Abstract
Topology, quantum geometry, and superconductivity in quantum materials have become central themes in modern condensed matter physics. In this thesis, we investigate several systems that exemplify the interplay among these concepts, including noncentrosymmetric achiral materials, Kagome antiferromagnets, and superconductors with finite-momentum pairing and anisotropic superconductors.
Specifically, in chapter II, we demonstrate the existence of the topological Fermi-arclike surface states (FALSSs) in Kramers nodal line metals (KNLMs). Notably, as achiral symmetries are gradually broken, the KNLM transitions into a Kramers Weyl semimetal (KWS), allowing the FALSSs to evolve continuously into the Fermi arc states of the KWS.
In Chapter III, we investigate the third-order nonlinear anomalous Hall effect (NLHE) in the Kagome antiferromagnet FeSn. Through a combination of symmetry analysis, tightbinding modeling, and first-principles calculations, we reproduce and explain the experimentally observed nonlinear transport behavior.
In Chapter IV, we propose a new mechanism for realizing Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) Cooper pairing states within flat bands, Unlike conventional the conventional paradigm such as the Zeeman effect, the mismatches in the quantum geometry of paired electrons drive the flat-band FFLO instability.
In chapter V, we show that a direct current bias injected off principal axes in twodimensional anisotropic superconductors converts anisotropy into transverse nonreciprocity, enabling supercurrent diode effect (SDE). When the control bias exceeds its critical value, the transverse dissipationless currents can only flow unidirectionally. Our findings open new avenues for developing nonreciprocal superconducting electronic devices.