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.

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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.

We develop a fully self-consistent model to describe scanning tunneling spectroscopy (STS) measurements of Bernalstacked bilayer graphene (BLG), and we compare the results of our model to experimental measurements. Our results show that the STS tip acts as a top gate that changes the BLG bandstructure and Fermi level, while simultaneously probing the voltage-dependent tunneling density of states (TDOS). These effects lead to differences between the TDOS and the local density of states (LDOS); in particular, we show that the bandgap of the BLG appears larger than expected in STS measurements, that an additional feature appears in the TDOS that is an artifact of the STS measurement, and that asymmetric charge distribution effects between the individual graphene layers are observable via STS. arXiv:1909.04280v2 [cond-mat.mtrl-sci]

The three-omega method, a powerful technique to measure the thermal conductivity of nanometer-thick films and the interfaces between them, has historically employed straight conductive wires to act as both heaters and thermometers. When investigating stochastically prepared samples such as two-dimensional materials and nanomembranes, residue and excess material can make it difficult to fit the required millimeter-long straight wire on the sample surface. There are currently no available criteria for how diverting three-omega heater wires around obstacles affects the validity of the thermal measurement. In this Letter, we quantify the effect of the wire curvature by performing three-omega experiments with a wide range of frequencies using both curved and straight heater geometries on SiO2/Si samples. When the heating wire is curved, we find that the measured Si substrate thermal conductivity changes by only 0.2%. Similarly, we find that wire curvature has no significant effect on the determination of the thermal resistance of an ∼65 nm SiO2 layer, even for the sharpest corners considered here, for which the largest measured ratio of the thermal penetration depth of the applied thermal wave to radius of curvature of the heating wire is 4.3. This result provides useful design criteria for three-omega experiments by setting a lower bound for the maximum ratio of the thermal penetration depth to wire radius of curvature.