Superlattices and quantum spin Hall states in graphene and hexagonal boron nitride heterostructures

Abstract

Two-dimensional (2d) layered materials, such as graphene and hexagonal boron nitride (hBN), can be isolated separately and then stacked together to form heterostructures with crystalline interfaces between the layers. In this thesis, I present a series of experiments which explore the quantum transport of electrons in heterostructures made from graphene and hBN. Depending on the relative alignment, or "twist", between the layers, a crystal of hBN can be either a non-perturbing substrate for the graphene, or a method to induce a band gap and superlattice potential for the graphene electrons. In the case of two stacked graphene layers, a relative twist can electronically decouple the layers from each other, despite a tiny 0.34nm interlayer spacing. This twist-dependent physics can be used to realize new electronic states in graphene, especially in the presence of strong magnetic fields and electron-electron interactions. By applying a strong tilted magnetic field to graphene which is decoupled from its hBN substrate, we are able to realize a quantum spin Hall state and measure its electronic properties. An analogous bilayer quantum spin Hall state is also realized in twisted bilayer graphene, by taking advantage of the twist decoupling between the layers and the effects of electron-electron interactions. A different set of experiments explores the competition of a magnetic field with the effects of the superlattice potential which arises when a graphene sheet is nearly aligned to its hBN substrates. The large superlattice potential allows us to study graphene transport in Hofstadter's butterfly-the fractal spectrum for electrons under the simultaneous influence of a lattice and a magnetic field.