Photon-Based Detection of Majorana Bound States and Spectral Analysis of Chiral Majorana Networks in Hybrid Semiconductor-Superconductor Heterostructures

Majorana states offer quite intriguing properties that make them potential building blocks for fault-tolerant topological quantum computing. However, despite advances in experimental techniques and material design, their existence has yet to be demonstrated. This thesis aims to characterize Majorana states in both one- and two-dimensional systems, proposing setups to probe their signatures and unambiguously distinguish them from trivial states. Specifically, we explore the signatures of Majorana excitations in hybrid structures that combine semiconductors and conventional superconductors. Our studies open a new way for probing MBSs using quantum optics, as well as exploring chiral Majorana modes in a novel scattering network. First, we locally probe Majorana bound states (MBSs) using an optical quantum dot (QD) embedded in a pn junction, whose electronic levels are coherently tunnel-coupled to the MBSs at the ends of a one-dimensional wire. In the pn setup, photons are emitted via electron-hole recombination, providing a direct link between the spin-properties of the MBSs and the polarization of emitted photons. By analyzing the resulting photon emission, we can differentiate between various parameter regimes and examine their distinct Majorana signatures. Furthermore, we can investigate the unwanted effect of quasiparticle poisoning, that breaks the parity conservation essential for building qubits, evident in the resulting photonic noise. However, our local probe does not enable us to determine whether these signatures have a topologically nontrivial origin. We therefore extend this setup by incorporating a second QD, forming a pnp junction, which enables us to investigate photonic cross-correlations. Our detection scheme allows us to probe the necessary condition for the emergence of MBSs. Furthermore, we compare our results with those obtained from nontopological quasi-MBSs that can mimic MBSs signatures. Within our detection scheme, we identify a tunneling regime that facilitates differentiation between topological MBSs and trivial quasi-MBSs. Furthermore, we propose a novel scattering network model to investigate chiral Majorana edge modes in a two-dimensional HgTe-based quantum well. In particular, we study a network model that varies its Chern number spatially with domains arranged in a chessboard pattern. We examine the scattering processes, the network energy bands, and the density of states, revealing intriguing phenomena related to interference effects. Additionally, we comment on potential conductance properties and the presence of MBSs in vortex cores.