Dynamic conductance of a ballistic quantum wire

Within the framework of exact linear response theory, we derive a general formula, with which the dynamic conductance of mesoscopic system can be determined in the absence of Coulomb interaction. In addition, we present a solution to the problem of current partition in the system. These allow the derivation of dynamic conductance in time-dependent case. As a natural consequence, the current (charge) conservation and gauge invariance conditions are fulfilled. To give an example, we discuss the dynamic conductance of a ballistic quantum wire, and the effect of contacts on the conductance is also discussed.     

Temperature-dependent conductance of quasi-one-dimensional electrons in a novel constricted channel with corrugated interfaces

Transport properties of a novel quasi-ballistic quantum wire field-effect transistor are studied experimentally and then discussed in relation to a theory for dirty Tomonaga–Luttinger (T–L) liquids. The sample was prepared by constricting lithographically an epitaxially grown In_0.1Ga_0.9As/GaAs quantum well channel, whose bottom interface is corrugated by a quasi-periodic array of multi-atomic steps of 20 nm in periodicity. A quasi-one-dimensional channel of about 200 nm in metallurgical width and in length was formed and its conductance parallel to the steps was measured at temperatures between 4 and 0.3 K as a function of gate voltage. Plateau-like structures substantially lower than 2e²/h were observed. The conductance at each gate voltage decreases sensitively as temperature lowers until it gets nearly constant below a critical temperature. These tendencies are found to be qualitatively consistent with the theory of Ogata and Fukuyama for dirty T–L liquids. The temperature dependence above the critical temperature is found to fit quantitatively with the formula of Ogata and Fukuyama, if the parameters are suitably chosen.     

Nonlinear conductance fluctuations in a mesoscopic ring

We study the conductance of a single particle on a ring subject to an arbitrary dc electric field, which is generated by a linearly in time increasing magnetic flux. The full quantum mechanical time development is calculated numerically by splitting the dynamics into independent consecutive Zener tunneling transitions and free motion on the ring. The Zener transitions occur near the avoided crossings of the bandstructure which arises from the adiabatic eigenstates as a function of flux in the presence of a static scattering potential. To account for the necessary dissipation the particle is coupled to an appropriate oscillator bath which is adjusted to give a strictly linear current-voltage characteristic for arbitrary voltage and temperature in the absence of scattering. Taking a single δ-function scatterer we find that the dissipative coupling eliminates the localization in energy space found previously and leads to a well defined resistive steady state. The scattering introduces reproducible fluctuations around the average Ohmic behavior which are caused by coherent backscattering. Their magnitude depends on the strength of the scattering potential and decays slowly for large voltages. The associated correlation energy is determined by the uncertainty of the eigenstates due to the dissipative bath coupling. Thermal averaging leads to a decrease of the conductance fluctuations proportional to T^?1.     

Reprint of : Semiclassical theory of persistent current fluctuations in ballistic chaotic rings

The persistent current in a mesoscopic ring has a Gaussian distribution with small non-Gaussian corrections. Here we report a semiclassical calculation of the leading non-Gaussian correction, which is described by the three-point correlation function. The semiclassical approach is applicable to systems in which the electron dynamics is ballistic and chaotic, and includes the dependence on the Ehrenfest time. At small but finite Ehrenfest times, the non-Gaussian fluctuations are enhanced with respect to the limit of zero Ehrenfest time.     

Semiclassical theory of persistent current fluctuations in ballistic chaotic rings

The persistent current in a mesoscopic ring has a Gaussian distribution with small non-Gaussian corrections. Here we report a semiclassical calculation of the leading non-Gaussian correction, which is described by the three-point correlation function. The semiclassical approach is applicable to systems in which the electron dynamics is ballistic and chaotic, and includes the dependence on the Ehrenfest time. At small but finite Ehrenfest times, the non-Gaussian fluctuations are enhanced with respect to the limit of zero Ehrenfest time.     

An effective screened Coulomb interaction in a quasi-one-dimensional system

In this paper, we derive an analytical expression for the screened Coulomb potential between charge carriers in quasi-one-dimensional (Q1D) semiconductor structures. As an application, this potential has been used to investigate the screening effect on the binding energy of a neutral donor (D⁰$D^0$) in quantum wires (QWRs). It is found that the screening effect decreases the neutral donor binding energy, and the screening effects are more obvious in wide QWRs than that in narrow ones. Dependence of screening length on temperature and carrier concentration has also been discussed.     

Phenomenology of the 0.7 conductance feature

We describe a phenomenological model for the conductance feature near 0.7×2e²/h that occurs in quantum point contacts. We focus on the transconductance at finite source–drain bias and contrast our model with the results expected from a single-particle picture. Good agreement is seen in comparing the model with experimental data, taken on ultra-low-disorder GaAs induced electron systems. Although simple, our phenomenology suggests important boundary conditions for an underlying microscopic theory.     

Localization length exponent,critical conductance distribution and multifractality in hierarchical network models for the quantum Hall effect

We study hierarchical network models which have recently been introduced to approximate the Chalker-Coddington model for the integer quantum Hall effect (A.G. Galstyan and M.E. Raikh, PRB 5 (1997) 1422; Arovas et al., PRB 56 (1997) 4751). The hierarchical structure is due to a recursive method starting from a finite elementary cell. The localization-delocalization transition occurring in these models is displayed in the flow of the conductance distribution under increasing system size. We numerically determine this flow, calculate the critical conductance distribution, the critical exponent of the localization length, and the multifractal exponents of critical eigenstates.     

Reprint of : Quantum point contacts as heat engines

The efficiency of macroscopic heat engines is restricted by the second law of thermodynamics. They can reach at most the efficiency of a Carnot engine. In contrast, heat currents in mesoscopic heat engines show fluctuations. Thus, there is a small probability that a mesoscopic heat engine exceeds Carnot's maximum value during a short measurement time. We illustrate this effect using a quantum point contact as a heat engine. When a temperature difference is applied to a quantum point contact, the system may be utilized as a source of electrical power under steady state conditions. We first discuss the optimal working point of such a heat engine that maximizes the generated electrical power and subsequently calculate the statistics for deviations of the efficiency from its most likely value. We find that deviations surpassing the Carnot limit are possible, but unlikely.     

AC-hopping conductance of self-organized Ge/Si quantum dot arrays

Dense (n=4×10¹¹ cm^-2) arrays of Ge quantum dots in a Si host were studied using attenuation of surface acoustic waves (SAWs) propagating along the surface of a piezoelectric crystal located near the sample. The SAW magneto-attenuation coefficient, ΔΓ=Γ(ω,H)-Γ(ω,0), and change of velocity of SAW, ΔV/V=(V(H)-V(0))/V(0), were measured in the temperature interval T=1.5–4.2 K as a function of magnetic field H up to 6 T for the waves in the frequency range f=30–300 MHz. Based on the dependences of ΔΓ on H, T and ω, as well as on its sign, we believe that the AC conduction mechanism is a combination of diffusion at the mobility edge with hopping between localized states at the Fermi level. The measured magnetic field dependence of the SAW attenuation is discussed based on existing theoretical concepts.     

On the environmental decoherence and spin interference in mesoscopic loop structures

Mechanisms of ‘environmental decoherence’ such as surface scattering, Elliot–Yafet process and precession mechanisms, as well as their influence on the spin phase relaxation are considered and compared. It is shown that the ‘spin ballistic’ regime is possible, when the phase relaxation length for the spin part of the wave function (L^(s)) is much greater than the phase relaxation length for the ‘orbital part’ (L^(e)). In the presence of an additional magnetic field, the spin part of the electron's wave function (WF) acquires a phase shift due to additional spin precession about that field. If the structure length L is chosen to be L^(s)>L>L^(e), it is possible to ‘wash out’ the quantum interference related to the phase coherence of the ‘orbital part’ of the WF, retaining at the same time that related to the phase coherence of the spin part and, hence, to reveal corresponding conductance oscillations.     

Large phase coherence effects in GaMnAs-based nanostructures: Towards a quantum spintronics

Quantum coherent transport of spin-polarized carriers is observed on a very unusual large scale within epitaxial nanowires of GaMnAs, a diluted ferromagnetic semiconductor. From the analysis of the amplitude of strong universal conductance fluctuations, an effective phase coherence length of about 100 nm is inferred at T=100 mK, which is one order of magnitude larger than in a granular 3d-metal ferromagnets. Together with the temperature and bias dependence of these reproducible fluctuations, their wire-length dependence is studied in single-domain sub-micron long nanowires with a perprendicular anisotropy. In particular, variations for two equivalent probe configurations are shown when the length becomes comparable to the actual phase coherence length. This result forecasts the possible observation of non-local voltage drops in GaMnAs nanostructures smaller than about 200 nm. Generally speaking, this research contributes to pave the way towards the realization of quantum spintronics devices.     

Thermal conductance in a two-slit quantum waveguide

Using the scattering-matrix method, we investigate the thermal conductance in a two-slit quantum waveguide at low temperature. The results show that the total thermal conductance decreases monotonically with temperature increasing. Moreover, we find that the behaviours of the thermal conductance versus temperature are different for different types of slits.     

Invariant imbedding theory of charge pumping in quantum wires

We have developed a method to study the theory of charge pumping through a continuous quantum wire using the invariant imbedding approach. Using this method, the general properties of quantum charge pumping, with and without inclusion of many-body interactions are investigated. Using the invariant imbedding approach allows us to address directly the complex reflection (R) and transmission (T) matrices across the wire instead of considering the spectrum of the Schrodinger equation. Using the Kohn-Sham version of density functional theory (DFT), the many-body interactions in the quantum wire is investigated. We calculated the pumped current in those two cases. In the case of ignoring the many-body effects, the pumped current depends on the width of the driven potential barriers and in the case of nonequality of the width of barriers, our study predicts a nonzero charge pumping at the phase difference φ=0 even when the driving potentials are equal. In the second case, although the pumped current had sinusoidal dependence on φ but its value significantly decreased and we also observed nonzero pumping at φ=0 even when the driving potentials and their widths are equal, which is consistent with the recent experimental result.     

Numerical study of localization length in disordered graphene nanoribbons

In this work, we study quantum transport properties of a defective graphene nanoribbon (DGNR) attached to two semi-infinite metallic armchair graphene nanoribbon (AGNR) leads. A line of defects is considered in the GNR device with different configurations, which affects on the energy spectrum of the system. The calculations are based on the tight-binding model and Green’s function method, in which localization length of the system is investigated, numerically. By controlling disorder concentration, the extended states can be separated from the localized states in the system. Our results may have important applications for building blocks in the nano-electronic devices based on GNRs.     

含半圆弧形腔的量子波导中声学声子输运和热导特性

采用散射矩阵方法,研究了在应力自由和硬壁两种典型的边界条件下含半圆弧形腔的量子波导中声学声子输运和热导性质.结果表明在两种边界条件下声子透射谱和热导有着不同的特征.在应力自由边界条件下,能观察到普适的量子化热导现象,当结构为一理想的量子线时,在低温区域有一个量子化平台出现,而当半圆弧形结构存在时,非均匀横向宽度引发的弹性散射使得量子化平台被破坏;在硬壁边界条件下,不可能观察到量子化热导现象,热导随温度的增加单调上升;计算结果表明还可以通过调节半圆弧形结构的半径来调控声子的输运概率和热导. 关键词： 声学声子输运 热导 量子体系     

Statistical properties of Lyapunov exponents and of quantum conductance of random systems in the regime of hopping transport

The statistics of the zero-temperature conductance and the Lyapunov exponents of one-, two- and three-dimensional disordered systems in the regime of strong localization is studied numerically. In one dimension, the origin of the universality of the moments of the conductance is explained. The relation between the most probable value of the conductance and its configurational average is discussed. The relative fluctuations of the conductance (and of the resistance) are shown to grow exponentially with the system length. In higher dimensions the conductance is almost entirely determined by the smallest of the Lyapunov exponents. The statistics of the conductance is therefore the same as in the one dimensional case. A model is proposed for the treatment of the fluctuations in hopping transport at finite temperatures. An exponential dependence of the relative fluctuations of the conductance/resistance on the temperature is predicted, log (δg/g) ∞ T^?a with α = 1/(d+1). It is concluded that the presently available experimental data on the temperature dependence of the conductance fluctuations in the hopping regime can be understood by replacing the system size in the zerotemperature result for the fluctuations of the conductance by the hopping length.     

Direct evidence for quantum contact resistance effects in V-groove quantum wires

The effect of quantum contact resistance on one-dimensional (1D) electrical conductance was investigated in quantum wires (QWR) realized with V-shaped GaAs/AlGaAs heterostructure. The transition length between the electron reservoir and the QWR was controlled by employing an electric field. The required transition length is found to decrease with increasing overlap between the 2D states in the reservoir and the 1D states in the QWR.