Dissertations / Theses on the topic 'One dimensional quasi periodic systems'

This thesis contributes a novel receptance coupling technique to analyse dynamic response localization induced by bandgap mechanisms in advanced periodic light weight material and structural systems. One-dimensional structural systems are used to illustrate the technique with experiments. Localization induced by disorder and nonlinearity is investigated using numerical simulations. Insights on bandgap localization mechanisms offered by the receptance technique can be used to design periodic composite materials such as Phononic Crystals and metamaterials, and periodic structures with enhanced vibroacoustic performance characteristics.

The study of electron transport in mesoscopic systems has recently turned to the observation of time dependent single electron e ects, where the electron transport is frequency locked to an external potential. Such devices are expected to form the basis of a standard of electric current, long sought after by the metrological community, to provide a representation of the ampere and to be compared with existing quantum standards of the volt and ohm. This thesis details new experimental investigations of one such system. The piezoelectric interaction between an acoustic wave travelling on the surface of a GaAs heterostructure and electrons in a quasi-1D sys- tem de ned therein generates a current which, under certain conditions, can be quantized in units of ef where e is the electron charge and f the surface acoustic wave frequency. The general conditions under which this 'single electron acoustoelectric effect' is observable are studied, and experimental results presented which demonstrate that the e ffect represents a possible route towards a current standard. The precision of the e ffect is assessed in a variety of experimental situations and device geometries. Several ways to enhance the precision of the eff ect are presented. Firstly a weak counterpropagating SAW beam produces a dynamic tuning of the SAW potential. Observations of a quantized acoustoelectric current are then presented in novel etched-channel SAW devices which aff ord a more precise current by allowing better control over the channel geometry. The presently attainable precision of the technique is at the level of 10's of ppm. Detailed measurements are presented of the single electron acoustoelectric e ffect in a magnetic fi eld applied perpendicular to the two-dimensional electron gas. Commensurability oscillations are observed for the interval of current between acoustoelectric current plateaux when the cyclotron diameter and SAW wavelength are comparable. The oscillations show a particular phase dependence which results in an oscillating plateau slope as a function of applied magnetic fi eld. Results are also presented from measurements of the interaction between a surface acoustic wave and open 1D systems. Here the quantized current is not observed, but instead the behaviour of the measured current depends sensitively on the geometry of the channel. Two situations are possible in this regime. Interaction between the SAW and slow electrons in the uppermost 1D subband within the channel produces an oscillatory acoustoelectric current as a function of subband occupancy. These oscillations are observed in all subbands of clean constrictions for the first time. Secondly, interaction between the SAW and electrons in the device leads causes a contribution to the acoustoelectric current which is proportional to the quantized channel conductance, this contribution dominating transport in certain device geometries.

En esta tesis estudiamos propiedades de transporte cuántico en guías de onda finitas periódicas quasi-unidimensionales, cuya dinámica clásica asociada es difusiva. Nos enfocamos en el límite semiclásico el cual nos permite emplear un modelo de Teoria de Matrices Aleatorias (TMA) para describir el sistema. El requisito de difusión normal de la dinámica clásica restringe la configuración de la celda unitaria a tener horizonte finito, y significa que los ensembles apropi- ados de TMA son los ensembles circulares de Dyson. El sistema que consideramos corresponde a una configuración de scattering, compuesto de una cadena finita de L celdas unitarias (clási- camente caóticas y con horizonte finito) la cual esta conectada a dos guías planas semi-infinitas en sus extremos. Las partículas dentro de esta cavidad son libres y solo interactúan con los bordes a través de choques elásticos; esto significa que las ondas son descritas por una ecuación de Helmholtz con condiciones de borde tipo Dirichlet en las paredes la guía. Por lo tanto, no hay desorden en el sistema y el scattering es debido a la geometría de la cadena la cual es estática. El análogo al ensemble de desorden es un ensemble de energía, definido sobre un intervalo clási- camente pequeño pero cuyo ancho es varias veces un espaciamiento de niveles promedio (mean level spacing). El número de canales propagativos en las guías planas es N y el límite semiclásico se alcanza cuando N → ∞. Un número importante para las propiedades de transporte en cadenas periódicas es el número de modos de Bloch NB del sistema extendido infinito asociado. Previamente, ha sido conjeturado que en sistemas fuertemente difusivos en el límite semiclásico ∼√(N D), donde D es la constante de difusión clásica. Hemos comprobado numéricamente este resultado en una guía de ondas con forma de coseno obteniendo excelente concordancia. Luego, mediante la aproximación de Machta-Zwanzig para D obtuvimos la expresión analítica N/π, la cual concuerda perfectamente con los ensembles circulares. Por otro lado, hemos estudiado la conductancia (adimensional) de Landauer g como función de L y N en la guía coseno y mediante nuestro modelo RMT para cadenas periódicas. Hemos encontrado que muestra dos regímenes. Primero, para cadenas de largo LN la dinámica es difusiva tal como en un cable desordenado en el régimen metálico, donde se observa el escalamiento ohmnico típico con = N/(L+1). En este régimen, la distribución de conductancias es Gaussiana con una varianza pequeña (tal que <1/g> ≈ 1/) pero que crece linealmente con L. Luego, para sistemas más largos con L ≫ N , su naturaleza periódica se hace relevante y la conductancia alcanza un valor asintótico constante ∼ NB. En este caso, la distribución de la conductancia pierde su forma Gaussiana convirtiéndose en una distribución multimodal debido a los valores discretos (enteros) que NB puede tomar. La varianza alcanza un valor constante ∼√N cuando L → ∞. Comparando la conductancia para los ensembles circulares unitario y ortogonal, mostramos que un efecto de localización débil está presente en ambos regímenes. Finalmente, estudiamos la parte no propagativa de la conductancia en el régimen Bloch-balístico, la cual está dominada por el modo con la longitud de decaimiento mayor ℓ que va a cero como gnp = 4 e−2L/ℓ cuando L → ∞. Usando nuestro modelo de TMA obtuvimos que bajo un escalamiento apropiado la pdf P (ℓ) converge, cuando N → ∞, a una distribución límite con cola algebraica P(ℓ) ∼ℓ−3 para ℓ → ∞; esto nos permitió conjeturar el decaimiento ∼ L−2, el cual fue observado en nuestra guía de ondas coseno.

In this thesis I present experimental measurements on a number of different quasi-one and quasi-two-dimensional metallic crystal systems susceptible to density-wave formation. I outline the discovery of a density-wave superstructure found via X-ray diffraction measurements in the quasi-two-dimensional Na2Ti2As2O and Na2Ti2Sb2O compounds. Na2Ti2Sb2O and Na2Ti2As2O are members of the Ti-based oxy-pnictides a group of compounds which exhibit complex phase diagrams and share structural similarities with the high temperature superconductors. Temperature-dependent X-ray diffraction measurements confirmed the superstructure in both materials to be concomitant with transitions seen in resistivity and magnetic data. The observation of the superstructure combined with results from other experimental techniques demonstrated the transition to be a charge-density-wave. I also present results on a series of intercalated charge-density-wave compounds NixZrTe3. NixZrTe3 was measured using X-ray diffraction and ARPES to investigate the effects of chemical pressure on charge-density-wave formation. The transition temperature for density-wave formation in this series of compounds had been previously shown to vary as a result of Ni-content. X-ray diffraction measurements on the series revealed no changes in the wavevector of the associated superstructure modulation across the series. However ARPES measurements on NixZrTe3 showed subtle changes in the binding energy of the one-dimensional band associated with the charge-density-wave thought to be a result of the Ni-intercalation. Through a combination of XPS, EDX and ARPES measurements the Ni-content in these crystals was deduced to be much lower than growth parameters suggested. Finally I describe the construction and testing of a straining device designed specifically for use with X-ray synchrotron type measurements. The straining device was successfully tested at the I16 beamline at the Diamond Light Source and shown to induce dynamic strain in a test sample of M2Mo6Se6. Further testing at the ID28 beamline at the ESRF revealed that the strain induced in a M2Mo6Se6 was significant and resulted in a change in the lattice dynamics of the material.

Thesis (Ph. D.)--Physics, Georgia Institute of Technology, 2005.
Jean Bellissard, Committee Member ; Turgay Uzer, Committee Member ; Roman Grigoriev, Committee Member ; Konstantin Mischaikow, Committee Member ; Predrag Cvitanovic, Committee Chair. Vita. Includes bibliographical references.

Cette thèse présente des mesures de transport électronique dans des systèmes quasi-unidimensionnels (quasi-1D) sous champ magnétique intense. Deux systèmes différents présentant un confinement électrique quasi-1D ont été considérés: les peapods de carbone (C60@SWCNTs) et les nanofils d'InAs. L’objectif de ces travaux consiste à sonder les propriétés électroniques spécifiques de ces systèmes quasi-1D par les mesures de magnétotransport sur les nano-objets uniques. Dans les deux cas, les expériences sous champs magnétiques intenses ont été accompagnée par des caractérisations structurales et des mesures de conductance à champ magnétique nul.L'encapsulation de diverses molécules à l'intérieur de nanotubes de carbone (CNTs), comme par exemple les fullerènes C60, constitue une des voies prometteuses vers l'accordabilité de la conductance des CNTs. Parmi la grande variété des nanotubes de carbone remplis, les peapods représentent une structure hybride pionnière découvert en 1998. Depuis lors, leur structure électronique a fait l’objet d’études théoriques controversées avec un nombre limité de réalisations expérimentales. Dans cette thèse, les propriétés électroniques des peapods individuels ont été étudiés en combinant les mesures de spectroscopie micro-Raman et de magnétotransport sur les mêmes échantillons. Nous avons constaté que les C60 encapsulés modifient fortement la structure de bande électronique des nanotubes semi-conducteurs au voisinage du point de neutralité de charge. Cette modification comprend un déplacement rigide de la structure électronique et un remplissage partiel de la bande interdite. Nous avons aussi montré que l’excitation UV sélective des fullerènes conduit à une forte modification du couplage électronique entre les C60 et le CNT induite par la coalescence partielle des C60 et de leur distribution à l'intérieur du tube. Les résultats expérimentaux sont supportés par des simulations numériques de la densité d'états et de la conductance des nanotubes de carbone avec des fullerènes fusionnés à l'intérieur (K. Katin, M. Maslov).Les nanofils semiconducteurs (sc-NWs) font l'objet de recherches actives depuis ces dix dernières années. Ils représentent des systèmes modèles pour l’étude des propriété électronique objet quasi-1D. Ils représentent en outre des possibilités de modulation de la structure de bande aussi que de contrôle de la densité de porteurs. Dans ce domaine de recherche, les nanofils semi-conducteurs à base de composes III-V tel que InAs, ont une place particulière en raison de la faible masse effective des porteurs de charge. Nous avons étudié la conductance de nanofils individuels dans une large gamme de champs magnétiques (jusqu'à 60T). Les mesures en champ nul et en champ faible ont démontré un transport faiblement diffusif dans ces nanofils. Les mesures de transport sous champ magnétique intense ont révélé une forte chute de la conductance au dessus d'un champ critique qui s'élève clairement avec l'énergie de Fermi. Cet effet est interprété par la perte de canaux de conduction une fois que toutes les sous-bandes magnéto-électriques, décalés vers les hautes énergies par le champ magnétique, ont traversé l'énergie de Fermi. Les calculs de structure de bande préliminaires (Y-M. Niquet), en prenant en compte les confinements latéraux et magnétiques, sont en bon accord qualitatif avec les résultats observés dans le régime de champ magnétique intense. Ce résultat est la première observation des effets de structure de bande dans les expériences de magnéto-transport sur les sc-NWs
The scope of this thesis is related to the electronic properties of quasi 1D systems probed by high field magnetotransport. Two different systems exhibiting quasi-1D confinement have been considered: carbon C60 peapods (C60@SWCNTs) and InAs semiconductor nanowires. The magnetotransport measurements on single nano-objets have been used to investigate the specific electronic structure of these 1D systems. In both cases, the high magnetic fields experiments have been supported by structural characterisation and conductance measurements at zero field.The encapsulation of various molecules inside carbon nanotubes (CNTs), as for instance C60 fullerenes encapsulated in SWCNT, constitutes promising routes towards the tunability of the CNT conductance. Among the wide variety of filled CNTs, peapods represent a pioneer hybrid structure discovered in 1998. Since that time, their electronic structure has been subjected to intense and controversial theoretical studies together with a limited number of experimental realizations. In this thesis the electronic properties of individual fullerene peapods have been investigated by combining micro-Raman spectroscopy and magnetotransport measurements on the same devices. We bring evidence that the encapsulated C60 strongly modify the electronic band structure of semiconducting nanotubes in the vicinity of the charge neutrality point, including a rigid shift and a partial filling of the energy gap. In addition by playing with a selective UV excitation of the fullerene, we demonstrate that the electronic coupling between the C60 and the CNT is strongly modified by the partial coalescence of the C60 and their distribution inside the tube. The experimental results are supported by numerical simulations of the Density of States and the conductance of CNTs with coalesced fullerenes inside (K. Katin, M. Maslov).Semiconductor nanowires (sc-NWs) are being the subject of intense researches started a decade ago. They represent model systems for the exploration of the electronic properties inerrant to the quasi1-D confinement. Moreover they offer the possibility to play with band structure tailoring and carrier doping. In this direction III-V sc-NWs such as InAs NWs have played a particular role due to the small electron effective mass. We have studied the high magnetic field conductance of single nanowires. Prior to the high field measurements, the zero and low field investigations have demonstrated a weakly diffusive regime of the carrier transport in these wires. The high field investigations have revealed a drastic conductance drop above a critical field, which clearly rises with the Fermi energy. This effect is interpreted by the loss of conducting channels once all the magneto-electric subbands, shifted toward the high energy range by the magnetic field, have crossed the Fermi energy. Preliminary band structure calculations (Y-M. Niquet), taking into account the lateral and magnetic confinements, are in fairly good qualitative agreement with the observed result in the high field regime. This result is the first observation of band structure effects in magneto-transport experiments on sc-NWs

We studied the structural instabilities of one-dimensional (1D) and quasi-one-dimensional (Q1D) electron-phonon systems at low temperature through two models, SuSchrieffer-Heeger (SSH) and molecular crystal (CM) with and without spin. The phase diagrams are obtained using a Kadanoff-Wilson renormalization group approach (GR). For the 1D half-filled system the study of the frequency dependence of the electronic gap allowed us to connect continuously the two limits, adiabatic and non-adiabatic. The Peierls and Cooper channels interference and the quantum fluctuations reduce the gap. A regime change occurs when the frequency becomes of the order of mean field gap, marking a quantum-classical crossover that is the Kosterlitz-Thouless type. At this level, the effective coupling behaves in power law function on frequency. For the case with spin, a gapped Peierls state is maintained in the non-adiabatic limit, while for the case without spin, the system transits to ungapped disordered state, namely the Luttinger liquid stat (LL). For the SSH model without spin, the GR confirms the existence of a threshold phonon coupling beyond which the gap is restored. The study of the rigidities of the two models without spin allowed us to trace the main features of the LL state predicted by the bosonization method. The study of the Holstein-Hubbard model has allowed us not only to reproduce the phase diagrams already obtained by the Monte Carlo method, but to highlight two additional phases, namely, free fermions phase and the bond charge-density-wave phase. We have extended this study to the quarter-filled Q1D Peierls systems at finite temperature. Within the SSH model, an unconventional superconducting phase with spin singlet symmetry SS-s emerges at low temperature when the deviation to the perfect nesting of the Fermi surface is strong enough. Peierls-SS transition is characterized by the presence of a quantum critical point at low frequency and by a power law behavior of the transition temperature as a function of frequency with an exponent identical to one of 1D system. This exponent which universality has been verified contrasts with the BCS result. Coulomb interactions have been introduced through the study of the extended SSH-Hubbard model. The extension of this work to half-filled SSH and CM cases was also performed.

Estudamos as propriedades eletrônicas de dois sistemas quase-unidimensionais distintos, resolvendo autoconsistentemente as equações de Schrödinger e Poisson.O método usado para calcular a estrutura eletrônica deste sistema e baseada na solução da equação de Schrödinger dependente do tempo usando a técnica do Split-Operator. No primeiro sistema estudamos os efeitos da corrugação periódica da interface da estrutura n-AlxGa1-xAs/GaAs na densidade eletrônica ao longo desta interface. A forma geométrica desta interface e do tipo dente de serra. Nas camadas de inversão convencionais, os elétrons estão distribuídos uniformemente ao longo da interface plana da heteroestrutura, mas devido à forma dente de serra desta estrutura, os elétrons se distribuem de maneira não uniforme ao longo da interface, produzindo um gás de elétrons quase-unidimensional. A estrutura que investigamos possui um período de 806 ANGSTROM e uma densidade residual uniforme de impurezas aceitadoras da ordem de 1015 cm-3. Calculamos a estrutura eletrônica do gás de elétrons unidimensional confinado na interface corrugada em função da voltagem aplicada ao gate, da densidade de impurezas doadoras e da temperatura. Os resultados obtidos para a densidade eletrônica mostram que, dependendo da densidade de impurezas doadoras, haverá formação de u gás de elétrons quase-unidimensional nos vértices da estrutura dente de serra. O segundo sistema que estudamos é constituído por um gás de elétrons bidimensional, formado na interface de uma camada de Al1-xGa1-xAs com uma camada de GaAs, sobre a qual, temos uma estrutura periódica de \"gates\". Aplicando-se uma voltagem negativa sobre os \"gates\" teremos a formação de fios quânticos nas regiões entre os \"gates\". Neste sistema observamos a transição de um sistema quase-bidimensional para um quase-unidimensional. Investigamos suas propriedades eletrônicas em funçãoo da temperatura, da voltagem aplicada aos \"gates\" e da densidade de impurezas doadoras.
We have studied the electronic properties of two different quasi-one-dimensional systems solving self-consistently the Schrödinger and Poisson equation. The method we use to calculate the electronic levels is based on the solution of the time-dependent Schrödinger equation using the split-operator technique. In the first system we have studied, we present a theoretical calculation of the electronic structure of v-groove quantum wires confined in modulation-doped n-AlxGa1-xAs/GaAs. The system investigated is saw tooth corrugated by bendings with period of 850 ANGSTROM. Results of the electronic structure are obtained as a function of the gate voltage and the donor impurity density. The electronic density shows the existence of a quasi one-dimensional electron gas. The second system studied here is composed by a two-dimensional electron gas confined at the interface of an Al1-xGa1-xAs/GaAs heterostructure, on top of which there is a periodic structure of gates. When a negative voltage is applied to the gates, the regions at the interface beneath them are depleted and quantum wires are formed. We have calculated the electronic structure of subband of that system. We investigated the electronic properties of the quantum wires as a function of gate voltage, from which we determine the threshold between the 2D and ID transitions, the temperature and the ionized donor density.

Consideramos os efeitos de desordem ou aperiodicidade sobre três sistemas magnéticos distintos. Inicialmente, apresentamos um modelo fenomenológico para descrever a dependência térmica da magnetização remanente induzida por diluição numa classe de antiferromagnetos quase-unidimensionais. O modelo trata exatamente as correlações ao longo da direção dominante, levando em conta as demais interações por meio de um campo efetivo. Em seguida, utilizamos uma aproximação autoconsistente de Bethe-Peierls para avaliar os efeitos de um campo cristalino aleatório sobre os diagramas de fases de um modelo de Ising de spins mistos. Mostramos que a desordem é capaz de modificar a natureza dos pontos multicríticos existentes no limite uniforme do modelo. Finalmente, estudamos os efeitos de interações aleatórias ou aperiódicas sobre o comportamento da cadeia XX quântica em baixas temperaturas, através de câlculos numéricos baseados no mapeamento do sistema em um modelo de férmions livres. Apontamos evidências de que, em temperatura zero, existe um único ponto fixo universal, característico de uma fase de singleto aleatório, que governa o comportamento do modelo na presença de interações desordenadas. No caso de interações aperiódicas,obtemos resultados consistentes com previsões de grupo de renormalização, indicando, para uma certa classe de seqüências de substituição, um comportamento semelhante àquele associado à desordem.
We consider effects of disorder or aperiodicity on three different magnetic systems. First, we present a phenomenological model to describe the thermal dependence of the dilution-induced remanent magnetization in a class of quasi-one-dimensional antiferromagnets. The model treats correlations along the dominant direction in an exact way, while including the remaining inte-. i ractions via an effective field. Then, we use a self-consistent Bethe-Peierls ~ j .. approximation to gauge the effects of a random crystal field on the phase diagram of a mixed-spin Ising mode!. We show that disorder may have profound effects on the multicritical behavior associated with the uniform limit of the mo de!. Finally, we study effects of random or aperiodic interactions on the behavior of the quantum XX chain at low temperatures, by performing numerical calculations based on a mapping of the system onto a free-fermion mo de!. . We present evidence that, at zero temperature, there exists a single, universal fixed-point, associated with a random-singlet phase, which governs the behavior of the model in the presence of disordered interactions. In the case of aperiodic interactions, our results are consistent with renormalizationgroup predictions, indicating, for a certain class of substitution sequences, a behavior similar to the one induced by disorder.

In this thesis, we study different aspects of many body localization in closed quantum systems. Many body localized systems are isolated interacting quantum systems that fail to thermalize on their own (non-ergodic) and thus violates the eigenstate thermalization hypothesis (ETH), which guarantees thermalization in quantum systems. These systems are known to have area law entanglement entropy even at high energy densities and have been argued to have emergent conservation laws, which prevent thermalization. The presence of thermal-MBL transitions has been confirmed in the interacting disordered systems and in the presence of deterministic quasiperiodic potentials, at least in one dimension. Initially, the MBL phase was introduced by showing that localization persists even in the presence of interactions in a system with a localized single particle spectrum. However, the fate of many body localization in interacting systems with coexisting localized and extended single particle states has been questioned recently and has been shown to be model-dependent. In the first work, we propose a dimensionless criterion based on the single particle spectrum, which can determine the presence or absence of the thermal-MBL transitions in the interacting quasiperiodic systems with coexisting localized and extended states. In the second work, we calculate the transport properties and the level spacing statistics in an interacting one dimensional system in the presence of similar quasiperiodic potential. The many-body spectrum of such a quasiperiodic system has been argued to have a non-ergodic extended phase, which is associated with the violation of ETH and volume law satisfying entanglement entropy. In this work, we show sub-diffusive transport in this non-ergodic extended phase in contrast to the diffusive transport in the thermal phase and no transport in the MBL phase. In the third work, we consider a tight-binding model in the Fock lattice with correlated onsite disorders and show the presence of a localization transition in such Fock lattice models. We consider different functional forms of correlations for the onsite Fock lattice potentials keeping the effective disorder strength fixed and discuss the possibility of localization transitions driven by the correlation among the onsite terms. In the fourth work, we develop a recursive method to calculate the exact Green’s functions in the Fock lattice, where each slice of the Fock lattice is added in recursion while calculating different elements of the total Green’s function. Using this method, we calculate different quantities to locate the thermal-MBL transition in interacting disordered systems as an alternative to the exact diagonalization method typically used in studies of MBL systems.

This thesis reports our work on transport related problems in mesoscopic physics using analytical as well as numerical techniques. Some of the problems we studied are: effect of interactions and static impurities on the conductance of a ballistic quantum wire[1], aspects of quantum charge pumping [2, 3, 4], DC and AC conductivity of a (dissipative) quantum Hall (edge) line junctions[5, 6], and junctions of three or more Luttinger liquid (LL)quantum wires[7]. This thesis begins with an introductory chapter which gives a brief glimpse of the underlying physical systems and the ideas and techniques used in our studies. In most of the problems we will look at the physical effects caused by e-e interactions and static scattering processes. In the second chapter we study the effects of a static impurity and interactions on the conductance of a 1D-quantum wire numerically. We use the non-equilibrium Green’s function (NEGF) formalism along with a self-consistent Hartree-Fock approximation to numerically study the effects of a single impurity and interactions between the electrons (with and without spin) on the conductance of a quantum wire [1]. We study the variation of the conductance with the wire length, temperature and the strength of the impurity and electron-electron interactions. We find our numerical results to be in agreement with the results obtained from the weak interaction RG analysis. We also discover that bound states produce large density deviations at short distances and have an appreciable effect on the conductance which is not captured by the renormalization group analysis. In the third chapter we use the equations of motion (EOM) for the density matrix and Floquet scattering theory to study different aspects of charge pumping of non-interacting electrons in a one-dimensional system. We study the effects of the pumping frequency, amplitude, band filling and finite bias on the charge pumped per cycle, and the spectra of the charge and energy currents in the leads[2]. The EOM method works for all values of parameters, and gives the complete time-dependences of the current and charge at any site of the system. In particular we study a system with oscillating impurities at several sites and our results agree with Floquet and adiabatic theory where these are applicable, and provides support for a mechanism proposed elsewhere for charge pumping by a traveling potential wave in such systems. For non-adiabatic and strong pumping, the charge and energy currents are found to have a marked asymmetry between the two leads, and pumping can work even against a substantial bias. We also study one-parameter charge pumping in a system where an oscillating potential is applied at one site while a static potential is applied in a different region [3]. Using Floquet scattering theory, we calculate the current up to second order in the oscillation amplitude and exactly in the oscillation frequency. For low frequency, the charge pumped per cycle is proportional to the frequency and therefore vanishes in the adiabatic limit. If the static potential has a bound state, we find that such a state has a significant effect on the pumped charge if the oscillating potential can excite the bound state into the continuum states or vice versa. In the fourth chapter we study the current produced in a Tomonaga-Luttinger liquid (TLL) by an applied bias and by weak, point-like impurity potentials which are oscillating in time[4]. We use bosonization to perturbatively calculate the current up to second order in the impurity potentials. In the regime of small bias and low pumping frequency, both the DC and AC components of the current have power law dependences on the bias and pumping frequencies with an exponent 2K−1 for spinless electrons, where Kis the interaction parameter. For K<1/2, the current grows large for special values of the bias. For non-interacting electrons with K= 1, our results agree with those obtained using Floquet scattering theory for Dirac fermions. We also discuss the cases of extended impurities and of spin-1/2 electrons. In chapter five, we present a microscopic model for a line junction formed by counter or co-propagating single mode quantum Halledges corresponding to different filling factors and calculate the DC [5] and AC[6] conductivity of the system in the diffusive transport regime. The ends of the line junction can be described by two possible current splitting matrices which are dictated by the conditions of both lack of dissipation and the existence of chiral commutation relations between the outgoing bosonic fields. Tunneling between the two edges of the line junction then leads to a microscopic understanding of a phenomenological description of line junctions introduced by Wen. The effect of density-density interactions between the two edges is considered exactly, and renormalization group (RG) ideas are used to study how the tunneling parameter changes with the length scale. The RG analysis leads to a power law variation of the conductance of the line junction with the temperature (or other energy scales) and the line junction may exhibit metallic or insulating phase depending on the strength of the interactions. Our results can be tested in bent quantum Hall systems fabricated recently. In chapter six, we study a junction of several Luttinger Liquid (LL) wires. We use bosonization with delayed evaluation of boundary conditions for our study. We first study the fixed points of the system and discuss RG flow of various fixed points under switching of different ‘tunneling’ operators at the junction. Then We study the DC conductivity, AC conductivity and noise due to tunneling operators at the junction (perturbative).We also study the tunneling density of states of a junction of three Tomonaga-Luttinger liquid quantum wires[7]. and find an anomalous enhancement in the TDOS for certain fixed points even with repulsive e-e interactions.

This thesis reports our work on transport related problems in mesoscopic physics using analytical as well as numerical techniques. Some of the problems we studied are: effect of interactions and static impurities on the conductance of a ballistic quantum wire[1], aspects of quantum charge pumping [2, 3, 4], DC and AC conductivity of a (dissipative) quantum Hall (edge) line junctions[5, 6], and junctions of three or more Luttinger liquid (LL)quantum wires[7]. This thesis begins with an introductory chapter which gives a brief glimpse of the underlying physical systems and the ideas and techniques used in our studies. In most of the problems we will look at the physical effects caused by e-e interactions and static scattering processes. In the second chapter we study the effects of a static impurity and interactions on the conductance of a 1D-quantum wire numerically. We use the non-equilibrium Green’s function (NEGF) formalism along with a self-consistent Hartree-Fock approximation to numerically study the effects of a single impurity and interactions between the electrons (with and without spin) on the conductance of a quantum wire [1]. We study the variation of the conductance with the wire length, temperature and the strength of the impurity and electron-electron interactions. We find our numerical results to be in agreement with the results obtained from the weak interaction RG analysis. We also discover that bound states produce large density deviations at short distances and have an appreciable effect on the conductance which is not captured by the renormalization group analysis. In the third chapter we use the equations of motion (EOM) for the density matrix and Floquet scattering theory to study different aspects of charge pumping of non-interacting electrons in a one-dimensional system. We study the effects of the pumping frequency, amplitude, band filling and finite bias on the charge pumped per cycle, and the spectra of the charge and energy currents in the leads[2]. The EOM method works for all values of parameters, and gives the complete time-dependences of the current and charge at any site of the system. In particular we study a system with oscillating impurities at several sites and our results agree with Floquet and adiabatic theory where these are applicable, and provides support for a mechanism proposed elsewhere for charge pumping by a traveling potential wave in such systems. For non-adiabatic and strong pumping, the charge and energy currents are found to have a marked asymmetry between the two leads, and pumping can work even against a substantial bias. We also study one-parameter charge pumping in a system where an oscillating potential is applied at one site while a static potential is applied in a different region [3]. Using Floquet scattering theory, we calculate the current up to second order in the oscillation amplitude and exactly in the oscillation frequency. For low frequency, the charge pumped per cycle is proportional to the frequency and therefore vanishes in the adiabatic limit. If the static potential has a bound state, we find that such a state has a significant effect on the pumped charge if the oscillating potential can excite the bound state into the continuum states or vice versa. In the fourth chapter we study the current produced in a Tomonaga-Luttinger liquid (TLL) by an applied bias and by weak, point-like impurity potentials which are oscillating in time[4]. We use bosonization to perturbatively calculate the current up to second order in the impurity potentials. In the regime of small bias and low pumping frequency, both the DC and AC components of the current have power law dependences on the bias and pumping frequencies with an exponent 2K−1 for spinless electrons, where Kis the interaction parameter. For K<1/2, the current grows large for special values of the bias. For non-interacting electrons with K= 1, our results agree with those obtained using Floquet scattering theory for Dirac fermions. We also discuss the cases of extended impurities and of spin-1/2 electrons. In chapter five, we present a microscopic model for a line junction formed by counter or co-propagating single mode quantum Halledges corresponding to different filling factors and calculate the DC [5] and AC[6] conductivity of the system in the diffusive transport regime. The ends of the line junction can be described by two possible current splitting matrices which are dictated by the conditions of both lack of dissipation and the existence of chiral commutation relations between the outgoing bosonic fields. Tunneling between the two edges of the line junction then leads to a microscopic understanding of a phenomenological description of line junctions introduced by Wen. The effect of density-density interactions between the two edges is considered exactly, and renormalization group (RG) ideas are used to study how the tunneling parameter changes with the length scale. The RG analysis leads to a power law variation of the conductance of the line junction with the temperature (or other energy scales) and the line junction may exhibit metallic or insulating phase depending on the strength of the interactions. Our results can be tested in bent quantum Hall systems fabricated recently. In chapter six, we study a junction of several Luttinger Liquid (LL) wires. We use bosonization with delayed evaluation of boundary conditions for our study. We first study the fixed points of the system and discuss RG flow of various fixed points under switching of different ‘tunneling’ operators at the junction. Then We study the DC conductivity, AC conductivity and noise due to tunneling operators at the junction (perturbative).We also study the tunneling density of states of a junction of three Tomonaga-Luttinger liquid quantum wires[7]. and find an anomalous enhancement in the TDOS for certain fixed points even with repulsive e-e interactions.

碩士
國立清華大學
物理學系
91
We discover a hidden structure for the complex renormalization group (RG) equations of quasi-one-dimensional (Q1D) systems. It turns out that we can rewrite RG equations by the derivative of a scalar function, which is referred as RG potential. This structure provides a clear picture for the existence of fixed rays in Q1D systems. We also investigate the stability of these fixed rays and therefore introduce a new classification for the interactions under RG.

碩士
國立臺灣大學
物理研究所
98
The thesis presents a theoretical study of spin transport in one-dimensional systems with periodic structures. In this thesis, all the transport is in the ballistic regime and one-dimensional systems are made by confining electrons in two-dimensional systems. The main purpose of this thesis is to investigate the effects of spin-orbit coupling (SOC) and magnetic field on spin transport, especially spin filtering in one-dimensional systems with periodic structures. In solids, SOC describes the interaction between the momentum of an electron and its own spin. The symmetry breaking of space inversion of the solid structure gives rise to two kinds of SOC: (i) Rashba SOC and (ii) Dresselhaus SOC. Rashba SOC, originated from structure inversion asymmetry (SIA), can be tuned by voltage gates while Dresselhaus SOC, originated from bulk inversion asymmetry (BIA), can be not easily controlled. Two methods are used to create periodic SOC in space: (i) to modulate Rashba SOC periodically by voltage gates and (ii) making a periodically curved wire. The periodic SOC in space can make a band structure with spin-dependent band gaps. SOC contributes an effective magnetic field, which has time reversal symmetry. With the two methods, we can control the effective magnetic field. The influences of the absolute value and the direction of the effective magnetic field are studied. It have been shown that without breaking time reversal symmetry, single-channel one-dimensional systems can not have spin filtering properties. Therefore, the effect of an exterior magnetic filed applied to the one-dimensional systems is examined. This exterior magnetic filed moves the spin-dependent band gaps to different energy levels. When electrons'' energies lie in these spin-dependent band gaps, full spin-polarized current is produced. In chapter 1, the motivation is mentioned in the start and an introduction to electron transport in the ballistic regime and the origin of SOC is given . Chapter 2 will be devoted to confined quantum systems in curvilinear space. The curvilinear effects on kinetic energy and SOC are both described. In chapter 3, the methods for transmittance and band structures are introduced to investigate the properties of spin transport. The transmittance and band structures of specific systems are calculated in chapter 4. The effects of SOC, magnetic filed and geometric structures are discussed in the separate sections. Conclusion of the thesis will be summarized in chapter 5.

碩士
國立成功大學
機械工程學系
102
This research was divided into two parts. In the first part, we investigated the band structure of one-dimensional quasi-periodic phononic crystal using transfer matrix method. The elastic wave propagation inside both the periodic and quasi-periodic structure was analyzed. The quasi-periodic structures with various thickness modulations were studied and the band structures were compared with the periodic one in order to understand the modulation effect. Meanwhile, the effects of material parameters and the filling ratios of the periodic thickness on band structure were examined. It can be found that both the constituted materials and the filling ratio would change the band gaps. In the second part, we investigated one-dimensional graded thickness layer structure constituting with positive and negative mass density medium. Under the assumption of long-wavelength limit, the layer structure can be modeled as an anisotropic material which have collimation phenomenon. Thus, we investigated the collimation phenomenon of the anisotropic structure with periodic arrangement and various thickness modulations. The propagation behavior was analyzed by examining the maximum intensity on the structure boundary and the pressure field distribution along the propagation direction. From finite element simulation, we found that the transmissions were direction dependent for the layer structure with graded thickness. The results showed that when the anisotropic structure with various thickness modulations, this structure can act as an acoustic diode. Meanwhile, we also discussed the mass density effect on the transmission contrast ratio of the diode.

博士
國立臺灣大學
物理研究所
98
Spin-dependent electronic transport through quasi-one-dimensional systems, including coupled quantum dots and wire-shaped conductor, is theoretically studied in this dissertation. Green function approach is particularly useful when considering an open system, i.e., a scattering region in contact with a couple of leads to reservoirs. Single-particle Green function for both one-particle Schrödinger equation and many-body system out of equilibrium are employed herein to investigate the transport properties and relevant physical quantities, such as conductance, charge and spin occupations, and density of states, upon which the analysis is organized. In summary, the discussions over considered devices with different geometry are mainly consisting in three phenomena: (i) quantum interference, (ii) controllable spin accumulation and spin-polarized current, and (iii) electric-field-induced spin polarization. As quantum phase coherence plays an important role in mesoscopic systems we present a simple work of coupled quantum dots in the presence of magnetic flux to illustrate the phenomenon (i). Starting from specific geometry one of molecular states could be totally uncoupled from the leads and becomes localized within the conduction band. As changing indirect coupling parameter and magnetic flux, bound state becomes well resolved, and meantime two antiresonances form due to destructive quantum interference and point out the gradual localization of molecular states, as manifested by the Fano and Breit-Wigner resonances in conductance spectrum, respectively. Then we present the central subjects of this dissertation, i.e., to lift and control the spin states of electrons by utilizing Rashba spin-orbit interaction, which has been shown to exist in semiconductor heterostructures due to the lack of inversion symmetry. Phenomenon (ii) is based on two kinds of coupled double quantum dots configurations. Owing to spin-orbit interaction the spatial motion of electrons are coupled to their spin degree of freedom. This results in spin precession, leading to a continuous evolution of antiresonances from strong overlapping Fano resonances, in serial configuration for example. Meantime combined effects of quantum interference and spin-orbit coupling generate an electrically tunable spin accumulation and a spin-polarized current. On the other hand, in phenomenon (iii) we demonstrate the spin polarization in finite disordered two-dimensional electron gas. Impurity scattering and drift velocity following electric field in strong bias condition lead to an evolution of spin accumulation. In the quasi-ballistic region electron wave function has not yet been strongly perturbed, while robust magnetoelectric effect develops in the diffusive region.

When a liquid is cooled below its equilibrium freezing temperature, it becomes supercooled and the molecular motions slow down until the system becomes kinetically arrested, forming a glass, at the glass transition temperature. These amorphous materials have the mechanical properties of a solid while retaining the structural properties of a liquid, but do not exhibit the usual features of a thermodynamic phase transition. As such, they present a number of important challenges to our understanding of the dynamics and thermodynamics of condensed phases. For example, supercooled liquids are classified on the basis of the temperature dependence of their transport properties and structural relaxations times. Strong liquids display an Arrhenius behavior, with the logarithm of their viscosity growing linearly with inverse temperature. Fragile liquids behave in a super-Arrhenius manner, where the viscosity appears to diverge at temperatures above absolute zero, suggesting the possibility of an underlying thermodynamic origin to the glass transition. Some complex, network forming liquids, such as water and silica have also been shown to have a dynamical crossover from fragile to strong liquid behavior as the temperature is decreased. The potential energy landscape paradigm, combined with inherent structure formalism, provide a framework for connecting the way particles pack together with the thermodynamics and dynamics of the liquid and glassy phases. However, the complexity of this multi-dimensional surface makes it difficult to fully characterize and rigorous relationships between the nature of particle packing and glass forming properties have not been established. The goal of this thesis is to study some of the general features of glass transition and find the connection between the dynamics and the thermodynamics of glass forming liquids. To this end, the packing landscapes of quasi-one-dimensional hard discs and hard spheres are studied. A two dimensional system of hard discs with diameter σ, confined between two hard walls (lines) of length L, separated by a distance 1