"Optics" with electrons in graphene

Contact Aaron Sharpe (aaronlsharpe@gmail.com) for more information.

Monte Carlo simulations: https://github.com/dgglab/ballistic_montecarlo

Now is an exciting time in condensed matter physics. Thanks to technical improvements in low temperature cryogenics and the development of a host of extraordinary material systems—such as single-atom-thick graphene—we are able to create conditions where electrons can propagate freely through a material as quantum-mechanical waves over long distances with minimal disturbance from imperfections. Much like light, these waves can refract, diffract, and interfere, yet electron waves arguably have more complexity. For example, electrons are charged particles interacting with each other and their electro-magnetic environment, and they are constrained by the Pauli exclusion principle—fundamentally inhibiting them from overlapping.

The crystalline structure in which electrons propagate also imparts character to the electron waves. In graphene, which is our model system of choice, the hexagonal carbon lattice makes electrons propagate as if they are massless, and their waves “chiral”. The chirality of these waves drastically affects how they scatter and transmit through barriers, which is a novel feature that is being actively explored in our group, but also presents a challenge: it is very hard to corral the electrons to stay where we want.

We are thus developing techniques that overcome this challenge to make narrow beams of electron waves. Specifically, we have constructed double pin-hole collimators that geometrically constrain the electrons that enter the device into a narrow band. This collimator is a first building block for a variety of electron optical measurements we hope to pursue. Borrowing from the field of optics, we can start to form resonant cavities, waveguides, and interferometers that can enable new technologies and teach us important new facets of electron wave propagation. For example, we may be able to sensitively probe how electron waves dephase in the presence of scattering and thermal energy.

Electron collimation — **Fig 1. Design of a double pinhole collimator.** a) schematic of double pinhole collimator. current is injected in the red lead and filtered by grounding the black lead. b) hall bar-like device with collimators in place of voltage probes. c) measurement of collimation: by flipping the switch in (a) we can inject as an ordinary contact (blue) and as a collimator (green). The narrower peak corresponds to a narrow angular distribution.

Ballistic phenomena in graphene/boron nitride heterostructures

The micron-scale mean free path we observe in our graphene heterostructures allow us to study ballistic transport. For example, Fabry-Perot interferences [1] are observed in micron-wide PNP cavities, due to electrons reflecting off the interfaces and self-interfering [Fig. 2]. More broadly, we study the fascinating properties of Dirac fermions in graphene and its multilayers when they go through PN interfaces.

Fabry-Perot interference in graphene bipolar junction — Fig. 2: Fabry-Perot interference in a graphene bipolar junction, measured at T=2K. The distance between both PN interfaces is 1.2 μm, indicating that the mean free path is well over 1μm at these temperatures.

F. Amet, J. R. Williams, K. Watanabe, T. Taniguchi & D. Goldhaber-Gordon. "Insulating Behavior at the Neutrality Point in Dual-Gated Monolayer Graphene," Physical Review Letters 110, 216601 (2013)