Near-perfect correlation of the resistance components of mesoscopic samples at the quantum Hall regime

We study the four-terminal resistance fluctuations of mesoscopic samples near the transition between the nu=2 and the nu=1 quantum Hall states. We observe near-perfect correlations between the fluctuations of the longitudinal and Hall components of the resistance. These correlated fluctuations appear in a magnetic-field range for which the two-terminal resistance of the samples is quantized. We discuss these findings in light of edge-state transport models of the quantum Hall effect. We also show that our results lead to an ambiguity in the determination of the width of quantum Hall transitions.     

The enigma of the quantum Hall effect in graphene

We apply Laughlin’s gauge argument to analyze the ν=0 quantum Hall effect observed in graphene when the Fermi energy lies near the Dirac point, and conclude that this necessarily leads to divergent bulk longitudinal resistivity in the zero temperature thermodynamic limit. We further predict that in a Corbino geometry measurement, where edge transport and other mesoscopic effects are unimportant, one should find the longitudinal conductivity vanishing in all graphene samples which have an underlying ν=0 quantized Hall effect. We argue that this ν=0 graphene quantum Hall state is qualitatively similar to the high field insulating phase (also known as the Hall insulator) in the lowest Landau level of ordinary semiconductor two-dimensional electron systems. We establish the necessity of having a high magnetic field and high mobility samples for the observation of the divergent resistivity as arising from the existence of disorder-induced density inhomogeneity at the graphene Dirac point.     

Even-odd effect in spontaneously coherent bilayer quantum Hall droplets

Using exact diagonalization in the disk geometry we predict a novel even-odd effect in the Coulomb-blockade spectra of vertically coupled double quantum dots under an external magnetic field. The even-odd effect in the tunneling conductance is a direct manifestation of spontaneous interlayer phase coherence, and is similar to the even-odd resonance in the Cooper pair box problem in mesoscopic superconducting grains. Coherent fluctuations in the number of Cooper pairs in superconductors are analogous to the fluctuations in the relative number difference between the two layers in quantum Hall droplets.     

Conductance fluctuations of chiral metals

We study conductance fluctuations of the edge-state sheath that forms in the integer quantum Hall effect from the coupled edge states of a GaAs/Al_xGa_1 − xAs multilayer. Comparison of the measured variance in the vertical conductance to recent theoretical predictions for mesoscopic fluctuations suggests dephasing lengths of 1–10 μm around the sheath perimeter at low temperatures. However, inconsistencies in the estimated inelastic lengths indicate that present understanding of dephasing on the sheath is incomplete.     

用热场动力学理论研究介观电路的Wigner函数

利用热场动力学及相干热态表象理论,重构了有限温度下介观RLC电路的Wigner函数,研究了有限温度下介观RLC电路的量子涨落.借助于Weyl-Wigner理论讨论了有限温度下介观RLC电路Wigner函数的边缘分布,并进一步阐明了Wigner函数边缘分布统计平均的物理意义.结果表明: 有限温度下介观RLC电路中电荷和电流的量子涨落随着温度和电阻值的增加而增加,回路中的电荷和电流之间存在着压缩效应,这种量子效应是由于系统零点振动的涨落而引起的; 有限温度下介观RLC电路Wigner函数边缘分布的统计平均正好是储存在介观RLC电路中电容和电感上的能量.     

用热场动力学理论研究介观电路的Wigner函数

利用热场动力学及相干热态表象理论,重构了有限温度下介观RLC电路的Wigner函数,研究了有限温度下介观RLC电路的量子涨落.借助于Weyl-Wigner理论讨论了有限温度下介观RLC电路Wigner函数的边缘分布,并进一步阐明了Wigner函数边缘分布统计平均的物理意义.结果表明:有限温度下介观RLC电路中电荷和电流的量子涨落随着温度和电阻值的增加而增加,回路中的电荷和电流之间存在着压缩效应,这种量子效应是由于系统零点振动的涨落而引起的;有限温度下介观RLC电路Wigner函数边缘分布的统计平均正好是储存在介观RLC电路中电容和电感上的能量.     

Low-field phase diagram of the spin Hall effect in the mesoscopic regime

When a mesoscopic two dimensional four-terminal Hall cross bar with spin-orbit interaction (SOI) is subjected to a perpendicular uniform magnetic field B, both integer quantum Hall effect (IQHE) and mesoscopic spin Hall effect (MSHE) may exist when disorder strength W in the sample is weak. We have calculated the low field "phase diagram" of MSHE in the (B,W) plane for disordered samples in the IQHE regime. For weak disorder, MSHE conductance G(sH) and its fluctuations rms(G(sH)) vanish identically on even numbered IQHE plateaus, they have finite values on those odd numbered plateaus induced by SOI, and they have values G(sH)=1/2 and rms(G(sH))=0 on those odd numbered plateaus induced by Zeeman energy. At larger disorders, the system crosses over into a regime where both G(sH) and rms(G(sH)) are finite, a chaotic regime, and finally a localized regime.     

Magnetic-field asymmetry of nonlinear mesoscopic transport

We investigate departures of the Onsager relations in the nonlinear regime of electronic transport through mesoscopic systems. We show that the nonlinear current-voltage characteristic is not an even function of the magnetic field due only to the magnetic-field dependence of the screening potential within the conductor. We illustrate this result for two types of conductors: A quantum Hall bar with an antidot and a chaotic cavity connected to quantum point contacts. For the chaotic cavity we obtain through random matrix theory an asymmetry in the fluctuations of the nonlinear conductance that vanishes rapidly with the size of the contacts.     

Mesoscopic effects in the quantum Hall regime

We report results of a study of (integer) quantum Hall transitions in a single or multiple Landau levels for non-interacting electrons in disordered two-dimensional systems, obtained by projecting a tight-binding Hamiltonian to the corresponding magnetic subbands. In finite-size systems, we find that mesoscopic effects often dominate, leading to apparent non-universal scaling behavior in higher Landau levels. This is because localization length, which grows exponentially with Landau level index, exceeds the system sizes amenable to the numerical study at present. When band mixing between multiple Landau levels is present, mesoscopic effects cause a crossover from a sequence of quantum Hall transitions for weak disorder to classical behavior for strong disorder. This behavior may be of relevance to experimentally observed transitions between quantum Hall states and the insulating phase at low magnetic fields.     

Fractional quantization of Hall resistance as a consequence of mesoscopic feedback

A nonlinear single-particle model is introduced, which captures the characteristic of systems in the quantum Hall regime. The model involves the magnetic Schrödinger equation with spatially variable magnetic flux density. The distribution of flux is prescribed via the postulates of the mesoscopic mechanics (MeM) introduced in my previous articles (cf. [9, 10]). The model is found to imply exact integer and fractional quantitzation of the Hall conductance. In fact, Hall resistance is found to be R _H = (h/e ²)(M/N) at the filling factor value N/M. The assumed geometry of the Hall plate is rectangular. Special properties of the magnetic Schrödinger equation with the mesoscopic feedback loop allow us to demonstrate quantization of Hall resistance as a direct consequence of charge and flux quantization. I believe results presented here shed light at the overall status of the MeM in quantum physics, confirming its validity.     

有源介观LC电路的量子涨落

本文利用含时微扰论,研究了电源幅值较小时介观LC电路中电荷与电流的量子涨落。在确定的温度下,系统将处在混合态,进一步得到有限温度下含源介观LC电路的量子涨落。研究表明有源介观LC电路的量子涨落不仅与电路参数有关,还与时间和温度有关。     

Multichannel Kondo models in non-Abelian quantum Hall droplets

We study the coupling between a quantum dot and the edge of a non-Abelian fractional quantum Hall state which is spatially separated from it by an integer quantum Hall state. Near a resonance, the physics at energy scales below the level spacing of the edge states of the dot is governed by a k-channel Kondo model when the quantum Hall state is a Read-Rezayi state at filling fraction nu=2+k/(k+2) or its particle-hole conjugate at nu=2+2/(k+2). The k-channel Kondo model is channel isotropic even without fine-tuning in the former state; in the latter, it is generically channel anisotropic. In the special case of k=2, our results provide a new venue, realized in a mesoscopic context, to distinguish between the Pfaffian and anti-Pfaffian states at filling fraction nu=5/2.     

The IWOP Technique and Wigner-Function Approach to Quantum Effect of Mesoscopic Biological Cell

Using the IWOP technique, Wigner function theory and TFD theory, the quantization of a mesoscopic biological cell equivalent circuit is proposed, The quantum fluctuations of the mesoscopic biological cell are researched in thermal vacuum state and vacuum state. It is shown that the IWOP technique, Wigner function theory and Umezawa-Takahashi’s TFD theory play the key role in quantizing a mesoscopic biological cell at finite temperature and the fluctuations and uncertainty increase with increasing temperature and decrease with prolonged time.     

无耗散介观电感耦合电路的库仑阻塞和电荷的量子效应

基于介观电路中电荷应是量子化的这一基本事实,给出了介观电感耦合电路的量子理论和库仑阻塞条件,并讨论了该介观电感耦合电路的量子涨落. 关键词： 介观电路 电感耦合 电荷的不连续性 库仑阻塞 量子涨落     

Dissipative quantum hall effect in graphene near the Dirac point

We report on the unusual nature of the nu=0 state in the integer quantum Hall effect (QHE) in graphene and show that electron transport in this regime is dominated by counterpropagating edge states. Such states, intrinsic to massless Dirac quasiparticles, manifest themselves in a large longitudinal resistivity rho(xx) > or approximately h/e(2), in striking contrast to rho(xx) behavior in the standard QHE. The nu=0 state in graphene is also predicted to exhibit pronounced fluctuations in rho(xy) and rho(xx) and a smeared zero Hall plateau in sigma(xy), in agreement with experiment. The existence of gapless edge states puts stringent constraints on possible theoretical models of the nu=0 state.     

介观RLC电路的量子效应

将介观电容器看作介观隧道结,对介观RLC电路作了相应的量子力学处理.研究了介观RLC电路系统的量子态演化.研究表明:考虑介观电容耦合效应的影响,介观RLC电路系统将由初始的Fock态演化到压缩Fock态,并讨论了电荷及磁通在压缩Fock态下的量子涨落.     

电荷离散化时相干态下介观金属环中电荷与电流以及能量的量子涨落

基于电荷量子化的事实,运用最小平移算符Q∧的性质等,计算对应的相干态下介观金属环中电荷、电流及能量的量子涨落,研究影响量子涨落的因素.结果表明:计及电荷的离散性,在相干态下介观金属环中电荷、能量的量子涨落不为零,分别与电荷量子、相干态参量等因素有关;此外,能量的量子涨落还决定于金属环的电感、外磁通及其时间变化率的大小.     

Low-temperature collapse of electron localization in two dimensions

We report direct experimental evidence that the insulating phase of a disordered, yet strongly interacting two-dimensional electron system becomes unstable at low temperatures. As the temperature decreases, a transition from insulating to metal-like transport behavior is observed, which persists even when the resistivity of the system greatly exceeds the quantum of resistivity h/e2. The results have been achieved by measuring transport on a mesoscopic length scale while systematically varying the strength of disorder.     

Role of coherence in resistance quantization

The quantization of resistances in the quantum Hall effect and ballistic transport through quantum point contacts is compared with the quantization of the charge relaxation resistance of a coherent mesoscopic capacitor. While the former two require the existence of a perfectly transmitting channel, the charge relaxation resistance remains quantized for arbitrary backscattering. The quantum Hall effect and the quantum point contact require only local phase coherence. In contrast quantization of the charge relaxation resistance requires global phase coherence.