We simulate scanning probe imaging of the local density of states related to scattering Fermi level wave functions inside a resonant cavity. We calculate potential landscape within the cavity taking into account the Coulomb charge of the probe and its screening by deformation of the twodimensional electron gas using the local density approximation. Approximation of the tip potential by a Lorentz function is discussed. The electron transfer problem is solved with a finite difference approach. We look for stable work points for the extraction of the local density of states from conductance maps. We find that conductance maps are highly correlated with the local density of states when the Fermi energy level enters into Fano resonance with states localized within the cavity. Generally outside resonances the correlation between the local density of states and conductance maps is low.

We consider quantum point contact (QPC) defined within a disordered two-dimensional electron gas as studied by scanning gate microscopy. We evaluate the conductance maps in the Landauer approach with a wave-function picture of electron transport for samples with both low and high electron mobility at finite temperatures. We discuss the spatial distribution of the impurities in the context of the branched electron flow. We reproduce the surprising temperature stability of the experimental interference fringes far from the QPC. Next, we discuss funnel-shaped features that accompany splitting of the branches visible in previous experiments. Finally, we study elliptical interference fringes formed by an interplay of scattering by the pointlike impurities and by the scanning probe. We discuss the details of the elliptical features as functions of the tip voltage and the temperature, showing that the first interference fringe is very robust against the thermal widening of the Fermi level. We present a simple analytical model that allows for extraction of the impurity positions and the electron-gas depletion radius induced by the negatively charged tip of the atomic force microscope, and apply this model on experimental scanning gate images showing such elliptical fringes.

We report on the observation of magnetoresistance oscillations in graphene p-n junctions. The oscillations have been observed for six samples, consisting of single-layer and bilayer graphene, and persist up to temperatures of 30 K, where standard Shubnikov-de Haas oscillations are no longer discernible. The oscillatory magnetoresistance can be reproduced by tight-binding simulations. We attribute this phenomenon to the modulated densities of states in the n-and p-regions. p-n junctions are among the basic building blocks of any electronic circuit. The ambipolar nature of graphene provides a flexible way to induce p-n junctions by elec-trostatic gating. This offers the opportunity to tune the charge carrier densities in the n-and p-doped regions independently. The potential gradient across a p-n interface depends on the thickness of the involved insula-tors and can also be modified by appropriate gate voltages. Due to the high electronic quality of present day graphene devices a number of transport phenomena in pnp or npn junctions have been reported, such as ballistic Fabry-Pérot oscillations 1-3 and so-called snake states 4,5 , both of which depend on characteristic length scales of the sample. Here we report on the discovery of yet another kind of oscillation, which does not depend on any such length scale. The oscillations occur in the bipolar regime, in the magnetic field range where Shubnikov-de Haas oscillations are observed in the unipolar regime. These novel oscillations in the bipolar regime are governed by the unique condition that the distance between two resistance minima (or maxima) in gate voltage space is given by a constant filling factor difference of ∆ν = 8. The features are remarkably robust: they occur in samples with one and two p-n interfaces; in single and bilayer graphene; up to temperatures of 30 K (where Shubnikov-de Haas oscillations have long disappeared); over a large density range; for interface lengths ranging from 1 µm to 3 µm and in both pnp and npn regimes. The oscillations have been observed in a magnetic field range of B = 0.4 T up to B = 1.4 T. Their periodicity does not sample name A B C D E F sample width W (µm) 1.3 1.4 1.1 0.9 3 1.2 sample length L (µm) 3.0 1.4 1.0 2.3 3 2.8 top gate length L TG (µm) 1.1 0.7 0.55 1.2 1.0 1.0 distance to top gate (nm) 23 44 28 57 35 25 number of graphene layers 2 1 2 2 2 2 junction type npn pn npn pn npn npn TABLE I. Characteristics of samples A-F match the periodicity of the aforementioned snake states. In this paper we address this phenomenon and suggest a model which can qualitatively explain the oscillations. Measurements were performed on six samples in total , which all consist of a graphene flake encapsulated between two hexagonal boron nitride (h-BN) flakes on a Si/SiO 2 substrate. They all show similar behavior. This paper focuses on measurements performed on one sample (sample A), with the device geometry sketched in Fig. 1a. Specifications of the other five samples are summarized in table I. The bilayer graphene (BLG) flake was e...

Quantum Hall effects offer a formidable playground for the investigation of quantum transport phenomena. Edge modes can be deflected, branched, and mixed by designing a suitable potential landscape in a two-dimensional conducting system subject to a strong magnetic field. In the present work, we demonstrate a buried split-gate architecture and use it to control electron conduction in large-scale single-crystal monolayer graphene grown by chemical vapor deposition. The control of the edge trajectories is demonstrated by the observation of various fractional quantum resistances, as a result of a controllable interedge scattering. Experimental data are successfully modeled both numerically and analytically within the Landauer-Buttiker formalism. Our architecture is particularly promising and unique in view of the investigation of quantum transport via scanning probe microscopy, since graphene constitutes the topmost layer of the device. For this reason, it can be approached and perturbed by a scanning probe down to the limit of mechanical contact

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