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Devices made from two dimensional materials such as graphene and transition metal dichalcogenides exhibit remarkable electronic properties of interest to many subdisciplines of nanoscience. Owing to their 2D nature, their quality is highly susceptible to contamination and degradation when exposed to the ambient environment. Protecting the 2D layers by encapsulation between hexagonal boron nitride layers significantly improves their quality. Locating these samples within the encapsulant and assessing their integrity prior to further processing then becomes challenging. Here we show that conductive scanning probe techniques such as electrostatic force and Kelvin force microscopy makes it possible to visualize the encapsulated layers, their charge environment and local defects including cracks and bubbles on the sub-micrometer scale. Our techniques are employed without requiring electrical contact to the embedded layer, providing valuable feedback on the local electronic quality prior to any device etching or electrode deposition. We show that these measurement modes, which are simple extensions of atomic force microscopy, are perfectly suited for imaging encapsulated conductors and their local charge environments.
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The flow of charge carriers in materials can, under some circumstances, mimic the flow of viscous fluids. In order to visualize the consequences of such effects, new methodologies must be developed that can probe the quasiparticle flow profile with nm-scale resolution as the geometric parameters of the system are continuously evolved. In this work, scanning tunneling potentiometry (STP) is used to image quasiparticle flow around engineered electrostatic barriers in graphene/hBN heterostructures. Measurements are performed as electrostatic dams - defined by lateral pn-junction barriers - are broken within the graphene sheet, and carriers move through conduction channels with physical widths that vary continuously from pinch-off to um-scale. Local, STP measurements of the electrochemical potential allow for direct characterization of the evolving flow profile, which we compare to finite-element simulations of a Stokesian fluid with varying parameters. Our results reveal distinctly non-Ohmic flow profiles, with charge dipoles forming across barriers due to carrier scattering and accumulation on the upstream side, and depletion downstream. Conductance measurements of individual channels, meanwhile, reveal that at low temperatures the quasiparticle flow is ballistic, but as the temperature is raised there is a Knudsen-to-Gurzhi regime crossover where the fluid becomes viscous and the channel conductance exceeds the ballistic limit set by Sharvin conductance. These results provide a clear illustration of how carrier flow in a Fermi fluid evolves as a function of carrier density, channel width, and temperature. They also demonstrate how STP can be used to extract key parameters of quasiparticle transport, with a spatial resolution that exceeds that of other methods by orders of magnitude.
Devices made from two-dimensional (2D) materials such as graphene or transition metal dichalcogenides possess interesting electronic properties that can become accessible to experimental probes when the samples are protected from deleterious environmental effects by encapsulating them between hexagonal boron nitride (hBN) layers. While the encapsulated flakes can be detected through post-processing of optical images or confocal Raman mapping, these techniques lack the sub-micrometer scale resolution to identify tears, structural defects or impurities, which is crucial for the fabrication of high-quality devices. Here we demonstrate a simple method to visualize such buried flakes with sub-micrometer resolution, by combining Kelvin force probe microscopy (KPFM) with electrostatic force microscopy (EFM). KPFM, which measures surface potential fluctuations, is extremely effective in spotting charged contaminants within and on top of the heterostructure, making it possible to distinguish contaminated regions in the buried flake. When applying a tip bias larger than the surface potential fluctuations, EFM becomes extremely efficient in highlighting encapsulated flakes and their sub-micron structural defects. We show that these imaging modes, which are standard extensions of atomic force microscopy (AFM), are perfectly suited for locating encapsulated conductors, for visualizing nanometer scale defects and bubbles, and for characterizing their local charge environment.
We report a proof-of-concept study of extraordinary magnetoresistance (EMR) in devices of monolayer graphene encapsulated in hexagonal boron nitride, having metallic edge contacts and a central metal shunt. Extremely large EMR values, $MR=(R(B) - R_0) / R_0sim 10^5$, are achieved in part because $R_0$ approaches or crosses zero as a function of the gate voltage, exceeding that achieved in high mobility bulk semiconductor devices. We highlight the sensitivity, $dR/dB$, which in two-terminal measurements is the highest yet reported for EMR devices, and in particular exceeds prior results in graphene-based devices by a factor of 20. An asymmetry in the zero-field transport is traced to the presence of $pn$-junctions at the graphene-metal shunt interface.
Accessing intrinsic properties of a graphene device can be hindered by the influence of contact electrodes. Here, we capacitively couple graphene devices to superconducting resonant circuits and observe clear changes in the resonance- frequency and -widths originating from the internal charge dynamics of graphene. This allows us to extract the density of states and charge relaxation resistance in graphene p-n junctions without the need of electrical contacts. The presented characterizations pave a fast, sensitive and non-invasive measurement of graphene nanocircuits.
A scalable tight-binding model is applied for large-scale quantum transport calculations in clean graphene subject to electrostatic superlattice potentials, including two types of graphene superlattices: moire patterns due to the stacking of graphene and hexagonal boron nitride (hBN) lattices, and gate-controllable superlattices using a spatially modulated gate capacitance. In the case of graphene/hBN moire superlattices, consistency between our transport simulation and experiment is satisfactory at zero and low magnetic field, but breaks down at high magnetic field due to the adopted simple model Hamiltonian that does not comprise higher-order terms of effective vector potential and Dirac mass terms. In the case of gate-controllable superlattices, no higher-order terms are involved, and the simulations are expected to be numerically exact. Revisiting a recent experiment on graphene subject to a gated square superlattice with periodicity of 35 nm, our simulations show excellent agreement, revealing the emergence of multiple extra Dirac cones at stronger superlattice modulation.
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