Induced currents, frozen charges and the quantum Hall effect breakdown

Puzzling results obtained from torque magnetometry in the quantum Hall effect regime are presented, and a theory is proposed for their explanation. Magnetic moment saturation, which is usually attributed to the quantum Hall effect breakdown, is shown to be related to the charge redistribution across the sample.     

Breakdown of the quantum Hall effect due to electron heating

The breakdown of the Quantum Hall effect observed on GaAs-AlGaAs samples is quantitatively explained in terms of peculiar electron-heating characteristic to the Quantum Hall regime. The current instability originates from an S-shaped current-voltage characteristic. Further, exponential dependence of the dissipative conductivity on the electric field, observed in the lower field range, is interpreted as a consequence of the finite size of the wave function of localized states in the presence of potential gradient.     

Dispersion of the conductance of quantum nanowires and Joule heating

The high-frequency ballistic conductance G(ω) of a quantum wire connecting two classical reservoirs is discussed. It is supposed that the transverse size of the wire is on the order of the de Broglie wavelength of the conduction electrons. An expression for G(ω) in a wide range of frequencies ω is given. The behavior of both active ReG(ω) and reactive ImG(ω) parts of the conductance is investigated. The frequency range is determined where the so-called kinetic inductance is dominant, i.e., ImG(ω) is positive and larger than ReG(ω). This range is defined by the condition that the time of flight of the conduction electrons along the wire length L exceeds the period of oscillation 2π/ω of the electric potential. The Joule heat generation that accompanies the current flow through the quantum wire takes place in the reservoirs over a distance on the order of the mean free path of conduction electrons. The total rates of Joule heat generation are the same in both reservoirs.     

Nonlinear current-voltage characteristic in narrow channels and low-voltage breakdown of the quantum hall effect

The current-voltage characteristic (CVC) and the breakdown of the quantum Hall effect (QHE) are considered in narrow quasi-two-dimensional channels subject to a strong perpendicular magnetic field B. The interaction of electrons with acoustical and piezoelectrical phonons leads to electron transitions at the edges of the channel and to the main dissipation if the channel width W is not too large. Nonheating negative differential conduction (dj_x/dE_x < 0), when an electric field E_x is applied along the channel, is possible for drift velocities v_D smaller, much smaller, or larger than the speed of sound s. The CVC j_x = j_x (E_x), is substantially nonlinear if v_D is not too small. The results agree with the observations [1] (v_D ∼ s/20) in metal oxide-semiconductor (MOS) structures. The observed exponential increase in the dissipation before breakdown [2], by two orders of magnitude, is explained as well. The anisotropy of the electron-phonon interaction in MOS structures and its substantial influence on the CVC and v_D is also considered.     

Collapse of quantized Hall resistance and breakdown of dissipationless state in the integer quantum Hall effect: filling factor dependence

Magnetic field dependence of critical current for collapse of quantized Hall resistance I_cr(collapse) and critical current for breakdown of dissipationless state I_cr(breakdown) have been measured near the filling factor ν=4 of Landau levels in a GaAs/AlGaAs heterostructure Hall bar. The difference I_cr(breakdown)−I_cr(collapse) decreases against the increase and the decrease in ν from 4 and the critical behavior disappears outside of the region 3.85<ν<4.15.     

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运用数值模拟方法对液态金属锂在导电壁面的哈特曼流中因焦耳热引起的升温进行了计算。结果表明,在壁液交界面自冷包层的出口处由于导电壁面内感应电流产生的焦耳热所引起的升温将可能超过100°C。     

Electric field dependent mobility edge and theory of the breakdown of the integer quantum Hall effect

We discuss the microscopic mechanism for the onset of dissipation in a quantum Hall system. Based on general results on the time dependence of the states in a disorder-broadened Landau band in the presence of a macroscopic electric field E, it is found that the mobility edges move from the band center towards the band tails when |E| is increased, in agreement with experiments. Since in real samples, |E| is space dependent, the mobility edges are also space dependent. Dissipation (i.e. breakdown of the quantum Hall effect) sets in at points (x, y), where |E(x, y)| has the value for which a mobility edge attains the Fermi energy. This value depends on the disorder potential and on the filling factor. Inside a sample, the conductivities depend on |E(x, y)| and hence on space. We discuss experimental applications, including dissipation in opposite corners of a Hall bar and related breakdown phenomena.     

Hall effect on MHD flow and heat transfer of nanofluids over a stretching wedge in the presence of velocity slip and Joule heating

This paper deals with the boundary layer flow and heat transfer of nanofluids over a stretching wedge with velocity-slip boundary conditions. In this analysis, Hall effect and Joule heating are taken into consideration. Four different types of water-base nanofluids containing copper (Cu), silver (Ag), alumina (Al₂O₃), and titania (TiO₂) nanoparticles are analyzed. The partial differential equations governing the flow and temperature fields are converted into a system of nonlinear ordinary differential equations using a similarity transformation. The resulting similarity equations are then solved by using the shooting technique along with the fourth order Runge-Kutta method. The effects of types of nanoparticles, the volume fraction of nanoparticles, the magnetic parameter, the Hall parameter, the wedge angle parameter, and the velocityslip parameter on the velocity and temperature fields are discussed and presented graphically, respectively.     

Zero-bias anomalies in narrow tunnel junctions in the quantum Hall regime

We report on the study of cleaved-edge-overgrown line junctions with a serendipitously created narrow opening in an otherwise thin, precise line barrier. Two sets of zero-bias anomalies are observed with an enhanced conductance for filling factors ν>1 and a strongly suppressed conductance for ν<1. A transition between the two behaviors is found near ν≈1. The zero-bias anomaly (ZBA) line shapes find explanation in Luttinger liquid models of tunneling between quantum Hall edge states. The ZBA for ν<1 occurs from strong backscattering induced by suppression of quasiparticle tunneling between the edge channels for the n=0 Landau levels. The ZBA for ν>1 arises from weak tunneling of quasiparticles between the n=1 edge channels.     

On the quantum Hall effect

We consider a particle in a 2 dimensional plane in a periodic potential and a homogeneous magnetic field perpendicular to the plane. Kubo's expression for conductivity of the Hall current is an integer.

This result of Thouless, Kohomoto, Nightingale and den Nijs is interpreted geometrically.     

锯齿型石墨烯纳米窄带中量子霍尔体系的电场调控

应用含自洽格点在位库仑作用的Kane-Mele模型,研究锯齿型石墨烯纳米窄带平面内横向电场对边界带能带结构和量子自旋霍尔(QSH)体系的影响.研究结果显示,当电场强度较弱时,外加电场的方向可以调控自旋向下的两个边界带一起朝不同方向移动,导致波矢q=0.5处自旋向下的两个纯边界态的能量简并劈裂方向可由电场调控;当电场强度进一步增强到超过0.69 V/nm,自旋向下的两个边界带出现较大带隙,能带反转,而自旋向上的电子结构无能隙,系统呈现半金属性,同时QSH体系不再是B类.特别当电场强度为1.17 V/nm时,在自旋向下能带的能隙中,q=0.5处存在自旋向上的纯边界态,意味着在8格点边界处可以产生自旋向上的纯边界电流.当电场强度持续增加时,QSH系统从B类到C类经历3个阶段的变化.当电场强度超过1.42 V/nm后,自旋向上的两个边界带也出现能带反转,分别成为导带和价带,系统成为C类的普通量子霍尔体系.     

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

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.     

Shape memory effect in Ti-Ni-Cu alloy caused by Joule heating

The properties of melt-spun Ti₅₀Ni₂₅Cu₂₅ alloy have been investigated by multiple thermocycling (up to 8000 cycles) within the martensitic transformation temperature range under constant mechanical stress from 5 to 200MPa, using electric current heating. A nearly linear relation is established between the alloy strain and electric resistance, which is independent of the applied stress and the number of thermal cycles.