Topological Phenomena in Two-Dimensional Electron Systems

Abstract

The search for fault-tolerant quantum computing is a major thrust in modern physics. Majorana zero modes are quasiparticles with non-abelian exchange statistics that can be used as a basis for topological quantum computing, which is much more robust against disorder than standard quantum computing. Two-dimensional semiconductor systems with strong Rashba spin-orbit coupling and induced superconductivity, in the presence of in-plane magnetic fields, are predicted to host Majorana zero modes. In this thesis, we describe several experiments centered around induced superconductivity in two types of semiconductor systems, HgTe and InAs. The first two experiments describe our measurements on HgTe. By measuring Fraunhofer interference in a Josephson junction as a magnetic field is applied parallel to the quantum well, we find that Cooper pairs acquire a tunable momentum that increases with the applied in-plane field, leading to the appearance of superconductivity with triplet-pairing. Our analysis leads to a method for studying the spin-orbit coupling and Fermi surface properties of two-dimensional materials. These experimental observations inspired a theoretical proposal to construct Majorana bound states on the edge of a two-dimensional induced superconductor with spin-orbit coupling. We investigate this theoretical proposal by measuring the local tunneling density of states on the edges of a Josephson junction. We observe a continuum of Andreev levels which disperse coherently with the phase difference. At high values of applied in-plane magnetic field, we observe an enhanced zero-energy conductance extending over a range of phase difference which range grows with the magnitude of the in-plane field, in accordance with the theoretical prediction. We then describe our experiments on InAs systems. The first InAs quantum well we study is a surface well with epitaxial aluminum grown on it in the molecular beam epitaxy chamber, which leads to a very strong induced superconducting gap. We discuss our attempts to repeat our HgTe experiments on this system, as well as our investigation of a recent theoretical prediction for ungapped superconducting states at high values of in-plane field. The second InAs experiment discusses a system with a deeper InAs quantum well, which yields mobilities much higher than in the surface case. We show our initial measurements on this system, as well as our initial attempt at measuring a zigzag junction, which is predicted to display a much larger topological gap than that of a planar junction.