Thesis (Ph. D.)--Ohio State University, 2006. / Title from first page of PDF file. Includes bibliographical references (p. 44)

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Thesis advisor: Ziqiang Wang / Graphene has emerged as an important two dimensional electron system with novel physical properties due to its relativistic-like linear energy-momentum dispersion relation at low energy. Alongside two dimensional electron systems in semiconductor heterostructures, it has a rich set of integer and fractional quantum Hall states. Significant progresses have been made recently, but a full understanding of these states is still lacking. The prevailing approach for fractional quantum Hall effects in graphene has been the numerical exact diagonalization. In this work, we develop a fermionic Chern-Simons effective theory for Dirac fermions as a complement to the existing theories, and to bring new insights in our understanding of the phenomena. In particular, we study the possibility for quantum Hall plateaus at even-denominator filling factors. We first construct a unitary Chern-Simons transformation to attach even number of flux quanta to Dirac fermions. To deal with the four-fold spin-valley degeneracy, a set of K-matrices is introduced. At even-denominator filling factors in the zeroth Landau level, the fictitious magnetic field of the Chern-Simons field cancels the external magnetic field on average. It is shown that the Chern-Simons field mediates an effective mutual statistical interaction between composite Dirac fermions. We further show the statistical interaction and Coulomb interaction favor the formation of an exciton condensate. Quasi-particles at finite filling factors can be regarded as excita- tions above the exciton condensate, and can be described as massive Dirac fermions. This means a mass is generated dynamically for Dirac fermions. Different types of K-matrices give rise to different mass gaps. The Chern numbers associated with different massive Dirac band structures can be used to classify the K-matrices. In the last part of the thesis, we study the pairing instability of the composite Dirac fermion liquid. We show the statistical interaction drives a complex p-wave pairing among the quasi-particles. As long as the Coulomb pair breaking effect is weak, the system can develop a superconducting energy gap, thus form a fractional quantum Hall state. / Thesis (PhD) — Boston College, 2012. / Submitted to: Boston College. Graduate School of Arts and Sciences. / Discipline: Physics.

Efeitos térmicos em teorias de calibre em (2+1) dimensões são estudados em espaços onde as coordenadas podem ou não comutar. No caso comutativo, a dependência com a temperatura do tensor de polarização é calculada a um laço em teorias envolvendo tanto bósons quanto férmions. Como aplicação, são calculados os processos de blindagem em tais modelos, chegando ao interessante resultado de que cargas magnéticas não sofrem tais efeitos na QED3. Uma prova válida em qualquer ordem de perturbação é desenvolvida, confirmando este comportamento. Em teorias não comutativas, são estudadas as correções a um laço ao coeficiente de Chern-Simons, sendo encontrado que não existe o fenômeno da mistura UV/IR na teoria Chern-Simons-Higgs. O comportamento assintótico de tal coeficiente é analisado no regime de altas temperaturas. Vários outros aspectos envolvendo os efeitos térmicos em teorias de Chern-Simons são explorados. / Thermal effects in (2+1)-dimensional gauge theories are studied in both commutative as well as noncommutative manifolds. In the first situation, the finite temperature polarization tensor is computed a tone loop for fermionic and bosonic couplings. As an application, the screening masses are evaluated and it is found the surprising result that magnetic charges are not screened in QED3. It is demonstrated that this result holds to any order in pertubationtheory. In the noncommutative case, the one loop correction to the Chern-Simons coefficient is studied, and it is found that there is no UV/IR mixing in the Chern-Simons-Higgs model. The asymptotic behavior of such coefficient is analised in the high temperature regime. Several other interesting aspects involving thermal effects of Chern-Simons theories are also discussed.

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Thesis (doctoral)--Rheinische Friedrich-Wilhelms-Universität Bonn, 2006 / Includes bibliographical references (p. 59-60).

We give a formula for the Chern character on the DG category of global matrix factorizations on a smooth scheme $X$ with superpotential $w\in \Gamma(\O_X)$. Our formula takes values in a Cech model for Hochschild homology. Our methods may also be adapted to get an explicit formula for the Chern character for perfect complexes of sheaves on $X$ taking values in right derived global sections of the De-Rham algebra. Along the way we prove that the DG version of the Chern Character coincides with the classical one for perfect complexes.

Made available in DSpace on 2018-08-01T22:30:12Z (GMT). No. of bitstreams: 1 tese_6078_.pdf: 752304 bytes, checksum: ed9d4ed9c633350db3bda61a07d55b5e (MD5) Previous issue date: 2012-12-07 / O objetivo deste trabalho é apresentar como se dá a correspondência entre teoria de calibre e conexões em espaços fibrados. Mais precisamente estabelecemos um dicionário entre a teoria de calibre da mecânica quântica de uma partícula carregada sujeita a um campo eletromagnético e o estudo das conexões em fibrados por círculos e por retas complexas. Em seguida, analisamos dois objetos de estudo em física utilizando o conhecimento adquirido no estudo da geometria de espaços fibrados. As classes de Chern e a holonomia de uma conexão nos fornecerão uma visualização geométrica de, respectivamente, monopolos magnéticos e o efeito Aharonov-Bohm.