant rate. The numerical integration of the measured valuesJ _g with respect to time gave the dependences of change inQ _s vsV _g or vsH. At low temperatureT<1 K there arise deviations from the linear dependenceQ _s(V _g) near those integer values of Landau level fillingν=n _s/n _H=2, 4, 6, 8, 12, which correspond to the most deep minima inρ _xx and flat plateaux inρ _xy. Heren _s is the 2D electron density,n _H being Landau level degeneracy number,ρ _xx andρ _xy —the resistivity tensor components. The inherent feature of the curveQ _s(V _g) is the hysteresis: at increasingV _g the chargeQ _s is less than the equilibrium value, while at decreasingV _g the charge exceeds the equilibrium one. The maximum difference of charges at an increase and decrease ofV _g grows-rapidly at loweringT and atT=0.42 K amounts to ～10% of the full charge confined by one Landau level (n _H.e.S). It is worth to note that such behaviour ofQ _s(V _g) does not influence the values ofρ _xy (with accuracy of ～ 10^?5) and the shape ofρ _xy plateaux andρ _xx-minima. Measurements at various sweep rates dV _g/dt demonstrated that if the sweep rate is lower, the hysteresis region is narrower and the deviation of chargesQ _s from its equilibrium value is smaller. By extrapolating the dependence of hysteresis loop width on dV _g/dt, the ultimate sweep rate may be estimated, for which a hysteresis will completely disappear. Thus, for instance, atT=0.42 K andν=4 it will occur when the time interval of one Landau level fillingτ _H will be equal to 100 years. A similar hysteresis in 2D-layer charge occurs in varying magnetic field also, when the gate voltage is disconnected with the battery and hence the charge in MOSFET is maintained constant. This hysteresis loop rapidly vanishes at temperatures >1 K. The long relaxation time of a nonequilibrium charge in 2D-layer can be connected phenomenologically with small drift velocities of electrons along the potential gradient due to a small value of conductivityσ _xx. This relaxation time may be estimated asτ～C/σ _xx whereC is the electrical capacitance of MOSFET area with a nonequilibrium charge. The value ofτ～10⁹ s givesσ _xx<10 _a ^?18 Ohm^?1/□, i.e.ρ _xx<10^?11 Ohm/□. Simultaneously with nonequilibrium charge relaxation in 2D-layer there arise circular Hall currents decaying with the same rate. In conclusion, we observed and investigated nonequilibrium charging of 2D-layer in quantum Hall effect regime. To explain the phenomenon we supposed that circular Hall currents is comparable to the eddy currents excited in a superconducting ring.     

Edge current switch of two-dimensional electron gas using carrier density control

We have investigated the effects of electron density discontinuity on the transports of edge currents of two-dimensional electron gas (2DEG). The electric field applied to a gate, which covers the 2DEG partially, gives rise to change in the carrier density and results in a density gradient, which deforms the edge currents. The transverse and longitudinal resistances were measured as functions of gate voltage V_G in the quantum Hall regime. The deviations of the longitudinal resistances from the normal quantum Hall resistances are attributed to the reflections of the edge currents under the influence of the abrupt density discontinuity. A switching behavior of the transverse resistance by controlling the gate voltage was observed when V_G=−2.2 and −2.0 V for magnetic field H=5 and 7.2 T, respectively.     

The absence of a measurable hall effect in the superionic conductor RbAg4I5

Thin film samples of RbAg₄I₅ have been prepared by evaporation and several of their electrical properties have been determined. The behavior of the conductivity of these films is identical to that found in bulk RbAg₄I₅. An attempt to reproduce the Hall effect results of Kaneda and Mizuki was unsuccessful, and we conclude that the Hall mobility of silver ions in this material is less than 2 × 10^-3cm²/V·sec.     

Anomalous Hall effect in Cu and Fe codoped In2O3 and ITO thin films

We present a systematic study of the structure, magnetization, resistivity, and Hall effect properties of pulsed laser deposited Fe- and Cu-codoped In₂O₃ and indium-tin-oxide (ITO) thin films. Both the films show a clear ferromagnetism and anomalous Hall effect at 300 K. The saturated magnetic moments are almost the same for the two samples, but their remanent moments M_r and coercive fields H_C are quite different. M_r and H_C values of ITO film are much smaller than that of In₂O₃. The ITO sample shows a typical semiconducting behavior in whole studied temperature range, while the In₂O₃ thin film is metallic in the temperature range between 147 and 285 K. Analysis of different conduction mechanisms suggest that charge carriers are not localized in the present films. The profile of the anomalous Hall effect vs. magnetic field was found to be identical to the magnetic hysteresis loops, indicating the possible intrinsic nature of ferromagnetism in the present samples.     

Induction kinetics in 2D electron systems at the Hall plateaus

Specific features of the induction excitation of 2D electron systems at the Hall plateaus are discussed. The corresponding kinetics is shown to have several frequency regimes. In the region ω ? ω_D, where ω_D is the frequency characteristic of the kinetics at the Hall plateaus, an induction-caused variation of electron density follows the magnetic-field variation with time. For the frequencies ω ≤ ω_D, a noticeable relaxation of the electron disturbance appears, and the induction polarization of 2D samples at the Hall plateaus noticeably decreases as compared to the maximum possible polarization. Finally, in the limit ω ≤ ω_slow, where ω_slow corresponds to another characteristic time of the quantum Hall effect, the so-called adiabatic approximation takes place with the 2D system responding to the derivative of magnetic field dH/dt rather than to the magnetic field itself H(t). The results of calculations are compared with the experimental data reported in the literature.     

Hall coefficients for A15 compounds: Nb-Sn and V-Si

The Hall coefficients, R_H, for A15 structure single crystal V₃Si and polycrystal V25.25 at.% Si and Nb 26 at.% Sn have been measured as functions of temperature. The data between the superconducting transition temperature, T_c, and 80 K for the Nb-Sn show a small dip centred arounf 30 K which accompanies a cubic-to-tetragonal lattice distortion commencing at about 45 K. R_H for the VSi samples, which are believed to be non-transforming, is temperature independent in the range 17–40 K and equal to 2.0 ± 0.2×10^?10m³C^?1. These result are discussed in relation to the effect of the tetragonal distortion on the band structures of these compounds.     

Microwave spectra of deuterated ethanes: Internal rotation potential function and rz structure

The microwave spectra of CH₃CHD₂ in the first excited torsional state and of CH₃CH₂D and CD₃CH₂D in the ground states have been observed by a source-modulation spectrometer and analyzed to determine the two potential constants, V₃ and V₆, simultaneously and also to assess the isotopic effects on the potential function. The results obtained for C₂H₆ are V₃ = 2.882 ± 0.010 and V₆ = 0.020 ± 0.010 kcal/mole. The staggered conformation in ethane was established by observing microwave spectra of gauche CH₂DCH₂D. The r_z structure of ethane was recalculated by adding precise rotational constants obtained in this work to previous microwave and infrared data.     

Hydrogen indium vacancy complex VInH4 in n-type InP studied by positron-lifetime

Positron-lifetime experiments have been carried out on two undoped n-type liquid encapsulated Czochralski (LEC)-grown InP samples with different stoichiometric compositions in the temperature range 10-300 K. For temperatures below 120 K for P-rich InP and 100 K for In-rich InP, the positron average lifetime began to increase rapidly and then leveled off, which was associated with the charge state change of hydrogen indium vacancy complexes from (V_InH₄)⁺ to (V_InH₄)⁰. This phenomenon was more obvious in P-rich samples that have a higher concentration of V_InH₄. The transformation temperature of approximately 120 K suggests that the complex V_InH₄ is a donor defect and that the ionization energy is about 0.01 eV. The ionization of neutral V_InH₄ accounted for the decrease of the positron average lifetime when the sample was illuminated with a photon energy of 1.32 eV at 70 K. These results provide evidence for hydrogen complex defects in undoped LEC InP.     

Low-Temperature anomalies of the Hall coefficient for a magnetic Kondo lattice of CeAl2

The Hall coefficient R _H and magnetoresistance of a magnetic Kondo lattice of CeAl₂ were investigated over a wide temperature range from 1.8 to 300 K in magnetic fields of up to 80 kOe. Analysis of the measured angular dependences R _H(?, T, H) made it possible to separate the contributions of skew scattering and anomalous magnetic scattering to the anomalous Hall effect. The results obtained were compared with the existing theoretical models.     

Structural and thermoelectric power properties of Na-doped V2O5·nH2O nanocrystalline thin films

X-ray diffraction (XRD), thermoelectric power (S) and at room temperature electrical conductivity (σ) of Na⁺¹-doped V₂O₅·nH₂O nanocrystalline thin films fabricated by sol gel technique (colloid route) were studied. XRD showed that the Na₂O–V₂O₅·nH₂O thin films are highly oriented nanocrystals. The average value of particle size was found to be about 7.5 nm. The thermoelectric power showed that the thermoelectric power for all present nanocrystalline thin films samples decreased with increasing Na⁺¹ content. However, the electrical conductivity increased with increasing Na⁺¹ content. There is evidence that small polarons are responsible for determining the transport properties of the Na⁺¹ doped V₂O₅·nH₂O nanocrystalline thin films samples. The high value of electrical conductivity and small value of thermoelectric power is ideal for device applications, where device to device variation of the thermoelectric power must be small. This preparation technique was demonstrated to fabricate high quality Na₂O–V₂O₅·nH₂O nanocrystalline thin films for thermoelectric device applications. However, this may be further used for deposition with an ink-jet printer.     

Integer and fractional quantum Hall effect in a strip of stripes

We study anisotropic stripe models of interacting electrons in the presence of magnetic fields in the quantum Hall regime with integer and fractional filling factors. The model consists of an infinite strip of finite width that contains periodically arranged stripes (forming supercells) to which the electrons are confined and between which they can hop with associated magnetic phases. The interacting electron system within the one-dimensional stripes are described by Luttinger liquids and shown to give rise to charge and spin density waves that lead to periodic structures within the stripe with a reciprocal wavevector 8k _F in a mean field approximation. This wavevector gives rise to Umklapp scattering and resonant scattering that results in gaps and chiral edge states at all known integer and fractional filling factors ν. The integer and odd denominator filling factors arise for a uniform distribution of stripes, whereas the even denominator filling factors arise for a non-uniform stripe distribution. We focus on the ground state of the system, and identify the quantum Hall regime via the quantized Hall conductance. For this we calculate the Hall conductance via the Streda formula and show that it is given by σ _H = νe ²/h for all filling factors. In addition, we show that the composite fermion picture follows directly from the condition of the resonant Umklapp scattering.     

Microscopic magnetic properties of nonstoichiometric V2O3+x—NMR and inelastic spin-flip neutron scattering measurements

The local magnetic properties of the V sites in the nonstoichiometric V₂O_3+x (0 ? x <0.08) have been examined by nuclear magnetic resonance and inelastic spin-flip neutron scattering techniques. The samples with x = 0.01 and 0.02 show a paramagnetic metal (PM)-antiferromagnetic insulator (AFI) transition. In the AFI phase, two distinct ⁵¹V NMR signals with hyperfine fields H_n = 184.9±0.5 kOe and 71±1 kOe were observed at 1.8 K, which were assigned as due to V³⁺ and V³⁺ sites, respectively. On the other hand, the samples with x = 0.04 and 0.06 were metallic down to 1.4K, and showed a paramagnetic (PM)-antiferromagnetic (AFM) transition at about 10 K. In these samples, a ⁵¹V NMR signal with H_n = 58±2 k0e and one with 〈H_n〉 = 9kOe were observed at 1.8 K, which were assigned as due to V³⁺-like sites and the matrix V sites, respectively. These results are entirely consistent with those obtained from the neutron experiment. We propose that in the metallic phase (0.04 ? x < 0.08) the minority V⁴⁺-like sites are magnetically localized in the delocalized V matrix and may be responsible for the antiferromagnetic long range order below 10 K.     

Hall effect and sign reversal in Gd(Ba2−xNdx)Cu3O7+δ

We have investigated the Hall measurement of Gd(Ba_2−xNd_x)Cu₃O_7+δ with x=0, 0.05, 0.1, 0.15, and 0.2 in a magnetic field of 0–1 T. The nominal samples has been prepared by the conventional solid-state reaction technique. The iodometric titration experiment was carried out for samples. The Rietveld analysis of the X-ray diffraction patterns indicates that samples are mainly single phase. The normal state Hall coefficient behaves as 1/T in all samples. All samples with nominal compositions show single sign reversal with variation of magnetic field and temperature. The Hall resistivity of the samples with x=0 and 0.1 close to the superconducting transition temperature changes its sign with decreasing temperature and tends to a minimum −Δ_max, and then monotonically goes to zero. The absolute value of −Δ_max decreases with the increase of magnetic field. This can be qualitatively explained by a model calculation based on the time-dependent Ginsburg–Landau theory.     

High-field magnetoresistance and Hall effect in Bi2Sr2CuO x single crystals

We investigated the in-plane magnetoresistance and the Hall effect of high-quality Bi₂Sr₂CuO_x single crystals with T _c (midpoint) = 3.7–9.6 K in dc magnetic fields up to 23 T. For T < 10 K, the crystals show the classical positive magnetoresistance. Starting at T ≈ 14 K, an anomalous negative magnetoresistance appears at low magnetic fields; for T ≥ 40 K, the magnetoresistance is negative in the whole studied range of magnetic fields. Temperature and magnetic field dependences of the negative-magnetoresistance single crystals are qualitatively consistent with the electron interaction theory developed for simple semiconductors and disordered metals. As is observed in other cuprate superconductors, the Hall resistivity is negative in the mixed state and changes its sign with increasing field. The linear T-dependence of cotθ_H for the Hall angle in the normal state closely resembles that of the normal-state resistivity as expected for a Fermi liquid picture.     

Experimentelle Bestimmung der Supraleitungsparameter einiger Verbindungen vom β-Wolframtyp aus Magnetisierungsmessungen

A complete analysis of magnetization curves is given for bulk sintered samples of Nb₃Sn with low hysteresis and for finely powdered sintered and melted samples of Nb₃Sn, Nb₃Al, V₃Si and V₃Ga. The Ginzburg-Landau parameterκ and the penetration depthλ of weak magnetic fields is calculated from the temperature dependence of the thermodynamic and upper critical fieldsH _c andH _c2. The slope of theH _c ?T curve is about 360 Oe/°K and approximately the same for all measured samples. There is an extremely high increase of the lower critical fieldH _c1 if the grain size approachesλ. The occurence of field expulsion and partially reversible magnetization curves of sintered Nb₃Sn samples with high sintering temperatures and high pore volumes is explained by means of connections between single grains which have lower transition temperatures.     

Dependence on substrate bias of the effective mass and dingle temperature of electrons in the surface inversion layer of silicon

The amplitude of the quantum oscillations in the magnetoconductance of a silicon inversion layer has been studied as a function of gate voltage V_g, for different values of the temperature T, applied magnetic field strength H and substrate bias V_s. By analyzing the amplitude of the oscillations at fixed V_g and V_g as a function of T and H, the dependence of the cyclotron effective mass m¹ and the Dingle temperature T_D on V_g and V_s can be obtained. The dependence of m¹ on V_g for different values of V_s is compared with the prediction of theory.