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

  • Author / Creator
    Kheirkhah, Majid
  • 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.

  • Subjects / Keywords
  • Graduation date
    Spring 2021
  • Type of Item
  • Degree
    Doctor of Philosophy
  • DOI
  • License
    This thesis is made available by the University of Alberta Libraries with permission of the copyright owner solely for non-commercial purposes. This thesis, or any portion thereof, may not otherwise be copied or reproduced without the written consent of the copyright owner, except to the extent permitted by Canadian copyright law.