The path of least resistance through topology

The primary focus of this dissertation is studying the interaction between topological materials and superconducting materials. Sandwiching a topological material between two superconductors, a structure known as a Josephson junction, is predicted to create a Majorana bound state. This state possesses the interesting property of non-Abelian exchange statistics. This allows the use of Majorana bound states for braiding, the process that is the foundation of topological quantum computation.

Junctions were made of several types of topological materials: three-dimensional topological insulators, Dirac semimetals and nodal line semimetals. To back up the measurements of these junctions, normal state transport measurements were also performed, pinpointing the origin of the induced superconductivity in these materials. These measurements also show the formation of Landau levels in the topological insulator at high magnetic field and their interaction at high separation.

The junctions based on the topological insulators and Dirac semimetals show signatures of Majorana bound states through a 4π periodicity of the current-phase relation. Through a careful study of the frequency and temperature dependence of the radio frequency response of the junctions, several other causes for the 4π periodicity could be excluded. The junctions based on the nodal line semimetal did not show any signs of the Majorana bound state, as their temperature dependence was different.

The results yielded by these junctions between topological materials and superconductors grant us a compelling incentive to definitively prove the presence of Majorana bound states in these systems. The prospect of producing an interesting topological quantum computer would certainly make this endeavor worthwhile.