Single-Electron Probes of Two-Dimensional Materials

Abstract

From the silicon MOSFET inversion layer to the gallium arsenide quantum well, two-dimensional electron systems (2DES) have revolutionized both physics and technology. In recent years, a novel class of atomically thin 2D materials has sparked renewed interest from the condensed matter community due to their ability to host a variety of interesting topological and correlated electronic phases. These materials are headlined by graphene, the semi-metallic sheet of carbon, and include such diverse compounds as boron nitride (an insulator), molybdenum disulfide (a semiconductor) and niobium diselenide (a superconductor). A special probe uniquely suited to the study of 2DES at the nanoscale is a device known as the single-electron transistor (SET). The SET contains a small metallic island which couples capacitively to the 2DES sample of interest and is strongly gated by variations in the local chemical potential of the sample. It can be used to locally measure the many-body density of states (known as the inverse compressibility) in the bulk of a 2DES, while requiring no steady-state current to flow through the sample. In the first part of this thesis, we discuss low-temperature compressibility measurements of graphene and bilayer graphene performed by a scanning SET on a tip. By positioning a ~100 nm diameter SET tip tens of nanometers above the 2DES, we can probe the fractional quantum Hall regime in these materials in intricate detail. The scanning SET is mounted in a specialized vacuum cryostat, and the second part of this thesis describes a series of design upgrades on this system. We detail the installation of new piezoelectric motors, thermometers, and other hardware for improved performance. In addition to scanning SETs on a tip, it is also possible to deposit SETs directly on the 2DES; these are known as fixed SETs. In the final part of this thesis, we describe our nanofabrication efforts towards patterning fixed SETs on the novel class of atomically thin van der Waals materials.