A Study on Majorana Zero Modes in Higher-Order Topological Superconductors

Abstract

Over the past decade, the interplay between symmetry and topology in condensed matter physics has not only deepened our understanding of matter by prompting a conceptual revolution in classifying all phases of matter, but it has also led to tremendous progress in finding new materials with low energy consumption and new applications such as fault-tolerant topological quantum computing and Weyltronics, to name but few. This thesis consists of two parts and presents a theoretical study in the field of condensed matter theory with a focus on higher-order topological superconductivity and Majorana zero modes. The first part of this thesis is concerned with high-temperature superconductivity in cuprates, and the last part is dedicated to the high-temperature iron-based superconductors. In the first part, it will be shown that using a harmonic potential to confine a two dimensional second-order topological superconductor leads to a proliferation of Majorana corner modes. The second-order topological superconductor can be obtained by incorporating a first-order topological insulator in proximity to a high-temperature superconductor. As a consequence, these circumstances result in the formation of Majorana corner flat bands, which have a fundamentally different origin from that of the conventional mechanism. Moreover, we will investigate the superconducting pairing instability of the two-dimensional extended Hubbard model with both Rashba and Dresselhaus spin-orbit coupling within the mean-field level at both zero and finite temperature. We find that both first- and second-order time-reversal symmetry-breaking topological gapped phases can be achieved under appropriate parameters and temperature regimes due to the presence of a favored even-parity s+id-wave pairing even in the absence of an external magnetic field or intrinsic magnetism. Our findings suggest new possibilities in interacting spin-orbit coupled systems by unifying both first- and higher-order topological superconductors in a simple but realistic microscopic model. In the last part of this thesis, the impact of second-order topology on the vortex lines topology in iron-based superconductors in both weak and strong Zeeman field regimes will be investigated. By incorporating a realistic assumption of inhomogeneous superconductivity, our findings can explain the recent experimental observation of the peculiar coexistence and evolution of topologically nontrivial and trivial vortex lines in iron-based superconductors, and hopefully advance our understanding of these materials.