We consider conductance mapping of systems based on the two-dimensional electron gas with scanning gate microscopy using two and more tips of the atomic force microscope. The paper contains results of numerical simulations for a model tip potential with a proposal of a few procedures for extraction and manipulation the ballistic transport properties. In particular, we demonstrate that the multi-tip techniques can be used for readout of the Fermi wavelength, detection of potential defects, filtering specific transverse modes, tuning the system into resonant conditions under which a stable map of a local density of states can be extracted from conductance maps using a third tip.
We use scanning gate microscopy to map out the trajectories of ballistic carriers in high-mobility graphene encapsulated by hexagonal boron nitride and subject to a weak magnetic field. We employ a magnetic focusing geometry to image carriers that emerge ballistically from an injector, follow a cyclotron path due to the Lorentz force from an applied magnetic field, and land on an adjacent collector probe. The local electric field generated by the scanning tip in the vicinity of the carriers deflects their trajectories, modifying the proportion of carriers focused into the collector. By measuri…
We demonstrate the emergence of classical features in electronic quantum transport for the scanning gate microscopy response in a cavity defined by a quantum point contact and a micron-sized circular reflector. The branches in electronic flow characteristic of a quantum point contact opening on a two-dimensional electron gas with weak disorder are folded by the reflector, yielding a complex spatial pattern. Considering the deflection of classical trajectories by the scanning gate tip allows to establish simple relationships of the scanning pattern, which are in agreement with recent experiment…
We study a theoretical model of virtual scanning tunneling microscopy (VSTM), a proposed application of interlayer tunneling in a bilayer system to locally probe a two-dimensional electron system (2DES) in a semiconductor heterostructure. We consider tunneling for the case where transport in the 2DESs is ballistic, and show that the zero-bias anomaly is suppressed by extremely efficient screening. Since such an anomaly would complicate the interpretation of data from a VSTM, this result is encouraging for efforts to implement such a microscopy technique.
We perform scanning gate experiments on ballistic constrictions in the presence of small perpendicular magnetic fields. The constrictions form the entrance and exit of a circular gate-defined ballistic stadium. Close to constrictions we observe sets of regular fringes creating a checker board pattern. Inside the stadium conductance fluctuations governed by chaotic dynamics of electrons are visible. The checker board pattern allows us to determine the number of transmitted modes in the constrictions forming between the tip-induced potential and gate-defined geometry. Spatial investigation of th…
Ballistic injection in a nanodevice is a complex process where electrons can either be transmitted or reflected, thereby introducing deviations from the otherwise quantized conductance. In this context, quantum rings (QRs) appear as model geometries: in a semiclassical view, most electrons bounce against the central QR antidot, which strongly reduces injection efficiency. Thanks to an analogy with Rutherford scattering, we show that a local partial depletion of the QR close to the edge of the antidot can counter-intuitively ease ballistic electron injection. On the contrary, local charge accum…
We present conductance measurements of a ballistic circular stadium influenced by a scanning gate. When the tip depletes the electron gas below, we observe very pronounced and regular fringes covering the entire stadium. The fringes correspond to transmitted modes in constrictions formed between the tip-induced potential and the boundaries of the stadium. Moving the tip and counting the fringes gives us exquisite control over the transmission of these constrictions. We use this control to form a quantum ring with a specific number of modes in each arm showing the Aharonov-Bohm effect in low-fi…
Numerous experimental and theoretical studies have focused on low-dimensional systems locally perturbed by the biased tip of a scanning force microscope. In all cases either open or closed weakly gate-tunable nanostructures have been investigated, such as quantum point contacts, open or closed quantum dots, etc. We study the behaviour of the conductance of a quantum point contact with a gradually forming adjacent cavity in series under the influence of a scanning gate. Here, an initially open quantum point contact system gradually turns into a closed cavity system. We observe branches and inte…
The effect on the vibrational and thermal properties of gradually interconnected nanoinclusions embedded in an amorphous silicon matrix is studied using MD simulations. The nanoinclusion arrangement ranges from an aligned sphere array to an interconnected mesh of nanowires. Wave-packet simulations scanning different polarizations and frequencies reveal that the interconnection of the nanoinclusions at constant volume fraction induces a strong increase of the mean free path of high frequency phonons, but does not affect the energy diffusivity. The mean free path and energy diffusivity are then …
We theoretically propose to directly observe the chiral nature of charge carriers in graphene mono- and bilayers within a controlled scattering experiment. The charge located on a capacitively coupled scanning probe microscope (SPM) tip acts as a scattering center with controllable position on the graphene sheet. Unambiguous features from the chirality of the particles in single and bilayer graphene arise in the ballistic transport in the presence of such a scattering center. To theoretically model the scattering from the smooth potential created by the SPM tip, we develop the scattering forma…
This article reports on tunable electron backscattering investigated with the biased tip of a scanning force microscope. Using a channel defined by a pair of Schottky gates, the branched electron flow of ballistic electrons injected from a quantum point contact is guided by potentials of a tunable height well below the Fermi energy. The transition from injection into an open two-dimensional electron gas to a strongly confined channel exhibits three experimentally distinct regimes: one in which branches spread unrestrictedly, one in which branches are confined but the background conductance is …
Tailored electrostatic potentials are the foundation of scanning gate microscopy. We present several aspects of the tip-induced potential on the two-dimensional electron gas. First, we give methods on how to estimate the size of the tip-induced potential. Then, a ballistic cavity is formed and studied as a function of the bias-voltage of the metallic top gates and probed with the tip-induced potential. It is shown how the potential of the cavity changes by tuning the system to a regime where conductance quantization in the constrictions formed by the tip and the top gates occurs. This conducta…
We measure transport through a Ga[Al]As heterostructure at temperatures between 0.1 K and 30 K. Increasing the temperature enhances the electron-electron scattering rate and viscous effects in the two-dimensional electron gas arise. To probe this regime we measure so-called vicinity voltages and use a voltage-biased scanning tip to induce a movable local perturbation. We find that the scanning gate images differentiate reliably between the different regimes of electron transport. Our data are in good agreement with recent theories for interacting electron liquids in the ballistic and viscous r…
We present an efficient numerical approach for treating ballistic quantum transport across devices described by tight binding (TB) Hamiltonians designated to systems with localized potential defects. The method is based on the wave function matching approach, Lippmann-Schwinger equation (LEQ) and the scattering matrix formalism. We show that the number of matrix elements of the Green's function to be evaluated for the unperturbed system can be essentially reduced by projection of the time reversed scattering wave functions on LEQ which radically improves the speed and lowers the memory consump…
Traditionally, the understanding of quantum transport, coherent and ballistic1, relies on the measurement of macroscopic properties such as the conductance. While powerful when coupled to statistical theories, this approach cannot provide a detailed image of "how electrons behave down there". Ideally, understanding transport at the nanoscale would require tracking each electron inside the nano-device. Significant progress towards this goal was obtained by combining Scanning Probe Microscopy (SPM) with transport measurements2-7. Some studies even showed signatures of quantum transport in the su…
The origin of the anomalous transport feature appearing at conductance G \approx 0.7 x (2e2/h) in quasi-1D ballistic devices - the so-called 0.7 anomaly - represents a long standing puzzle. Several mechanisms were proposed to explain it, but a general consensus has not been achieved. Proposed explanations are based on quantum interference, Kondo effect, Wigner crystallization, and more. A key open issue is whether point defects that can occur in these low-dimensional devices are the physical cause behind this conductance anomaly. Here we adopt a scanning gate microscopy technique to map indivi…
We report numerical simulation result of a recently proposed \{P. Bruno, Phys. Rev. Lett {\bf 79}, 4593, (1997)\} approach to perform magnetic scanning tunneling microscopy with a two terminal non-magnetic tip. It is based upon the spin asymmetry effect of the tunneling current between a ferromagnetic surface and a two-terminal non-magnetic tip. The spin asymmetry effect is due to the spin-orbit scattering in the tip. The effect can be viewed as a Mott scattering of tunneling electrons within the tip. To obtain quantitative results we perform numerical simulation within the single band tight b…
A theoretical study is presented of the ballistic electron emission spectra (BEES) of individual insulating and conducting organic molecules chemisorbed on a silicon substrate and buried under a thin gold film. It is predicted that ballistic electrons injected into the gold film from a scanning tunneling microscope tip should be transmitted so weakly to the silicon substrate by alkane molecules of moderate length (decane, hexane) and their thiolates that individual buried molecules of this type will be difficult to detect in BEES experiments. However, resonant transmission by molecules contain…
We investigate the transport of electrons in disordered and pristine graphene devices. Fano shot noise, a standard metric to assess the mechanism for electronic transport in mesoscopic devices, has been shown to produce almost the same magnitude ($\approx 1/3$) in ballistic and diffusive graphene devices and is therefore of limited applicability. We consider a two-terminal geometry where the graphene flake is contacted by narrow metallic leads. We propose that the dependence of the conductance on the position of one of the leads, a conductance profile, can give us insight into the charge flow,…
Quantum spin Hall (QSH) insulators have unique electronic properties, comprising a band gap in their two-dimensional interior and one-dimensional spin-polarized edge states in which current flows ballistically. In scanning tunneling microscopy (STM), the edge states manifest themselves as a localized density of states. However, there is a significant research gap between the observation of edge states in nanoscale spectroscopy, and the detection of ballistic transport in edge channels which typically relies on transport experiments with microscale lithographic contacts. Here, we study few-laye…
We have used the scanning charged tip of an Atomic Force Microscope (AFM) to produce images of the conductance variation of a quantised 1D ballistic channel. The channel was formed using electron beam defined 700 nm wide split gate surface electrodes over a high mobility GaAs/AlGaAs heterostructure with a two dimensional electron gas (2DEG) 98 nm beneath the surface. We operate the AFM at 1.5 K and 4.2 K in magnetic fields up to 2 T to observe several phenomena. With a dc voltage on the AFM tip we have produced conduction images of the tip potential perturbation, as the channel is a sensitive …
We use a cooled Scanning Probe Microscope (SPM) to electron motion in nanoscale devices. The charged tip of the SPM is raster scanned at a constant height above the surface as the conductance of the device is measured. The image charge scatters electrons away, changing the path of electrons through the sample.1-3 Using this technique, we have imaged cyclotron orbits3 for ballistic hBN-graphene-hBN devices that flow between two narrow contacts in the magnetic focusing regime. Here we present an analysis of our magnetic focusing imaging results based on the effects of the tip-created charge dens…
Quantum Coherent Transport of 1D ballistic states in second order topological insulator Bi$_4$Br$_4$
Université Paris-Saclay（巴黎萨克雷大学）；CNRS（法国国家科学研究中心）；Laboratoire de Physique des Solides（固体物理实验室）；Materials and Structures Laboratory, Institute of Science Tokyo（东京科学材料结构实验室）；Centre de Nanosciences et de Nanotechnologies（纳米科学与纳米技术中心）；Université de Lille（里尔大学）；Institut d’Electronique, de Microélectronique et de Nanotechnologie（电子、微电子和纳米技术研究所）
Scanning gate microscopy measurements in a circular ballistic cavity with a tip placed near its center yield a non-monotonic dependence of the conductance on the tip voltage. Detailed numerical quantum calculations reproduce these conductance oscillations, and a classical scheme leads to its physical understanding. The large-amplitude conductance oscillations are shown to be of classical origin, and well described by the effect of a particular class of short trajectories.
We have prepared solutions of multiwalled carbon nanotubes in Aroclor 1254, a mixture of polychlorinated biphenyls. The solutions are stable at room temperature. Transport measurements were performed using a scanning--tunneling probe on a sample prepared by spin--coating of the solution on gold substrates. Conductance steps were clearly seen. An histogram of a high number of traces shows maximum peaks at integer values of the conductance quantum $G_0 = 2e^2/h$, demonstrating ballistic transport at room temperature along the carbon nanotube over distances longer than $1.4μm$.
By combining quantum simulations of electron transport and scanning-gate microscopy, we have shown that the current transmitted through a semiconductor two-path rectangular network in the ballistic and coherent regimes of transport can be paradoxically degraded by adding a third path to the network. This is analogous to the Braess paradox occurring in classical networks. Simulations reported here enlighten the role played by congestion in the network.
The existence of strong trigonal warping around the K point for the low energy electronic states in multilayer (N$\geq$2) graphene films and graphite is well established. It is responsible for phenomena such as Lifshitz transitions and anisotropic ballistic transport. The absolute orientation of the trigonal warping with respect to the center of the Brillouin zone is however not agreed upon. Here, we use quasiparticle scattering experiments on a gated bilayer graphene/hexagonal boron nitride heterostructure to settle this disagreement. We compare Fourier transforms of scattering interference m…
Ballistic conductance through a single atom adsorbed on a metallic surface and probed by a scanning tunneling microscope (STM) tip can be decomposed into eigenchannel contributions, which can be potentially obtained from shot noise measurements. Our density functional theory calculations provide evidence that transmission probabilities of these eigenchannels encode information on the modifications of the adatom's local density of states caused by its interaction with the STM tip. In the case of open shell atoms, this can be revealed in nonmonotonic behavior of the eigenchannel's transmissions …
The pattern of branched electron flow revealed by scanning gate microscopy shows the distribution of ballistic electron trajectories. The details of the pattern are determined by the correlated potential of remote dopants with an amplitude far below the Fermi energy. We find that the pattern persists even if the electron density is significantly reduced such that the change in Fermi energy exceeds the background potential amplitude. The branch pattern is robust against changes in charge carrier density, but not against changes in the background potential caused by additional illumination of th…
Scanning Gate Microscopy Modulation of Supercurrent in Graphene Josephson Junctions
Istituto Nanoscienze–CNR, NEST-Scuola Normale Superiore（意大利国家研究委员会纳米科学研究所，NEST-比萨高等师范学校）；Dipartimento di Fisica, Università di Genova（热那亚大学物理系）；CNR-SPIN（意大利国家研究委员会自旋物理学研究所）；Center for Nanotechnology Innovation, Laboratorio NEST, Istituto Italiano di Tecnologia（意大利理工大学NEST纳米技术创新中心）；Research Center for Electronic and Optical Materials, National Institute for Materials Science（日本物质材料研究机构电子与光学材料研究中心）；Research Center for Materials Nanoarchitectonics, National Institute for Materials Science（日本物质材料研究机构材料纳米构造研究中心）
Graphene has evolved as a platform for quantum transport that can compete with the best and cleanest semiconductor systems. Recently, many interesting local properties of carrier transport in graphene have been investigated by various scanning probe techniques. Here, we report on the observation of distinct electronic jets emanating from a narrow split-gate defined channel in bilayer graphene. We find that these jets, which are visible via their interference patterns, occur predominantly with an angle of 60° between each other. This observation is related to the specific bandstructure of bilay…
Hydrodynamics is a general description for the flow of a fluid, and is expected to hold even for fundamental particles such as electrons when inter-particle interactions dominate. While various aspects of electron hydrodynamics were revealed in recent experiments, the fundamental spatial structure of hydrodynamic electrons, the Poiseuille flow profile, has remained elusive. In this work, we provide the first real-space imaging of Poiseuille flow of an electronic fluid, as well as visualization of its evolution from ballistic flow. Utilizing a scanning nanotube single electron transistor, we im…
A low-temperature scanning tunneling microscope is employed to build a junction comprising a Co atom bridging a copper-coated tip and a Cu(100) surface. An Abrikosov-Suhl-Kondo resonance is evidenced in the differential conductance and its width is shown to vary exponentially with the ballistic conductance regardless of the tip structure. Using a theoretical description based on the Anderson model, we show that the Kondo effect and the conductance are related through the atomic relaxations affecting the environment of the Co atom.
Nanoscale solid-solid contacts define a wealth of material behaviours from the electrical and thermal conductivity in modern electronic devices to friction and losses in micro- and nanoelectromechanical systems. For modern ultra-high integration processor chips, power electronic devices and thermoelectrics one of the most essential, but thus far most challenging, aspects is the assessment of the heat transport at the nanoscale sized interfaces between their components. While this can be effectively addressed by a scanning thermal microscopy, or SThM, which demonstrates the highest spatial reso…
Geometry-Induced Skin Effect in Electron Hydrodynamics
Wrocław University of Science and Technology（弗罗茨瓦夫科技大学）；Nordita, KTH Royal Institute of Technology and Stockholm University（诺迪塔，皇家理工学院和斯德哥尔摩大学）；Niels Bohr Institute, Copenhagen University（尼尔斯·玻尔研究所，哥本哈根大学）
Graphene p-n junctions offer a potentially powerful approach towards controlling electron trajectories via collimation and focusing in ballistic solid-state devices. The ability of p-n junctions to control electron trajectories depends crucially on the doping profile and roughness of the junction. Here, we use four-probe scanning tunneling microscopy and spectroscopy (STM/STS) to characterize two state-of-the-art graphene p-n junction geometries at the atomic scale, one with CMOS polySi gates and another with naturally cleaved graphite gates. Using spectroscopic imaging, we characterize the lo…
Imaging flat band electron hydrodynamics in biased bilayer graphene
University of California, Santa Barbara（加州大学圣塔芭芭拉分校）；University of Colorado, Boulder（科罗拉多大学博尔德分校）；National Institute for Materials Science（国立材料研究所）；University of Colorado, Denver（科罗拉多大学丹佛分校）
