UC Santa Cruz

Graphene is our viewing window into two-dimensions. Just a single atom thick, this sheet of carbon confines electron in the x-y plane, drastically transforming their properties from those in free space. In order to access the intriguing, surprising and applicable physics that results from 2D confinement, it is necessary to develop tools to accurately probe graphene. In the fifteen years since electrical current was first run through graphene, transport measurements of two-dimensional materials have reached new heights of cleanliness and sophistication—showing novel states of matter by pushing current through graphene near equilibrium at ultra-high magnetic fields. Additionally, spectroscopy techniques involving tunneling have also developed to provide fundamental insight on graphene’s electronic structure far from equilibrium. While both of these techniques, device-based transport and tip-based tunneling, have revolutionized the study of graphene and its relatives, neither technique is capable of directly probing these 2D materials in ultra-high magnetic fields and away from equilibrium. In my thesis I will present a third technique that hybridizes transport and tunneling. The method is called planar tunneling spectroscopy (PTS) and it has three attributes that enable the access of new information on graphene: (1) PTS can spectroscopically probe occupied and unoccupied states; (2) PTS is fully compatible with the world’s highest sustained magnetic fields; and (3) PTS has full control over the external electric field and the amount of charge within the graphene sheet. Each of these three attributes have enabled other techniques to reveal novel physics in graphene. Here, I will show all three attributes work together for the first time.

With the unconventional power of PTS, we will tour through many of the properties that make graphene interesting: its linear dispersion, anomalous quantum Hall states, and unique screening behavior, to name a few. Afterward, we will take one step towards three dimensions by adding another sheet of carbon. Bilayer graphene is more than the sum of its parts. We will see that the coupling between its component layers bends and warps its band structure in ways that are compelling for a material-by-design applications. Finally, we will explore how to probe the inherent electronic structure of BLG without changing it, as is often unintentionally done. To make these subtle but substantial corrections, we will harness the true power of PTS—its simplicity and its control. The new techniques developed in this thesis for building devices, conducting tunneling spectroscopy, rendering data and thinking about tunneling physics will hopefully inform upcoming spectroscopic studies of 2D materials as this young field reaches maturity.