Strong Correlation, Topology in Unconventional Superconductors and Quantum Magnetism

Abstract

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.