Research Projects

Majorana fermions (MFs), first predicted by the Italian physicist Ettore Majorana in 1937, are hypothetical elementary particles that are their own antiparticles. Majorana fermions are predicted to exist in condensed matter physics at the interface between a superconductor and a topological insulator. When a topological insulator is in contact with a superconductor, the electrons in the topological insulator can form Cooper pairs with the electrons in the superconductor, creating a special kind of quasiparticle called a Majorana fermion at the interface. MFs are also predicted to occur in topological semiconductor-superconductor heterostructure, where a Zeeman field and Rashba spin-orbit coupling assist in inducing p-wave superconductivity. Despite being electrically neutral, Majorana fermions possess unique properties that greatly interest physicists and material scientists. One of the most exciting potential applications of Majorana fermions is in quantum computing. They could be used to build topological qubits that are much more stable and immune to decoherence effects than traditional qubits. This project proposes a theoretical and numerical investigation of some promising candidates for implementing Majorana-based topological qubits. While experimental investigation on MFs has witnessed unprecedented growth over the last decade, explicit confirmation of MFs remains challenging, especially since many trivial and non-topological states can also result in identical experimental signatures, leading to serious "confirmation bias" problems and a "reproducibility crisis." Therefore, our proposal focuses on the stability, visibility, controllability of MFs, and their distinguishability from all the other trivial states. We will use mathematical and numerical tools incorporating experimentally-relevant factors such as disorder, inhomogeneity, temperature, and finite system-size effects. The prime systems of our investigation are two-dimensional Van der Waal structures. Specifically, we will study finite-size graphene strips with high mobility and transition metal dichalcogenides (TMDs) with intrinsic spin-orbit coupling. We will use real-space tight-binding models and Green function methods to model these systems and study the robustness of MF and non-topological states (Andreev-bound states) against non-ideal environmental factors. We will calculate measurable quantities to be compared with experimental results. Finally, we will investigate practical routes toward the realization of a topological qubit.