Theoretical study of Majoranas in one- and two- dimensional hybrid system

Abstract

In contemporary condensed matter physics, a pivotal focal point lies in the pursuit of topological states of matter. Topological quantum computing posits the encoding of qubits within quantum states that are safeguarded by topological properties, namely the non-Abelian anyons with non-trivial braiding statistics. The act of exchanging the positions of these anyons, or equivalently, executing a meticulously chosen sequence of measurements, facilitates the realization of quantum operations on the qubits. Among the simplest varieties of non-Abelian anyons are Majorana zero modes.

Numerous practical proposals for the realization of topological superconductivity and Majorana zero modes have been proffered and subject to rigorous theoretical and experimental scrutiny. Despite occasional inconclusive experimental results, the robust theoretical underpinnings of the field have consistently propelled ongoing advancements.

In this thesis, we go beyond the simple one-dimensional hybrid system model. The examination of the orbital effects within a three-dimensional Majorana nanowire is present. A comparison between local and non-local conductance reveals that the latter serves as a superior indicator of the presence of Majoranas.

The layered assembly of two-dimensional materials has opened up versatile opportunities for engineering material properties, facilitated by interlayer hybridization and the effects of moir\'{e} superlattice. We propose to realize two-dimensional superstructures of topological superconductors based on marginally twisted bilayers of transition metal dichalcogenides in proximity to a conventional s-wave superconductor. Majorana Fermions arise at domain boundaries of the AB and A'B' stacking domains as a result of the sign flip across the domain wall in the Rashba spin-orbit coupling coefficient at the valence band edge. Unlike previous models that only allow for one Majorana per boundary, each domain wall can host two helical Majorana edge states with the same Majorana polarization, preventing hybridization. This offers a promising new platform for studying Majorana physics.

Furthermore, our investigation delves into the intricate interplay between the moire defined textures and the Majorana Fermions along the domain wall. In the context of chiral channels of Majorana, a gapless Dirac cone emerges within the mini Brillouin zone, originating from the presence of chiral Majoranas. Conversely, gapped states with finite energy are observed on the domain wall for helical channels of Majorana.