Heat transport in low-dimensional systems

Recent results on theoretical studies of heat conduction in low-dimensional systems are presented. These studies are on simple, yet non-trivial, models. Most of these are classical systems, but some quantum-mechanical work is also reported. Much of the work has been on lattice models corresponding to phononic systems, and some on hard-particle and hard-disc systems. A recently developed approach, using generalized Langevin equations and phonon Green's functions, is explained and several applications to harmonic systems are given. For interacting systems, various analytic approaches based on the Green–Kubo formula are described, and their predictions are compared with the latest results from simulation. These results indicate that for momentum-conserving systems, transport is anomalous in one and two dimensions, and the thermal conductivity κ diverges with system size L as κ ～ L ^α. For one-dimensional interacting systems there is strong numerical evidence for a universal exponent α = 1/3, but there is no exact proof for this so far. A brief discussion of some of the experiments on heat conduction in nanowires and nanotubes is also given.     

Quantum transport in low-dimensional AlGaN/GaN systems

In this work, we investigated the magnetotransport properties of a two dimensional electron gas hosted in an AlGaN/AlN/GaN heterostructure and one-dimensional devices fabricated on it. At cryogenic temperature, high mobility and long mean free path is achieved, allowing ballistic transport experiments. Longitudinal resistivity measured in Hall bar geometry shows well-developed Shubnikov–de Haas oscillations with amplitude modulation. Amongst possible mechanisms, the zero-field spin splitting may be the origin of the observed effects. Split gate quantum point contacts were fabricated by electron beam lithography. Linear conductance measurements at zero magnetic field show clear quantized conductance plateaus at 2e ²/h and 4e ²/h. Non-perfectly quantized conductance values are found for higher plateaus, suggesting the presence of impurity scattering.     

Optical properties of nonequilibrium low-dimensional systems

The optical properties of low-dimensional carrier systems ("quantum wire" type) driven away from equilibrium are studied. The frequency and wave-vector-dependent dielectric function of a quasi-one-dimensional electron system under the action of an exciting external pumping source is derived. The optical responses of the system are obtained in terms of its nonequilibrium thermodynamic state, the latter characterized resorting to a nonequilibrium statistical ensemble formalism.     

Dynamical properties of low-dimensional and spin-Peierls systems

Properties of low-dimensional spin-Peierls systems are described by using a one-dimensional S =1/2 antiferromagnetic Heisenberg chain linearly coupled to a single phonon mode of wave vector (whose contribution is expected to be dominant). By exact diagonalizations of small rings with up to 24 sites supplemented by a finite size scaling analysis, static and dynamical properties are investigated. Numerical evidences are given for a spontaneous discrete symmetry breaking towards a spin gapped phase with a frozen lattice dimerization. Special emphasis is put on the comparative study of the two inorganic spin-Peierls compounds CuGeO₃ and NaV₂O₅ and the model parameters are determined from a fit of the experimental spin gaps. We predict that the spin-phonon coupling is 2 or 3 times larger in NaV₂O₅ than in CuGeO₃. Inelastic neutron scattering spectra are calculated and similar results are found in the single phonon mode approximation and in the model including a static dimerization. In particular, the magnon S =1 branch is clearly separated from the continuum of triplet excitations by a finite gap. Received: 30 July 1997 / Revised: 16 September 1997 / Accepted: 10 October 1997     

Correlation-induced resonances in transport through coupled quantum dots

We investigate the effect of local electron correlations on transport through parallel quantum dots. The linear conductance as a function of gate voltage is strongly affected by the interplay of the interaction U and quantum interference. We find a pair of novel correlation-induced resonances separated by an energy scale that depends exponentially on U. The effect is robust against a small detuning of the dot energy levels and occurs for arbitrary generic tunnel couplings. It should be observable in experiments on the basis of presently existing double-dot setups.     

Electric-field-dependent dispersive transport of carriers in band tails of low-dimensional systems

A theory for the dispersive transport of carriers in the presence of an electric field for the quasi-one-dimensional systems has been developed. It is assumed that localized states are distributed randomly in both space and energy coordinates and that hopping of the carriers occurs in both coordinates. The exponential form of the density of states for band tails is considered. Expressions for the time-dependent demarcation energy and mobility are calculated. The theory predicts that the mobility has three power-law decay branches with exponents nm 1, mm 1 and mm m1. Here nand mare directly proportional to the temperature and electric field respectively. The first power law is associated with the multiple-trapping mechanism and is well known. The other two power laws are new findings of the present theory. The time-of-flight experiments for hydrogenated amorphous SiN x Si/hydrogenated amorphous multilayers can be understood by the present theory on the qualitative basis.     

New quantum electron transport phenomena in low-dimensional systems in a magnetic field

In low-dimensional electron systems with an asymmetric quantizing potential in a magnetic field, the electromotive force appears in the presence of a standing acoustic wave [O.V. Kibis, Phys. Lett. A 237 (1998) 292]. The consequence of this quantum macroscopic effect is that homogeneous heating of the electron system leads to the emergence of a phonon drag of electrons, which leads to a new class of electron transport phenomena.     

Cu低维体系的结构和电子性质

基于密度泛函理论，选择generalized gradient approximation(缩写为GGA)交换作用势，使用自洽场全势的线性缀加平面波方法，计算了Cu原子组成的5种不同体系，包括面心立方晶体，两种原子面和两种原子链.结果显示，平面正六边形晶格要比正方形晶格从能量上更加稳定，原子最近邻距离稍长；而平面锯齿形原子链与直线形原子链相比也有类似的计算结果.计算还发现，锯齿形原子链中的电子态密度表现异常，能带出现间隙.另外，对比不同体系的态密度和结构，分析了量子限制和原子构型对体系电子性质的影响. 关键词： 原子链 电子结构 平面波方法 密度泛函理论     

Collective effects in the transport properties of two-dimensional electron systems

The results of the experimental study of the nontraditional manifestations of collective effects in the transport properties of two-dimensional electron systems are reported.     

Heat transport in low-dimensional Heisenberg antiferromagnets

In this paper we study thermal transport in the one-dimensional spin S=1 and the two dimensional spin S=1/2 Heisenberg antiferromagnets, using the modified spin wave theory and the Kubo linear response formalism, to calculate the thermal conductivity. The low-temperature thermal Drude weights, in both cases, are non-zero at finite temperature indicating a ballistic behavior.     

Frustrations in low-dimensional magnetic systems

On the basis of exact analytical solutions for spin-spin correlation functions in the one-dimensional 3-state [1] and 4-state [2] standard Potts models and Ising model [3] with allowance for the interactions between nearest neighbors J and next-nearest neighbors J′, phenomena of the appearance and disappearance of frustrations have been investigated, depending on the signs of J and J′ and the ratio of the interactions. In the Ising model, these phenomena have been studied on triangular, hexagonal, and kagomé lattices on the basis of exact analytical solutions for the maximum values of the Kramers-Wannier matrices obtained in [4, 5].     

Short-wavelength plasmons in low-dimensional systems

The dispersion of plasma waves in systems of various dimensions is investigated up to the end point of the spectrum. In 2D and 3D systems, the plasmon spectrum still ends (due to Landau damping) within the applicability range of the quasi-classical approximation, i.e., for ?k ? p _F (?k is the plasmon momentum and p _F is the electron Fermi momentum). In 1D systems, the results are qualitatively different, since the Landau damping is concentrated in a region where the quantum effects cannot be ignored. This peculiarity of 1D systems gives rise to undamped branches of acoustic plasmons with a phase velocity lower than the electron Fermi velocity in multicomponent 1D plasmas.     

Correlation-induced spectral changes dependent upon spatiotemporal interference effects

A wave-front folded interferometer consisting of a Kösters prism and an image forming lens provides an excellent way to make a precision measurement of correlation-induced spectral changes. Experiments are successfully made by incorporating a primary spectral source of super-luminescent diodes. The diode emits a Gaussian-like spectrum. Theoretical background for the measurement is given in the framework of geometric optics. It is shown theoretically and experimentally that the spectral changes are induced by two causes: one is the complex degree of spectral coherence of the secondary source, and the other the time delay between the interfering optical waves. No spectral change takes place if the secondary source satisfies a spatially incoherent condition at particular optical frequency, whereas the spectrum changes most clearly if a spatially coherent condition is satisfied.     

Multiplasmon laser gain in low-dimensional systems

The light absorption and laser gain in quantum wells are calculated using the cumulant expansion method and the fluctuation-dissipation theorem with allowance made for the strong Coulomb interaction of charge carriers. It is shown that the multiplasmon transitions result in a smoothening of the absorption spectrum and a shift in the absorption edge toward the long-wavelength range. The theoretical laser gain spectra are in agreement with the available experimental data. For In_0.05Ga_0.95As quantum wells, the laser gain g = 50 cm^?1 is reached at an electron density nd₀ = 1.64 × 10¹² cm^?2.     

Quasi-stationary states in low-dimensional Hamiltonian systems

We address a simple connection between results of Hamiltonian non-linear dynamical theory and thermostatistics. Using a properly defined dynamical temperature in low-dimensional symplectic maps, we display and characterize long-standing quasi-stationary states that eventually cross over to a Boltzmann–Gibbs-like regime. As time evolves, the geometrical properties (e.g., fractal dimension) of the phase space change sensibly, and the duration of the anomalous regime diverges with decreasing chaoticity. The scenario that emerges is consistent with the non-extensive statistical mechanics one.     

Exotic quantum order in low-dimensional systems

Strongly correlated quantum systems in low dimensions often exhibit novel quantum ordering. This ordering is sometimes hidden and can be revealed only by examining new “dual” types of correlations. Such ordering leads to novel collection modes and fractional quantum numbers. Examples will be presented from quantum spin chains and the quantum Hall effect.     

Dynamic self-polarization of nuclei in low-dimensional systems

A mechanism of dynamic self-polarization of nuclei is studied which is weakly temperature-dependent and operates efficiently in low-dimensional systems (quantum wells, quantum dots). It is due to the hyperfine interaction of nuclei with excitons whose spin polarization is artificially maintained at zero (by illuminating with unpolarized light) but for which nonequilibrium alignment occurs. Nuclear self-polarization arises as a result of the conversion of the alignment of excitons into nuclear orientation in the effective magnetic field of the polarized nuclei. Pis’ma Zh. éksp. Teor. Fiz. 70, No. 2, 124–129 (25 July 1999)