Majorana Zero Modes in Solid State Systems
Majorana Zero Modes in Solid State Systems
Loading...
Files
Publication or External Link
Date
2015
Authors
Hui, Hoi Yin
Advisor
Das Sarma, Sankar
Citation
DRUM DOI
Abstract
Majorana zero modes are zero-energy excitations that are their own anti-particles, and obey non-Abelian statistics which could be harnessed for topological quantum computation. There are many theoretical proposals to realize them in solid state systems, but experimental realizations are confronted by a number of non-idealities. In this thesis, we theoretically investigate such complications, thereby suggesting improvement and directions that could be pursued. We first develop a theoretical framework to analyze the effect of ensemble-averaged disorder on the Majorana zero modes, generalizing the Eilenberger theory to handle 1D systems while retaining short-distance fluctuations. We then consider disordered topological insulator-based heterostructures, showing that extra subgap states are potentially induced, obscuring the density-of-states signature of the Majorana zero mode. We also analyze in depth the experimentally observed soft gap feature, suggesting that a cleaner interface in the semiconductor-based proposal can harden the gap.
In view of some of the limitations of the proposals based on semiconductors or topological insulators, we look into a new class of systems in which a ferromagnetic atomic chain is put on the surface of a bulk spin-orbit-coupled superconductor. This system is analyzed in two limits, corresponding to weak or strong inter-atomic hopping on the chain. In each of these cases, the topological criteria are obtained. We also find that in the limit of strong chain-superconductor coupling, the length scales of the effective Hamiltonian of the chain are significantly suppressed, potentially explaining some of the recent observations in experiments.