Topological Superconductivity in Two-Dimensional Electronic Systems

Abstract

The study of topological phases has been at the forefront of condensed matter physics since the turn of the century and has generated a productive synergy between theoretical and experimental efforts. Characterized by their insulating bulk and conducting boundary states, topological insulators are ideal platforms both for testing novel theories and for inspiring new discoveries. Moreover, the ingredients that give rise to topological insulators can produce similar topological effects when combined with superconductivity, forming topological superconductors, which can host exotic excitations such as Majorana fermions. Such quasiparticles are predicted to exhibit non-abelian exchange statistics and hence serve as a basis for topological quantum computing. In this thesis, we describe a set of experiments centered around induced superconductivity in the first quantum spin Hall insulator discovered - HgTe quantum wells. Resulting from a topological band gap, the quantum spin Hall insulator support counter-propagating edge states which are the time-reversed partners. In our experiments, we place a section of quantum spin Hall insulator between two superconducting leads to form a Josephson junction. By measuring Fraunhofer interference, we can study the spatial distribution of supercurrent in the junction. In the quantum spin Hall regime, this supercurrent becomes confined to the topological edge states. In addition to providing a microscopic picture of these states, our measurement scheme generally provides a way to investigate the edge structure of any topological insulator. In a second experiment, we tune the chemical potential into the conduction band of the HgTe system and investigate the behavior of Fraunhofer interference as a magnetic field is applied parallel to the plane of the quantum well. By theoretically analyzing the interference in a parallel field, we find that Cooper pairs in the material acquire a tunable momentum that grows with the magnetic field strength. This finite pairing momentum leads to the appearance of triplet pair correlations at certain locations within the junction, which we can control with the external magnetic field. Our measurements and analysis also provide a method to obtain information about the Fermi surface properties and spin-orbit coupling in two-dimensional materials. Furthermore, these experimental observations have inspired a theoretical proposal to construct Majorana bound states on the edge of a two-dimensional induced superconductor with spin-orbit coupling, identified by their emergence as a function of both the phase difference and the Zeeman energy. To investigate the sub-gap spectrum, we measure the local tunneling spectrum on the edge of a planar Josephson junction and control its phase difference through a flux loop. Overall, we observe a continuum of Andreev levels, dispersing coherently with the phase difference. At high in-plane magnetic fields, we observe enhanced zero-energy conductance extending over a range in the phase difference, and this range grows with the magnitude of the in-plane field, confirming the predictions of recent theoretical calculations.