Majorana zero modes in condensed matter: Theoretical and numerical study in one and two dimensional systems

The search for conclusive and robust Majorana Zero Modes (MZM) signatures has been of great experimental and theoretical interest due to its potential quantum computing applications. This thesis theoretically furthers this search with three investigations: in the first work, we study a system formed by a Double Quantum Dot (DQD) structure coupled to two normal leads, while each QD is independently connected to a Topological Superconducting Nanowire (TSCN) hosting MZMs at its ends. We focus on the linear conductance through the DQD, the QD’s density of states, and the MZMs spectral functions, which are calculated employing the Green’s functions (GFs) formalism. We aim to identify signatures of quantum interference phenomena, emergence of bound states in the continuum (BICs), MZMs leakage into the QDs-BICs, and the interplay between MZM and BIC by direct control of the magnetic flux over all the bound states of our setup. Our results show that both MZMs and BICs appear in high-symmetry configurations, depending on the QD-MZM coupling strength and the length of the TSCN. We also find a transport suppression anomaly in the linear conductance as a function of the magnetic flux, which appears for the same symmetric configurations mentioned above. Furthermore, both the MZMs leaking into the QDs and the BICs can be controlled by the magnetic flux, suggesting that this external parameter suffices for manipulating the above states. In the second work, we examine the thermoelectric characteristics of a system consisting of two topological superconducting nanowires, each exhibiting Majorana zero modes at their ends, connected to leads within an interferometer configuration. By employing Green’s function formalism, we derive the spectral properties and transport coefficients. Our findings indicate that bound states in the continuum (BICs) manifest in symmetric setups, influenced by the length of the wires and coupling parameters. Deviations of the magnetic flux from specific values transform BICs into quasi-BICs with finite width, resulting in conductance antiresonances. The existence and interplay of Majorana zero modes enhance the thermoelectric performance in asymmetric configurations. Modulating the magnetic flux induces transitions from BICs to quasi-BICs and significantly enhances the Seebeck coefficient and figure of merit, thereby suggesting a strategy for optimizing thermoelectric efficiency in systems based on Majorana zero modes.