Edge channels of broken-symmetry quantum Hall states in graphene visualized by atomic force microscopy.

The quantum Hall (QH) effect, a topologically non-trivial quantum phase, expanded the concept of topological order in physics bringing into focus the intimate relation between the "bulk" topology and the edge states. The QH effect in graphene is distinguished by its four-fold degenerate zero energy Landau level (zLL), where the symmetry is broken by electron interactions on top of lattice-scale potentials. However, the broken-symmetry edge states have eluded spatial measurements. In this article, we spatially map the quantum Hall broken-symmetry edge states comprising the graphene zLL at integer filling factors of [Formula: see text] across the quantum Hall edge boundary using high-resolution atomic force microscopy (AFM) and show a gapped ground state proceeding from the bulk through to the QH edge boundary. Measurements of the chemical potential resolve the energies of the four-fold degenerate zLL as a function of magnetic field and show the interplay of the moiré superlattice potential of the graphene/boron nitride system and spin/valley symmetry-breaking effects in large magnetic fields.

Tuning single-electron charging and interactions between compressible Landau level islands in graphene.

Interacting and tunable quantum dots (QDs) have been extensively exploited in condensed matter physics and quantum information science. Using a low-temperature scanning tunneling microscope (STM), we both create and directly image a new type of coupled QD system in graphene, a highly interacting quantum relativistic system with tunable density. Using detailed scanning tunneling spectroscopy (STS) measurements, we show that Landau quantization inside a potential well enables novel electron confinement via the incompressible strips between partially filled Landau levels (LLs), forming isolated and concentric LL QDs. By changing the charge density and the magnetic field we can tune continuously between single- and double-concentric LL QD systems within the same potential well. In the concentric QD regime, single-electron charging peaks of the two dots intersect, displaying a characteristic avoidance pattern. At moderate fields, we observe an unconventional avoidance pattern that differs significantly from that observed in capacitively coupled double-QD systems. We find that we can reproduce in detail this anomalous avoidance pattern within the framework of the electrostatic double-QD model by replacing the capacitive interdot coupling with a phenomenological charge-counting system in which charges in the inner concentric dot are counted in the total charge of both islands. The emergence of such strange forms of interdot coupling in a single potential well, together with the ease of producing such charge pockets in graphene and other two-dimensional (2D) materials, reveals an intriguing testbed for the confinement of 2D electrons in customizable potentials.

Nanoscale Mapping of the Double Layer Potential at the Graphene-Electrolyte Interface.

The electrical double layer (EDL) governs the operation of multiple electrochemical devices, determines reaction potentials, and conditions ion transport through cellular membranes in living organisms. The few existing methods of EDL probing have low spatial resolution, usually only providing spatially averaged information. On the other hand, traditional Kelvin probe force microscopy (KPFM) is capable of mapping potential with nanoscale lateral resolution but cannot be used in electrolytes with concentrations higher than several mmol/L. Here, we resolve this experimental impediment by combining KPFM with graphene-capped electrolytic cells to quantitatively measure the potential drop across the EDL in aqueous electrolytes of decimolar and molar concentrations with a high lateral resolution. The surface potential of graphene in contact with deionized water and 0.1 mol/L solutions of CuSO4 and MgSO4 as a function of counter electrode voltage is reported. The measurements are supported by numerical modeling to reveal the role of the graphene membrane in potential screening and to determine the EDL potential drop. The proposed approach proves to be especially useful for imaging spatially inhomogeneous systems, such as nanoparticles submerged in an electrolyte solution. It could be suitable for in operando and in vivo measurements of the potential drop in the EDL on the surfaces of nanocatalysts and biological cells in equilibrium with liquid solutions.

Unveiling Defect-Mediated Charge-Carrier Recombination at the Nanometer Scale in Polycrystalline Solar Cells.

Solar cells made of polycrystalline thin-films can outperform their single-crystalline counterparts despite the presence of grain boundaries (GBs). To unveil the influence of GBs, high spatial resolution characterization techniques are needed to measure local properties in their vicinity. However, results obtained using single technique may provide limited aspects about the GB effect. Here, we employ two techniques, near-field scanning photocurrent microscopy (NSPM) and scanning transmission electron microscope based cathodoluminescence spectroscopy (STEM-CL), to characterize CdTe solar cells at the nanoscale. The signal contrast from the grain interiors (GIs) to the GBs, for high-efficiency cells where CdTe is deposited at a high substrate temperature (500 °C) and treated by CdCl2, is found reverse from one technique to another. NSPM reveals increased photocurrents at the GBs, while STEM-CL shows reduced CL intensity and energy redshifts of the spectral peak at the GBs. The results are attributed to the increased nonradiative recombination and the band bending mediated by the surface defects and the shallow-level defects at GBs, respectively. We discuss the advantages of sample geometry for room-temperature STEM-CL and present numerical simulations as well as analytical models to extract the ratio of GB recombination velocity to minority carrier diffusivity that can be used for evaluating the GB effect in other polycrystalline solar cells.

Direct-Write Lithiation of Silicon Using a Focused Ion Beam of Li.

Electrochemical processes that govern the performance of lithium ion batteries involve numerous parallel reactions and interfacial phenomena that complicate the microscopic understanding of these systems. To study the behavior of ion transport and reaction in these applications, we report the use of a focused ion beam of Li+ to locally insert controlled quantities of lithium with high spatial resolution into electrochemically relevant materials in vacuo. To benchmark the technique, we present results on direct-write lithiation of 35 nm thick crystalline silicon membranes using a 2 keV beam of Li+ at doses up to 1018 cm-2 (104 nm-2). We confirm quantitative sub-µm control of lithium insertion and characterize the concomitant morphological, structural, and functional changes of the system using a combination of electron and scanning probe microscopy. We observe saturation of interstitial lithium in the silicon membrane at ≈10% dopant number density and spillover of excess lithium onto the membrane's surface. The implanted Li+ is demonstrated to remain electrochemically active. This technique will enable controlled studies and improve understanding of Li+ ion interaction with local defect structures and interfaces in electrode and solid-electrolyte materials.

Interaction-driven quantum Hall wedding cake-like structures in graphene quantum dots.

Quantum-relativistic matter is ubiquitous in nature; however, it is notoriously difficult to probe. The ease with which external electric and magnetic fields can be introduced in graphene opens a door to creating a tabletop prototype of strongly confined relativistic matter. Here, through a detailed spectroscopic mapping, we directly visualize the interplay between spatial and magnetic confinement in a circular graphene resonator as atomic-like shell states condense into Landau levels. We directly observe the development of a "wedding cake"-like structure of concentric regions of compressible-incompressible quantum Hall states, a signature of electron interactions in the system. Solid-state experiments can, therefore, yield insights into the behavior of quantum-relativistic matter under extreme conditions.

Nanoscale imaging of photocurrent enhancement by resonator array photovoltaic coatings.

Nanoscale surface patterning commonly used to increase absorption of solar cells can adversely impact the open-circuit voltage due to increased surface area and recombination. Here, we demonstrate absorptivity and photocurrent enhancement using silicon dioxide (SiO2) nanosphere arrays on a gallium arsenide (GaAs) solar cell that do not require direct surface patterning. Due to the combined effects of thin-film interference and whispering gallery-like resonances within nanosphere arrays, there is more than 20% enhancement in both absorptivity and photocurrent. To determine the effect of the resonance coupling between nanospheres, we perform a scanning photocurrent microscopy based on a near-field scanning optical microscopy measurement and find a substantial local photocurrent enhancement. The nanosphere-based antireflection coating (ARC), made by the Meyer rod rolling technique, is a scalable and a room-temperature process; and, can replace the conventional thin-film-based ARCs requiring expensive high-temperature vacuum deposition.

Improving dielectric nanoresonator array coatings for solar cells.

Antireflection coatings based on dielectric nanosphere arrays are discussed in application to photovoltaic materials including silicon and gallium arsenide. We perform macro- and nanoscale characterization and finite-difference time-domain calculations demonstrating the enhanced optoelectronic properties. A significant absorptivity enhancement is achieved due to the collective resonant coupling of excited whispering gallery-like modes and thin-film interference effects. The resonant coupling is masked in macroscale measurements by the size variation of nanospheres, but it is clearly seen through imaging photocurrent at the nanoscale with near-field scanning photocurrent microscopy. The resonant coupling can be effectively tuned by the material, configuration, or size of nanospheres. Hybrid coatings combining nanospheres of different materials yield the highest efficiency gain, more than 30 %. We also evaluate an impact of manufacturing defects such as double layer formation. While the performance degrades, the antireflection coating still offers marked improvement in comparison with bare cells.

Paper in Electronic and Optoelectronic Devices.

Paper, one of the oldest materials for storage and exchange of human's information, has been reinvented as a building component of electronic and optoelectronic devices over the past decades with successful demonstration of paper-based or paper-using devices. These recent achievements can meet the demand for lightweight, cost-effective, and/or flexible electronic and optoelectronic devices with advanced functionality and reduced manufacturing costs. This article provides a review of electronic and optoelectronic devices relying on or making use of the unique properties achievable with paper-based materials. Basic scientific/technical principles, quantitative comparisons of material, electronic and/or optical properties, and benefits for each paper-based application are given. Application-specific research challenges, future design considerations, and development directions are also discussed.

Strain Engineering a 4a×√3a Charge Density Wave Phase in Transition Metal Dichalcogenide 1T-VSe2.

We report a rectangular charge density wave (CDW) phase in strained 1T-VSe2 thin films synthesized by molecular beam epitaxy on c-sapphire substrates. The observed CDW structure exhibits an unconventional rectangular 4a×√3a periodicity, as opposed to the previously reported hexagonal 4a×4a structure in bulk crystals and exfoliated thin layered samples. Tunneling spectroscopy shows a strong modulation of the local density of states of the same 4a×√3a CDW periodicity and an energy gap of 2ΔCDW = (9.1 ± 0.1) meV. The CDW energy gap evolves into a full gap at temperatures below 500 mK, indicating a transition to an insulating phase at ultra-low temperatures. First-principles calculations confirm the stability of both 4a×4a and 4a×√3a structures arising from soft modes in the phonon dispersion. The unconventional structure becomes preferred in the presence of strain, in agreement with experimental findings.

An on/off Berry phase switch in circular graphene resonators.

The phase of a quantum state may not return to its original value after the system's parameters cycle around a closed path; instead, the wave function may acquire a measurable phase difference called the Berry phase. Berry phases typically have been accessed through interference experiments. Here, we demonstrate an unusual Berry phase-induced spectroscopic feature: a sudden and large increase in the energy of angular-momentum states in circular graphene p-n junction resonators when a relatively small critical magnetic field is reached. This behavior results from turning on a π Berry phase associated with the topological properties of Dirac fermions in graphene. The Berry phase can be switched on and off with small magnetic field changes on the order of 10 millitesla, potentially enabling a variety of optoelectronic graphene device applications.

Tomography of a Probe Potential Using Atomic Sensors on Graphene.

Our ability to access and explore the quantum world has been greatly advanced by the power of atomic manipulation and local spectroscopy with scanning tunneling and atomic force microscopes, where the key technique is the use of atomically sharp probe tips to interact with an underlying substrate. Here we employ atomic manipulation to modify and quantify the interaction between the probe and the system under study that can strongly affect any measurement in low charge density systems, such as graphene. We transfer Co atoms from a graphene surface onto a probe tip to change and control the probe's physical structure, enabling us to modify the induced potential at a graphene surface. We utilize single Co atoms on a graphene field-effect device as atomic scale sensors to quantitatively map the modified potential exerted by the scanning probe over the whole relevant spatial and energy range.

Depletion region surface effects in electron beam induced current measurements.

Electron beam induced current (EBIC) is a powerful characterization technique which offers the high spatial resolution needed to study polycrystalline solar cells. Current models of EBIC assume that excitations in the p-n junction depletion region result in perfect charge collection efficiency. However we find that in CdTe and Si samples prepared by focused ion beam (FIB) milling, there is a reduced and nonuniform EBIC lineshape for excitations in the depletion region. Motivated by this, we present a model of the EBIC response for excitations in the depletion region which includes the effects of surface recombination from both charge-neutral and charged surfaces. For neutral surfaces we present a simple analytical formula which describes the numerical data well, while the charged surface response depends qualitatively on the location of the surface Fermi level relative to the bulk Fermi level. We find the experimental data on FIB-prepared Si solar cells is most consistent with a charged surface, and discuss the implications for EBIC experiments on polycrystalline materials.

Scanning Tunneling Spectroscopy of Proximity Superconductivity in Epitaxial Multilayer Graphene.

We report on spatial measurements of the superconducting proximity effect in epitaxial graphene induced by a graphene-superconductor interface. Superconducting aluminum films were grown on epitaxial multilayer graphene on SiC. The aluminum films were discontinuous with networks of trenches in the film morphology reaching down to exposed graphene terraces. Scanning tunneling spectra measured on the graphene terraces show a clear decay of the superconducting energy gap with increasing separation from the graphene-aluminum edges. The spectra were well described by Bardeen-Cooper-Schrieffer (BCS) theory. The decay length for the superconducting energy gap in graphene was determined to be greater than 400 nm. Deviations in the exponentially decaying energy gap were also observed on a much smaller length scale of tens of nanometers.

Strong Asymmetric Charge Carrier Dependence in Inelastic Electron Tunneling Spectroscopy of Graphene Phonons.

The observation of phonons in graphene by inelastic electron tunneling spectroscopy has been met with limited success in previous measurements arising from weak signals and other spectral features which inhibit a clear distinction between phonons and miscellaneous excitations. Utilizing a back-gated graphene device that allows adjusting the global charge carrier density, we introduce an averaging method where individual tunneling spectra at varying charge carrier density are combined into one representative spectrum. This method improves the signal for inelastic transitions while it suppresses dispersive spectral features. We thereby map the total graphene phonon density of states, in good agreement with density functional calculations. Unexpectedly, an abrupt change in the phonon intensity is observed when the graphene charge carrier type is switched through a variation of the back-gate electrode potential. This sudden variation in phonon intensity is asymmetric in the carrier type, depending on the sign of the tunneling bias.

Electron beam induced current in the high injection regime.

Electron beam induced current (EBIC) is a powerful technique which measures the charge collection efficiency of photovoltaics with sub-micron spatial resolution. The exciting electron beam results in a high generation rate density of electron-hole pairs, which may drive the system into nonlinear regimes. An analytic model is presented which describes the EBIC response when the total electron-hole pair generation rate exceeds the rate at which carriers are extracted by the photovoltaic cell, and charge accumulation and screening occur. The model provides a simple estimate of the onset of the high injection regime in terms of the material resistivity and thickness, and provides a straightforward way to predict the EBIC lineshape in the high injection regime. The model is verified by comparing its predictions to numerical simulations in one- and two-dimensions. Features of the experimental data, such as the magnitude and position of maximum collection efficiency versus electron beam current, are consistent with the three-dimensional model.

Physics. Creating and probing electron whispering-gallery modes in graphene.

The design of high-finesse resonant cavities for electronic waves faces challenges due to short electron coherence lengths in solids. Complementing previous approaches to confine electronic waves by carefully positioned adatoms at clean metallic surfaces, we demonstrate an approach inspired by the peculiar acoustic phenomena in whispering galleries. Taking advantage of graphene's gate-tunable light-like carriers, we create whispering-gallery mode (WGM) resonators defined by circular pn junctions, induced by a scanning tunneling probe. We can tune the resonator size and the carrier concentration under the probe in a back-gated graphene device over a wide range. The WGM-type confinement and associated resonances are a new addition to the quantum electron-optics toolbox, paving the way to develop electronic lenses and resonators.

Nanoscale imaging of photocurrent and efficiency in CdTe solar cells.

The local collection characteristics of grain interiors and grain boundaries in thin-film CdTe polycrystalline solar cells are investigated using scanning photocurrent microscopy. The carriers are locally generated by light injected through a small aperture (50-300 nm) of a near-field scanning optical microscope in an illumination mode. Possible influence of rough surface topography on light coupling is examined and eliminated by sculpting smooth wedges on the granular CdTe surface. By varying the wavelength of light, nanoscale spatial variations in external quantum efficiency are mapped. We find that the grain boundaries (GBs) are better current collectors than the grain interiors (GIs). The increased collection efficiency is caused by two distinct effects associated with the material composition of GBs. First, GBs are charged, and the corresponding built-in field facilitates the separation and the extraction of the photogenerated carriers. Second, the GB regions generate more photocurrent at long wavelength corresponding to the band edge, which can be caused by a smaller local band gap. Resolving carrier collection with nanoscale resolution in solar cell materials is crucial for optimizing the polycrystalline device performance through appropriate thermal processing and passivation of defects and surfaces.

Renormalization of the graphene dispersion velocity determined from scanning tunneling spectroscopy.

In graphene, as in most metals, electron-electron interactions renormalize the properties of electrons but leave them behaving like noninteracting quasiparticles. Many measurements probe the renormalized properties of electrons right at the Fermi energy. Uniquely for graphene, the accessibility of the electrons at the surface offers the opportunity to use scanned probe techniques to examine the effect of interactions at energies away from the Fermi energy, over a broad range of densities, and on a local scale. Using scanning tunneling spectroscopy, we show that electron interactions leave the graphene energy dispersion linear as a function of excitation energy for energies within ±200 meV of the Fermi energy. However, the measured dispersion velocity depends on density and increases strongly as the density approaches zero near the charge neutrality point, revealing a squeezing of the Dirac cone due to interactions.