In this thesis, we study persistent currents and quantum critical phenomena in the systems of mesoscopic physics. As an introduction in Chapter 1 we familiarize the reader with the area of mesoscopic physics. We explain how mesoscopic systems are different from quantum systems of single atoms and molecules and bulk systems with an Avogadro number of elements. We also describe some important mesoscopic phenomena. One of the mathematical tools that we extensively use in our studies is Random Matrix Theorty. This theory is not a part of standard physics courses and for educational purposes we provide the basics of Random Matrix Theory in Chapter 2. In Chapter 3 we study the persistent current of noninteracting electrons in quantum billiards. We consider simply connected chaotic Robnik-Berry quantum billiard and its annular analog. The electrons move in the presence of a point-like magnetic flux at the center of the billiard. For the simply connected billiard, we find a large diamagnetic contribution to the persistent current at small flux, which is independent of the flux and is proportional to the number of electrons (or equivalently the density since we keep the area fixed). The size of this diamagnetic contribution is much larger than the previously studied mesoscopic fluctuations in the persistent current in the simply connected billiard. This behavior of persistent current can ultimately be traced to the response of the angular-momentum l = 0 levels (neglected in semiclassical expansions) on the unit disk to a point-like flux at its center. We observe the same behavior for the annular billiard when the inner radius is much smaller than the outer one. We also find that the usual fluctuating persistent current and Anderson-like localization due to boundary scattering are seen when the annulus tends to a one-dimensional ring. We explore the conditions for the observability of this phenomenon. In Chapter 4 we study quantum critical phenomena in a system of two coupled quantum dots connected by a hopping bridge. Both the dots and connecting region are assumed to be in universal Random Matrix crossover regimes between Gaussian orthogonal and unitary ensembles (defined in Chapter 2). We exploit a diagrammatic approach appropriate for energy separations much larger than the level spacing, to obtain the ensemble-averaged one- and two-particle Greens functions. We find that two main components of the twoparticle Green’s function (diffuson and Cooperon) can be described by separate scaling functions. We then use this information to investigate a model interacting system in which one dot has an attractive s-wave reduced Bardeen-Cooper-Schrieffer interaction, while the other is noninteracting but subject to an orbital magnetic field. We find that the critical temperature TC of the mean-field transition into the superconducting state in the first dot is non-monotonic in the flux through the second dot in a certain regime of interdot coupling. Likewise, the fluctuation magnetization above the critical temperature is also non-monotonic in this regime, can be either diamagnetic or paramagnetic, and can be deduced from the Cooperon scaling function. We end this thesis with conclusion in Chapter 5.

This thesis studies the intrinsic disorder effects and the transport and magnetic properties of ring-shaped epitaxial thin films and superconducting tunnel junctions (STJs) of the high temperature superconductor YBa$_2$Cu$_3$O$_{7-delta}$. We used an unconventional contactless technique that allows us to directly measure the persistent current of superconducting rings. In order to study the disorder effects on the persistent current, we slowly increased oxygen vacancies in YBa$_2$Cu$_3$O$_{7-delta}$ by changing $delta$ from 0.03 to 0.55 in steps of $sim$0.021. Monitoring the corresponding changes in the temperature dependence of the persistent current revealed an anomaly in its flow within a certain range of disorder. We found that this anomaly is directly related to the occurrence of a spinodal decomposition of oxygen vacancies in YBCO, which we explain as a competition between two coexisting phases, oxygen rich and oxygen deficient. The analysis of the time dependence of the persistent current revealed that increasing oxygen vacancies transforms the vortex structure from quasi-lattice into a glass and subsequently into a pinned liquid phase. Our results also exhibited the first evidence of self-organization of the vortex structure with increasing disorder. We also performed the first direct measurement of the temperature dependence of the $c$-axis persistent current ($J_c$) that is purely due to tunnelling Cooper-pairs through intrinsic Josephson junctions (IJJs) of YBCO. This is made possible by incorporating IJJs of YBCO into ring-shaped films. Then, we studied the temperature dependence of the persistent current of YBCO nanowires embedded in SrTiO$_3$-barrier integrated between two semi-ring-shaped YBCO thin films and systematically varied the nanowires length. Our observations revealed that $J_c$ has two different temperature dependences: a GL-dependence ($J_c propto (T_c - T)^{3/2}$) at low temperatures which we found the same in all studied samples, and another power law dependence ($J_c propto (T_c - T)^{alpha > 3/2}$) at high temperatures which turned out to depend on the length of the nanowires. We attribute the cross-over between these two temperature dependences to the depinning and the dissipative motion of vortices. These experimental approaches and findings not only provide new information, but more importantly open new avenues of investigating the transport and magnetic properties of superconducting films, junctions, and nanowires.

No description available.

学位授与大学：京都大学 ; 取得学位: 博士(工学) ; 学位授与年月日: 2007-09-25 ; 学位の種類: 新制・課程博士 ; 学位記番号: 工博第2864号 ; 請求記号: 新制/工/1421 ; 整理番号: 25549 / Kyoto University (京都大学) / 0048 / 新制・課程博士 / 博士(工学) / 甲第13393号 / 工博第2864号 / 新制||工||1421(附属図書館) / 25549 / UT51-2007-Q794 / 京都大学大学院工学研究科電気工学専攻 / (主査)教授 引原 隆士, 教授 小林 哲生, 准教授 中村 武恒 / 学位規則第4条第1項該当

Orientador: Amir Ordacgi Caldeira / Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Física Gleb Wataghin / Made available in DSpace on 2018-08-27T16:19:57Z (GMT). No. of bitstreams: 1 Trevisan_ThaisVicta_M.pdf: 4124547 bytes, checksum: 599b58df77b4451dd1db391d5d3f78fd (MD5) Previous issue date: 2015 / Resumo: Na presença de um campo magnetico externo, um anel, com resistencia eletrica nao nula, sustenta uma corrente eletrica sem dissipacao, desde que ele seja sufientemente pequeno (com um diametro da ordem de micrometros ou nanometros), altamente puro e mantido a baixisimas temperaturas. Trata-se de um fenomeno quantico, devido a coerencia entre os eletrons do sistema. Uma corrente desse tipo tambem esta presente em moleculas aromaticas: um loop de corrente se estabelece no anel aromatico e e o responsavel pela anisotropia da susceptibilidade magnetica dessas moleculas. Atualmente, esses aneis de corrente sao utilizados como um criterio para aromaticidade. Assim sendo, o transporte de corrente eletrica em sistemas meso e microscopicos e um assunto de grande interesse tanto para a Fisica, quanto para a Quimica. Nessa Dissertacao de Mestrado, estudamos o transporte de corrente eletrica em aneis discretos, unidimensionais, de 3 [<ou =] N [<ou=] 6 sitios e Ne [<ou=] 2N eletrons. Esses aneis podem ser vistos como moleculas bastante simplificadas, de modo que o sistema de seis sitios com seis eletrons corresponde a um prototipo da molecula de benzeno. Propomos um modelo microscopico com a finalidade de obter um estado fundamental transportador de corrente nesses aneis. O nosso modelo consiste de uma extensao do Hamiltoniano de Hubbard, com um termo extra de interacao inter-eletronica, postulado de maneira ad hoc. Os resultados obtidos a partir do nosso modelo, bem como uma possivel origem e interpretacao para o termo extra de interacao sao apresentados ao longo desse trabalho / Abstract: In the presence of an external magnetic feld, a ring, with finite electrical resistance, supports a dissipationless electric current, provided that the ring is small enough (its diameter must be of the order of some micrometer or nanometer), clean and cooled down to very low temperatures. It is a quantum phenomena, due to the high electronic phase coherence in this system. A current like this can also be seen in aromatic molecules: a loop of current is established in the aromatic ring and it is the responsible for the high anisotropic magnetic susceptibility of these molecules. Nowadays, these ring currents are used as a criteria for aromaticity. Therefore, the electrical transport properties in mesoscopic and microscopic systems is a subject of great interest both in Physics and Chemistry. In this thesis, we study the electrical transport in some discrete and unidimensional rings with 3 [<or=] N [<or=] 6 sites and Ne [<or=] 2N electrons. These rings can be seen as simplified molecules and the ring with six sites and six electrons is our prototype for the benzene molecule. We propose a microscopic model for obtaining a current-carrying ground state in these rings. Our model consists of a extension of the Hubbard Hamiltonian, with an ad hoc extra term for the interaction between the electrons of the system. The results obtained from our model as well as a possible origin and interpretation of the extra interaction term are presented throughout this work / Mestrado / Física / Mestra em Física

abstract: This dissertation aims to study and understand relevant issues related to the electronic, spin and valley transport in two-dimensional Dirac systems for different given physical settings. In summary, four key findings are achieved. First, studying persistent currents in confined chaotic Dirac fermion systems with a ring geometry and an applied Aharonov-Bohm flux, unusual whispering-gallery modes with edge-dependent currents and spin polarization are identified. They can survive for highly asymmetric rings that host fully developed classical chaos. By sustaining robust persistent currents, these modes can be utilized to form a robust relativistic quantum two-level system. Second, the quantized topological edge states in confined massive Dirac fermion systems exhibiting a remarkable reverse Stark effect in response to an applied electric field, and an electrically or optically controllable spin switching behavior are uncovered. Third, novel wave scattering and transport in Dirac-like pseudospin-1 systems are reported. (a), for small scatterer size, a surprising revival resonant scattering with a peculiar boundary trapping by forming unusual vortices is uncovered. Intriguingly, it can persist in arbitrarily weak scatterer strength regime, which underlies a superscattering behavior beyond the conventional scenario. (b), for larger size, a perfect caustic phenomenon arises as a manifestation of the super-Klein tunneling effect. (c), in the far-field, an unexpected isotropic transport emerges at low energies. Fourth, a geometric valley Hall effect (gVHE) originated from fractional singular Berry flux is revealed. It is shown that gVHE possesses a nonlinear dependence on the Berry flux with asymmetrical resonance features and can be considerably enhanced by electrically controllable resonant valley skew scattering. With the gVHE, efficient valley filtering can arise and these phenomena are robust against thermal fluctuations and disorder averaging. / Dissertation/Thesis / Doctoral Dissertation Electrical Engineering 2017

Made available in DSpace on 2016-06-02T20:16:43Z (GMT). No. of bitstreams: 1 1994.pdf: 1761798 bytes, checksum: 183ce1c471cf1079a1302b309c923a68 (MD5) Previous issue date: 2002-04-11 / Financiadora de Estudos e Projetos / In the present work the Drude weight is calculated to study the capacity of conduction at finite temperatures in one-dimensional rings with the potencial given by the sequences of different degrees of randomness and threaded by a time independent magnetic flux. In this context, the tight-binding approximation is used to solve the Schrödinger equation,also permitting the potencials, given by substitution sequences, to be implemented in a simple way. We study four situations in which the potencial is given by periodic and random sequence. The transport properties exhibited by the system in each case are to reflect the degree of randomness presented by these potencials, although in a nontrivial manner if one considers a hierarchy of disorder based on the Fourier transform of the sequences. The role played by temperature in the capacity of conduction, as compared with the role played by the potencials, is also described. / No presente trabalho, através do cálculo do peso de Drude estudamos a capacidade de condução a temperaturas finitas, em anéis unidimensionais com potenciais dados por seqüências de diferentes graus de desordem e atravessados por fluxo magnético independente do tempo. Neste contexto, utilizamos o modelo tight-binding na resolução da equação de Schrödinger, o que permite inserir os potenciais, dados por seqüências de substituição, de maneira simples. Estudamos quatro casos em que esse potencial seja dado por seqüências não periódicas. Os resultados são comparados com os dois casos limites de organização, a saber, as seqüências periódica e desordenada. Observa-se que o grau de desordem apresentado por estes potenciais reflete-se nas propriedades de transporte exibidas pelo sistema em cada caso, embora de maneira não trivial se considerada uma hierarquia de desordem baseada na transformada de Fourier das seqüências. Descreve-se também a influência da temperatura, frente à influência dos potenciais, na capacidade de condução.