Majoranas can be lonely

Abstract

At a fundamental level, a fermionic excitation can be represented as two Majorana quasiparticles. Studying the properties of these Majoranas in isolation is of interest to a wide range of applications. From a theoretical perspective, they can be used to study the behaviour of particles that lie outside the typical boson-fermion classification: Majoranas are expected to exhibit non-abelian, anyonic exchange statistics. Practically, these properties could enable the construction of new types of intrinsically stable qubits and robust qubit operations, making Majoranas a potential building block for a topological quantum computer.

These compelling prospects have driven significant experimental efforts over the past decades. While the experimental realization of Majoranas has historically been challenging, recent advances have introduced techniques that allow for the reliable creation of these modes. Notably, the team of Leo Kouwenhoven in Delft pioneered an approach that combines quantum dots with superconductivity to construct a so-called Kitaev chain, providing a systematic method to isolate Majorana modes. In such chains, Majoranas are expected to localize at the edges, appearing as zero-energy excitations in tunneling spectroscopy measurements.

This thesis extends the development of these experimental techniques to a new material platform, with the goal of probing the fundamental properties of Majoranas. To do so, we implement a series of experiments demonstrating the construction of a Kitaev chain in an InSbAs two-dimensional electron gas. As first experiment, we couple two quantum dots to either side of a small semiconducting segment in proximity to a superconductor. In this setup, we demonstrate that elastic co-tunnelling and crossed Andreev reflection can be mediated by an Andreev bound state, that their relative amplitudes can be controlled and that spin-orbit interactions enable spin-triplet processes. Leveraging this system, we show that a minimal two-site Kitaev chain can be created, as evidenced by the study of zero-bias conductance features. Building on these results, we investigate extending the system to implement a three-site Kitaev chain. This allows us to show experimentally that the edges of the system, where Majoranas are expected to appear, have distinct properties from the middle of the system, demonstrating a key property of the Kitaev chain. The results in this thesis hope to provide a solid understanding for creating Majoranas in a two-dimensional system, opening up the path toward more complex configurations and the systematic exploration of Majorana physics.