Thesis advisor: Ziqiang Wang / The discovery of high-Tc superconductivity in cuprates, quantum Hall effect greatly challenge the single-electron understanding of condensed matter physics. In contrast to phonon-mediated BCS mechanism, the unconventional high-Tc superconductivity is widely believed to come from strongly electronic correlation. Strong electron-electron repulsion leads to the interplay among spin, charge, orbital and lattice degrees of freedom, resulting in high-temperature superconductivity, charge or spin density wave, Mott insulator, orbital order, nematicity etc. On the other hand, quantum Hall effect brings us the realization of the mathematical concept of topology in condensed matter. Topology has been widely explored in the topological insulator, topological superconductors, symmetry protected topological order etc. In this dissertation, we study theoretically the physics of electronic correlation and topology in various systems, including superconductivity in single layer CuO₂, electronic nematicity in FeSe, chiral spin density wave in honeycomb lattice and antiferromagnetic Chern insulator in 2D non-centrosymmetric systems. / Thesis (PhD) — Boston College, 2018. / Submitted to: Boston College. Graduate School of Arts and Sciences. / Discipline: Physics.

PrOs₄Sb₁₂ is the first known heavy fermion superconductor containing Pr. Many experiments show results indicating unconventional superconductivity in this system. Most notably, PrOs₄Sb₁₂ exhibits two superconducting transitions. The upper transition occurs at Tc₁ ≈ 1.89 K and the lower transition occurs at Tc₂ ≈ 1.72 K. There are many features of this system that are not understood and do not have a unifi ed consensus among researchers. Many issues remain unanswered, such as the origin of superconductivity, symmetry of the superconducting energy gap, and the nature of the two superconducting transitions. We present specific heat data for a single PrOs₄Sb₁₂ crystal. The data show two superconducting transitions. Variance in the lower superconducting transition (among various samples) suggests multiple superconducting phases. Power law dependence of the low temperature specific heat is indicative of asymmetric energy gap. Cuprates are unconventional high temperature superconductors. The theory on origin and characteristics of superconductivity in these systems is still a debated issue. Experiments indicate presence of a phase in these systems that occurs above the superconducting transition temperature which exhibits some common characteristics with the superconducting state. An important issue is the nature of this so-called "pseudogap" phase and its relationship to the superconducting state. We have developed an experimental apparatus and procedure for measuring the specific heat of a high temperature superconductor and demonstrated it by measuring the heat capacity of a YBCO high-Tc superconductor sample.

PrOs₄Sb₁₂ is the first known heavy fermion superconductor containing Pr. Many experiments show results indicating unconventional superconductivity in this system. Most notably, PrOs₄Sb₁₂ exhibits two superconducting transitions. The upper transition occurs at Tc₁ ≈ 1.89 K and the lower transition occurs at Tc₂ ≈ 1.72 K. There are many features of this system that are not understood and do not have a unifi ed consensus among researchers. Many issues remain unanswered, such as the origin of superconductivity, symmetry of the superconducting energy gap, and the nature of the two superconducting transitions. We present specific heat data for a single PrOs₄Sb₁₂ crystal. The data show two superconducting transitions. Variance in the lower superconducting transition (among various samples) suggests multiple superconducting phases. Power law dependence of the low temperature specific heat is indicative of asymmetric energy gap. Cuprates are unconventional high temperature superconductors. The theory on origin and characteristics of superconductivity in these systems is still a debated issue. Experiments indicate presence of a phase in these systems that occurs above the superconducting transition temperature which exhibits some common characteristics with the superconducting state. An important issue is the nature of this so-called "pseudogap" phase and its relationship to the superconducting state. We have developed an experimental apparatus and procedure for measuring the specific heat of a high temperature superconductor and demonstrated it by measuring the heat capacity of a YBCO high-Tc superconductor sample.

[pt] A teoria de Bardin, Cooper e Schrieffer (BSC) teve enorme sucesso na explicação das propriedades da maior parte dos materiais supercondutores. Esses materiais, onde a teoria BCS se aplica, são denominados supercondutores convencionais. A observação do aparecimento de supercondutividade não-convencional em diversos materiais reabriu as discussões sobre o fenômeno. Enquanto a transição para fase supercondutora em materiais convencionais envolve apenas a quebra da simetria de calibre, no caso dos materiais não-convencionais, a mesma é caracterizada pela quebra de diversas simetrias adicionais. O mecanismo microscópico da supercondutividade nessas novas classes de materiais ainda é uma questão em aberto. no entanto, muitas propriedades físicas podem ser extraídas apenas de conciderações sobre as simetrias do parâmetro de ordem supercondutor, que está intimamente ligadoá função de onda do par de Cooper. Neste trabalho são analisadas algumas propriedades destes novos supercondutores baseadas em critérios de simetria. Um enfoque especial é dado à classe dos supercondutores não-convencionais onde há uma quebra de simetria de reversão temporal. Para estes materiais são previstas algumas propriedade bem pouco usuais. Quando a estrutura cristalina tiver alta simetria, é possível o surgimento de uma polarização de um spin no condensado. Nestes casos, a magnetização intrínseca pode levar à formação de uma fase espontânea de vórtices. Ocorre também uma forte anisotropia na resposta do supercondutor frente à aplicação de campos magnéticos externos. / [en] The theory of Bardeen, Cooper and Schrieffer (BCS) had great success in explaining most properties of superconducting materials. These materials, where BCS applies, are denominated conventional superconductors. the experimental evidence of unconventional superconductivity in several materials reopened discussions about the phenomenon. While, in conventional materials, the superconducting phase involves only the breaking of gauge symmetry, in the unconventional materials the phase is characterized by several additional broken symmetries. The microscope mechanism of superconductivity in this new classes of materials is still an open question. However, many phisical properties can be understood considering only symmetries of the superconducting order parameter, which is intimately linked to Cooper pair wave function. In this work some properties of these new superconductors are analyzed based symmetry criteria. Special emphasis is given to the class of unconventional superconductors where time- reversal symmetry is broken. For these materials, some unusual properties are predicted. When the crystal structure has high symmetry, the appearence of a spin polarization in the condensate is possible. In these cases, an intrinsic magnetization can lead to the information of a spontanous vortex phase. A strong anisotropic response to an externally applied magnetic field also occurs.