Imaging the breaking of electrostatic dams in graphene for ballistic and viscous fluids.

The charge carriers in a material can, under special circumstances, behave as a viscous fluid. In this work, we investigated such behavior by using scanning tunneling potentiometry to probe the nanometer-scale flow of electron fluids in graphene as they pass through channels defined by smooth and tunable in-plane p-n junction barriers. We observed that as the sample temperature and channel widths are increased, the electron fluid flow undergoes a Knudsen-to-Gurzhi transition from the ballistic to the viscous regime characterized by a channel conductance that exceeds the ballistic limit, as well as suppressed charge accumulation against the barriers. Our results are well modeled by finite element simulations of two-dimensional viscous current flow, and they illustrate how Fermi liquid flow evolves with carrier density, channel width, and temperature.

Measuring and Tuning the Potential Landscape of Electrostatically Defined Quantum Dots in Graphene.

We use Kelvin probe force microscopy (KPFM) to probe the carrier-dependent potential of an electrostatically defined quantum dot (QD) in a graphene/hexagonal boron nitride (hBN) heterostructure. We show that gate-dependent measurements enable a calibration scheme that corrects for uncertainty inherent in typical KPFM measurements and accurately reconstructs the potential well profile. Our measurements reveal how the well changes with carrier concentration, which we associate with the nonlinear dependence of graphene's work function on carrier density. These changes shift the energy levels of quasi-bound states in the QD which we can measure via scanning tunneling spectroscopy (STS). We show that the experimentally extracted energy levels closely compare with wave functions calculated from the reconstructed KPFM data. This methodology, where KPFM and STS data are simultaneously acquired from 2D materials, allows the quasiparticle response to an electrostatic potential to be determined in a self-consistent way.

Alignment of semiconducting graphene nanoribbons on vicinal Ge(001).

Chemical vapor deposition of CH4 on Ge(001) can enable anisotropic growth of narrow, semiconducting graphene nanoribbons with predominately smooth armchair edges and high-performance charge transport properties. However, such nanoribbons are not aligned in one direction but instead grow perpendicularly, which is not optimal for integration into high-performance electronics. Here, it is demonstrated that vicinal Ge(001) substrates can be used to synthesize armchair nanoribbons, of which ∼90% are aligned within ±1.5° perpendicular to the miscut. When the growth rate is slow, graphene crystals evolve as nanoribbons. However, as the growth rate increases, the uphill and downhill crystal edges evolve asymmetrically. This asymmetry is consistent with stronger binding between the downhill edge and the Ge surface, for example due to different edge termination as shown by density functional theory calculations. By tailoring growth rate and time, nanoribbons with sub-10 nm widths that exhibit excellent charge transport characteristics, including simultaneous high on-state conductance of 8.0 µS and a high on/off conductance ratio of 570 in field-effect transistors, are achieved. Large-area alignment of semiconducting ribbons with promising charge transport properties is an important step towards understanding the anisotropic nanoribbon growth and integrating these materials into scalable, future semiconductor technologies.