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An undirected graph is said to be cordial if there is a friendly (0,1)-labeling of the vertices that induces a friendly (0,1)-labeling of the edges. An undirected graph $G$ is said to be $(2,3)$-orientable if there exists a friendly (0,1)-labeling of the vertices of $G$ such that about one third of the edges are incident to vertices labeled the same. That is, there is some digraph that is an orientation of $G$ that is $(2,3)$-cordial. Examples of the smallest noncordial/non-$(2,3)$-orientable graphs are given and upper bounds on the possible number of edges in a cordial/$(2,3)$-orientable graph are presented. It is also shown that if $T$ is a linear operator on the set of all undirected graphs on $n$ vertices that strongly preserves the set of cordial graphs or the set of $(2,3)$-orientable graphs then $T$ is a vertex permutation.., Comment: 11 pages

A $(0,1)$-labeling of a set is said to be friendly if the number of elements of the set labeled 0 and the number labeled 1 differ by at most 1. Let $g$ be a labeling of the edge set of a graph that is induced by a labeling $f$ of the vertex set. If both $g$ and $f$ are friendly then $g$ is said to be a cordial labeling of the graph. We extend this concept to directed graphs and investigate the cordiality of directed graphs. We show that all directed paths and all directed cycles are cordial. We also discuss the cordiality of oriented trees and other digraphs.

In this article we investigate the existence of (2,3)-cordial labelings of oriented hypercubes. In this investigation, we determine that there exists a (2,3)-cordial oriented hypercube for any dimension divisible by 3. Next, we provide examples of (2,3)-cordial oriented hypercubes of dimension not divisible by 3 and state a conjecture on existence for dimension 3k + 1. We close by presenting the only 3D oriented hypercubes up to isomorphism that are not (2,3)-cordial., Comment: 13 pages, 8 figures, 2021 Southeastern International Conference on Combinatorics, Graph Theory, and Computing. 2021 Mar 11. Boca Raton, FL

Perpendicular magnetic tunnel junctions with GdOX tunneling barriers have shown a unique voltage controllable interlayer magnetic coupling effect. Here we investigate the quality of the GdOX barrier and the coupling mechanism in these junctions by examining the temperature dependence of the tunneling magnetoresistance and the interlayer coupling from room temperature down to 11 K. The barrier is shown to be of good quality with the spin independent conductance only contributing a small portion, 14%, to the total room temperature conductance, similar to AlOX and MgO barriers. The interlayer coupling, however, shows an anomalously strong temperature dependence including sign changes below 80 K. This non-trivial temperature dependence is not described by previous models of interlayer coupling and may be due to the large induced magnetic moment of the Gd ions in the barrier., Comment: 14 pages, 4 figures

(Abridged) In the framework of the BinaMicS project, we have begun a study of the magnetic properties of a sample of intermediate-mass and massive short-period binary systems, as a function of binarity properties. We report in this paper the characterisation of the magnetic field of HD 5550, a double-lined spectroscopic binary system of intermediate-mass, using high-resolution spectropolarimetric Narval observations of HD 5550. We first fit the intensity spectra using Zeeman/ATLAS9 LTE synthetic spectra to estimate the effective temperatures, microturbulent velocities, and the abundances of some elements of both components, as well as the light-ratio of the system. We then fit the least-square deconvolved $I$ profiles to determine the radial and projected rotational velocities of both stars. We then analysed the shape and evolution of the LSD $V$ profiles using the oblique rotator model to characterise the magnetic fields of both stars. We confirm the Ap nature of the primary, previously reported in the literature, and find that the secondary displays spectral characteristics typical of an Am star. While a magnetic field is clearly detected in the lines of the primary, no magnetic field is detected in the secondary, in any of our observation. If a dipolar field were present at the surface of the Am star, its polar strength must be below 40 G. The faint variability observed in the Stokes $V$ profiles of the Ap star allowed us to propose a rotation period of $6.84_{-0.39}^{+0.61}$ d, close to the orbital period ($\sim$6.82 d), suggesting that the star is synchronised with its orbit. By fitting the variability of the $V$ profiles, we propose that the Ap component hosts a dipolar field inclined with the rotation axis at an angle $\beta=156\pm17$ $^{\circ}$ and a polar strength $B_{\rm d}=65 \pm 20$ G. The field strength is the weakest known for an Ap star., Comment: 13 pages, 12 figures, accepted for publication in Astronomy & Astrophysics

Aims. The main-sequence B-type star $\zeta$ Cassiopeiae is known as a N-rich star with a magnetic field discovered with the Musicos spectropolarimeter. We model the magnetic field of the star by means of 82 new spectropolarimetric observations of higher precision to investigate the field strength, topology, and effect. Methods. We gathered data with the Narval spectropolarimeter installed at T\'elescope Bernard Lyot (TBL, Pic du Midi, France) and applied the least-squares deconvolution technique to measure the circular polarisation of the light emitted from $\zeta$ Cas. We used a dipole oblique rotator model to determine the field configuration by fitting the longitudinal field measurements and by synthesizing the measured Stokes V profiles. We also made use of the Zeeman-Doppler Imaging technique to map the stellar surface and to deduce the difference in rotation rate between the pole and equator. Results. $\zeta$ Cas exhibits a polar field strength $B_{\rm pol}$ of 100-150 G, which is the weakest polar field observed so far in a massive main-sequence star. Surface differential rotation is ruled out by our observations and the field of $\zeta$ Cas is strong enough to enforce rigid internal rotation in the radiative zone according to theory. Thus, the star rotates as a solid body in the envelope. Conclusions. We therefore exclude rotationally-induced mixing as the cause of the surface N-enrichment. We discuss that the transport of chemicals from the core to the surface by internal gravity waves is the most plausible explanation for the nitrogen overabundance at the surface of $\zeta$ Cas., Comment: Accepted for publication in Astronomy & Astrophysics on 14/01/2016

The MiMeS project is a large-scale, high resolution, sensitive spectropolarimetric investigation of the magnetic properties of O and early B type stars. Initiated in 2008 and completed in 2013, the project was supported by 3 Large Program allocations, as well as various programs initiated by independent PIs and archival resources. Ultimately, over 4800 circularly polarized spectra of 560 O and B stars were collected with the instruments ESPaDOnS at the Canada-France-Hawaii Telescope, Narval at the T\'elescope Bernard Lyot, and HARPSpol at the European Southern Observatory La Silla 3.6m telescope, making MiMeS by far the largest systematic investigation of massive star magnetism ever undertaken. In this paper, the first in a series reporting the general results of the survey, we introduce the scientific motivation and goals, describe the sample of targets, review the instrumentation and observational techniques used, explain the exposure time calculation designed to provide sensitivity to surface dipole fields above approximately 100 G, discuss the polarimetric performance, stability and uncertainty of the instrumentation, and summarize the previous and forthcoming publications., Comment: Accepted by MNRAS

Some colliding-wind massive binaries, called particle-accelerating colliding-wind binaries (PACWB), exhibit synchrotron radio emission, which is assumed to be generated by a stellar magnetic field. However, no measurement of magnetic fields in these stars has ever been performed. We aim at quantifying the possible stellar magnetic fields present in PACWB to provide constraints for models. We gathered 21 high-resolution spectropolarimetric observations of 9 PACWB available in the ESPaDOnS, Narval and HarpsPol archives. We analysed these observations with the Least Squares Deconvolution method. We separated the binary spectral components when possible. No magnetic signature is detected in any of the 9 PACWB stars and all longitudinal field measurements are compatible with 0 G. We derived the upper field strength of a possible field that could have remained hidden in the noise of the data. While the data are not very constraining for some stars, for several stars we could derive an upper limit of the polar field strength of the order of 200 G. We can therefore exclude the presence of strong or moderate stellar magnetic fields in PACWB, typical of the ones present in magnetic massive stars. Weak magnetic fields could however be present in these objects. These observational results provide the first quantitative constraints for future models of PACWB., Comment: Accepted in A&A

gam Peg is a bright B pulsator showing both p and g modes of beta Cep and SPB types. It has also been claimed to be a magnetic star by some authors while others do not detect a magnetic field. We aimed at checking for the presence of a field, characterise it if it exists or provide a firm upper limit of its strength if it is not detected. If gam Peg is magnetic, it would make an ideal asteroseismic target to test various theoretical scenarios. If it is very weakly magnetic, it would be the first observation of an extension of Vega-like fields to early B stars. Finally, if it is not magnetic and we can provide a very low upper limit on its non-detected field, it would make an important result for stellar evolution models. We acquired high resolution, high signal-to-noise spectropolarimetric Narval data at TBL. We also gathered existing dimaPol@DAO and Musicos@TBL spectropolarimetric data. We analysed the Narval and Musicos observations using the LSD technique to derive the longitudinal magnetic field and Zeeman signatures in lines. The longitudinal field strength was also extracted from the Hbeta line observed with the DAO. With a Monte Carlo simulation we derived the maximum strength of the field possibly hosted by gam Peg. We find that no magnetic signatures are visible in the very high quality spectropolarimetric data. The average longitudinal field measured in the Narval data is Bl=-0.1+/-0.4 G. We derive a very strict upper limit of the dipolar field strength of Bpol~40 G. We conclude that gamma Peg is not magnetic: it does not host a strong stable fossil field as observed in a fraction of massive stars, nor a very weak Vega-like field. There is therefore no evidence that Vega-like fields exist in B stars contrary to the predictions by fossil field dichotomy scenarios. These scenarios should thus be revised. Our results also provide strong constraints for stellar evolution models., Comment: 8 pages, accepted in A&A

Raman spectroscopy, a fast and nondestructive imaging method, can be used to monitor the doping level in graphene devices. We fabricated chemical vapor deposition (CVD) grown graphene on atomically flat hexagonal boron nitride (hBN) flakes and SiO$_2$ substrates. We compared their Raman response as a function of charge carrier density using an ion gel as a top gate. The G peak position, 2D peak position, 2D peak width and the ratio of the 2D peak area to the G peak area show a dependence on carrier density that differs for hBN compared to SiO$_2$. Histograms of two-dimensional mapping are used to compare the fluctuations in the Raman peak properties between the two substrates. The hBN substrate has been found to produce fewer fluctuations at the same charge density owing to its atomically flat surface and reduced charged impurities.

A promising way of testing the impact of a magnetic field on internal mixing (core overshooting, internal rotation) in main-sequence B-type stars is to perform asteroseismic studies of a sample of magnetic pulsators. The CoRoT satellite revealed that the B3IV star HD 43317 is a hybrid SPB/beta Cep-type pulsator that has a wealth of pulsational constraints on which one can perform a seismic modelling, in particular, probing the extent of its convective core and mixing processes. Moreover, indirect indicators of a magnetic field in the star were observed: rotational modulation due to chemical or temperature spots and X-ray emission. Our goal was to directly investigate the field in HD 43317 and, if it is magnetic, to characterise it. We collected data with the Narval spectropolarimeter installed at TBL (T\'elescope Bernard Lyot, Pic du Midi, France) and applied the least-squares deconvolution technique to measure the circular polarisation of the light emitted from HD 43317. We modelled the longitudinal field measurements directly with a dipole. Zeeman signatures in the Stokes V profiles of HD 43317 are clearly detected and rotationally modulated, which proves that this star exhibits an oblique magnetic field. The modulation with the rotation period deduced from the CoRoT light curve is also confirmed, and we found a field strength at the poles of about 1 kG. Our result must be taken into account in future seismic modelling work of this star., Comment: Accepted for publication as a Letter in Astronomy and Astrophysics on 12/08/2013

The Kepler spacecraft is providing time series of photometric data with micromagnitude precision for hundreds of A-F type stars. We present a first general characterization of the pulsational behaviour of A-F type stars as observed in the Kepler light curves of a sample of 750 candidate A-F type stars. We propose three main groups to describe the observed variety in pulsating A-F type stars: gamma Dor, delta Sct, and hybrid stars. We assign 63% of our sample to one of the three groups, and identify the remaining part as rotationally modulated/active stars, binaries, stars of different spectral type, or stars that show no clear periodic variability. 23% of the stars (171 stars) are hybrid stars, which is a much larger fraction than what has been observed before. We characterize for the first time a large number of A-F type stars (475 stars) in terms of number of detected frequencies, frequency range, and typical pulsation amplitudes. The majority of hybrid stars show frequencies with all kinds of periodicities within the gamma Dor and delta Sct range, also between 5 and 10 c/d, which is a challenge for the current models. We find indications for the existence of delta Sct and gamma Dor stars beyond the edges of the current observational instability strips. The hybrid stars occupy the entire region within the delta Sct and gamma Dor instability strips, and beyond. Non-variable stars seem to exist within the instability strips. The location of gamma Dor and delta Sct classes in the (Teff,logg)-diagram has been extended. We investigate two newly constructed variables 'efficiency' and 'energy' as a means to explore the relation between gamma Dor and delta Sct stars. Our results suggest a revision of the current observational instability strips, and imply an investigation of other pulsation mechanisms to supplement the kappa mechanism and convective blocking effect to drive hybrid pulsations., Comment: Accepted for publication in Astronomy and Astrophysics (language edited version). 70 pages, 4 tables, 13 figures. The tables can be found as an appendix to the paper. The quality of the figures has been downgraded compared to the original

Graphene has demonstrated great promise for future electronics technology as well as fundamental physics applications because of its linear energy-momentum dispersion relations which cross at the Dirac point. However, accessing the physics of the low density region at the Dirac point has been difficult because of the presence of disorder which leaves the graphene with local microscopic electron and hole puddles, resulting in a finite density of carriers even at the charge neutrality point. Efforts have been made to reduce the disorder by suspending graphene, leading to fabrication challenges and delicate devices which make local spectroscopic measurements difficult. Recently, it has been shown that placing graphene on hexagonal boron nitride (hBN) yields improved device performance. In this letter, we use scanning tunneling microscopy to show that graphene conforms to hBN, as evidenced by the presence of Moire patterns in the topographic images. However, contrary to recent predictions, this conformation does not lead to a sizable band gap due to the misalignment of the lattices. Moreover, local spectroscopy measurements demonstrate that the electron-hole charge fluctuations are reduced by two orders of magnitude as compared to those on silicon oxide. This leads to charge fluctuations which are as small as in suspended graphene, opening up Dirac point physics to more diverse experiments than are possible on freestanding devices., Comment: Nature Materials advance online publication 13/02/2011

Using scanning tunneling microscopy, we have imaged local charge density fluctuations in monolayer graphene. By placing a small gold nanoparticle on the end of the STM tip, a charge sensor is created. By raster scanning the tip over the surface and using Coulomb blockade spectroscopy, we map the local charge on the graphene. We observe a series of electron and hole doped puddles with a characteristic length scale of about 20 nm. Theoretical calculations for the correlation length of the puddles based on the number of impurities are in agreement with our measurements., Comment: 5 pages, 5 figures

Classical Be stars are rapid rotators of spectral type late O to early A and luminosity class V-III, wich exhibit Balmer emission lines and often a near infrared excess originating in an equatorially concentrated circumstellar envelope, both produced by sporadic mass ejection episodes. The causes of the abnormal mass loss (the so-called Be phenomenon) are as yet unknown. For the first time, we can now study in detail Be stars outside the Earth's atmosphere with sufficient temporal resolution. We investigate the variability of the Be Star CoRoT-ID 102761769 observed with the CoRoT satellite in the exoplanet field during the initial run. One low-resolution spectrum of the star was obtained with the INT telescope at the Observatorio del Roque de los Muchachos. A time series analysis was performed using both cleanest and singular spectrum analysis algorithms to the CoRoT light curve. To identify the pulsation modes of the observed frequencies, we computed a set of models representative of CoRoT-ID 102761769 by varying its main physical parameters inside the uncertainties discussed. We found two close frequencies related to the star. They are 2.465 $\rm c\,d^{-1}$ (28.5 $\mathrm{\mu Hz}$) and 2.441 $\rm c\,d^{-1}$ (28.2 $\mathrm{\mu Hz}$). The precision to which those frequencies were found is 0.018 $\rm c\,d^{-1}$ (0.2 $\mathrm{\mu Hz}$). The projected stellar rotation was estimated to be 120 $\rm km\,s^{-1}$ from the Fourier transform of spectral lines. If CoRoT-ID 102761769 is a typical Galactic Be star it rotates near the critical velocity. The critical rotation frequency of a typical B5-6 star is about 3.5 $\rm c\,d^{-1}$(40.5 $\mathrm{\mu Hz}$), which implies that the above frequencies are really caused by stellar pulsations rather than star's rotation., Comment: 9 pages, 8 figures, accepted: 13 June 2010 Astronomy & Astrophysics

We report on the first asteroseismic analysis of solar-type stars observed by Kepler. Observations of three G-type stars, made at one-minute cadence during the first 33.5d of science operations, reveal high signal-to-noise solar-like oscillation spectra in all three stars: About 20 modes of oscillation can clearly be distinguished in each star. We discuss the appearance of the oscillation spectra, including the presence of a possible signature of faculae, and the presence of mixed modes in one of the three stars., Comment: 5 pages, 4 figure, submitted to Astronomische Nachrichten

We present a lithography-free technique for fabrication of clean, high quality graphene devices. This technique is based on evaporation through hard Si shadow masks, and eliminates contaminants introduced by lithographical processes. We demonstrate that devices fabricated by this technique have significantly higher mobility values than those by standard electron beam lithography. To obtain ultra-high mobility devices, we extend this technique to fabricate suspended graphene samples with mobility as high as 120,000 cm^2/Vs.

We present preliminary asteroseismic results from Kepler on three G-type stars. The observations, made at one-minute cadence during the first 33.5d of science operations, reveal high signal-to-noise solar-like oscillation spectra in all three stars: About 20 modes of oscillation may be clearly distinguished in each star. We discuss the appearance of the oscillation spectra, use the frequencies and frequency separations to provide first results on the radii, masses and ages of the stars, and comment in the light of these results on prospects for inference on other solar-type stars that Kepler will observe., Comment: 16 pages, 3 figures, 1 table; now accepted for publication in ApJ Letters

We have mapped the Dirac point in exfoliated monolayer and bilayer graphene using spatially resolved scanning tunneling spectroscopy (STS) measurements at low temperature. The Dirac point shifts in energy at different locations in graphene. However, a cross correlation with the topography shows no correlation indicating that topographic features such as ripples are not the primary source of the variation. Rather, we attribute the shift of the Dirac point to random charged impurities located near the graphene. Our findings emphasize the need to advance exfoliated graphene sample preparation to minimize the effect of impurities., Comment: 4 pages, 3 figures

We have performed low temperature scanning tunneling spectroscopy measurements on exfoliated bilayer graphene on SiO2. By varying the back gate voltage we observed a linear shift of the Dirac point and an opening of a band gap due to the perpendicular electric field. In addition to observing a shift in the Dirac point, we also measured its spatial dependence using spatially resolved scanning tunneling spectroscopy. The spatial variation of the Dirac point was not correlated with topographic features and therefore we attribute its shift to random charged impurities., Comment: 3 pages, 3 figures

The presence of pulsations in late-type Be stars is still a matter of controversy. It constitutes an important issue to establish the relationship between non-radial pulsations and the mass-loss mechanism in Be stars. To contribute to this discussion, we analyse the photometric time series of the B8IVe star HD 50209 observed by the CoRoT mission in the seismology field. We use standard Fourier techniques and linear and non-linear least squares fitting methods to analyse the CoRoT light curve. In addition, we applied detailed modelling of high-resolution spectra to obtain the fundamental physical parameters of the star. We have found four frequencies which correspond to gravity modes with azimuthal order m=0,-1,-2,-3 with the same pulsational frequency in the co-rotating frame. We also found a rotational period with a frequency of 0.679 \cd (7.754 $\mu$Hz). HD 50209 is a pulsating Be star as expected from its position in the HR diagram, close to the SPB instability strip., Comment: 7 pages, 8 figures, accepted fot publication in the A&A CoRoT special feature

We have carried out scanning tunneling spectroscopy measurements on exfoliated monolayer graphene on SiO$_2$ to probe the correlation between its electronic and structural properties. Maps of the local density of states are characterized by electron and hole puddles that arise due to long range intravalley scattering from intrinsic ripples in graphene and random charged impurities. At low energy, we observe short range intervalley scattering which we attribute to lattice defects. Our results demonstrate that the electronic properties of graphene are influenced by intrinsic ripples, defects and the underlying SiO$_2$ substrate., Comment: 6 pages, 7 figures, extended version

We have performed low-temperature scanning tunneling spectroscopy measurements on suspended single-wall carbon nanotubes with a gate electrode allowing three-terminal spectroscopy measurements. These measurements show well-defined Coulomb diamonds as well as side peaks from phonon-assisted tunneling. The side peaks have the same gate voltage dependence as the main Coulomb peaks, directly proving that they are excitations of these states., Comment: 6 pages, 5 figures

An imaging interferometer was created in a two-dimensional electron gas by reflecting electron waves emitted from a quantum point contact (QPC) with a circular mirror. Images of electron flow obtained with a scanning probe microscope at liquid He temperatures show interference fringes when the mirror is energized. A quantum phase shifter was created by moving the mirror via its gate voltage, and an interferometric spectrometer can be formed by sweeping the tip over many wavelengths. Experiments and theory demonstrate that the interference signal is robust against thermal averaging., Comment: 16 pages, 4 figures, to appear in Phys. Rev. Lett. Movies associated with this paper at http://www.mb.tn.tudelft.nl/user/brian/interferometer.html

We have developed a fabrication process for incorporating a gate electrode into suspended single-walled carbon nanotube structures for scanning tunneling spectroscopy studies. The nanotubes are synthesized by chemical vapor deposition directly on a metal surface. The high temperature ~800 C involved in the growth process poses challenging issues such as surface roughness and integrity of the structure which are addressed in this work. We demonstrate the effectiveness of the gate on the freestanding part of the nanotubes by performing tunneling spectroscopy that reveals Coulomb blockade diamonds. Our approach enables combined scanning tunneling microscopy and gated electron transport investigations of carbon nanotubes., Comment: 4 pages, 3 figures, to appear in Applied Physics Letters

The interplay between discrete vibrational and electronic degrees of freedom directly influences the chemical and physical properties of molecular systems. This coupling is typically studied through optical methods such as fluorescence, absorption, and Raman spectroscopy. Molecular electronic devices provide new opportunities for exploring vibration-electronic interactions at the single molecule level. For example, electrons injected from a scanning tunneling microscope tip into a metal can excite vibrational excitations of a molecule in the gap between tip and metal. Here we show how current directly injected into a freely suspended individual single-wall carbon nanotube can be used to excite, detect, and control a specific vibrational mode of the molecule. Electrons inelastically tunneling into the nanotube cause a non-equilibrium occupation of the radial breathing mode, leading to both stimulated emission and absorption of phonons by successive electron tunneling events. We exploit this effect to measure a phonon lifetime on the order of 10 nanoseconds, corresponding to a quality factor well over 10000 for this nanomechanical oscillator., Comment: 17 pages, 4 figures

A novel formal equivalence between thermal averages of coherent properties (e.g. conductance), and time averages of a single wavepacket arises for Fermi gasses and certain geometries. In the case of one open channel in a quantum point contact (QPC), only one wavepacket history, with wavepacket width equal to thermal length, completely determines thermally averaged conductance. The formal equivalence moreover allows very simple physical interpretations of interference features surviving under thermal averaging. Simply put, pieces of thermal wavepacket returning to the QPC along independent paths must arrive at the same time in order to interfere. Remarkably, one immediate result of this approach is that higher temperature leads to narrower wavepackets and therefore better resolution of events in the time domain. In effect, experiments at 4.2 K are performing time gated experiments at better than a gigahertz. Experiments involving thermally averaged ballistic conductance in 2DEGS are presented as an application of this picture.

We have performed low-temperature STM measurements on single-wall carbon nanotubes that are freely suspended over a trench. The nanotubes were grown by CVD on a Pt substrate with predefined trenches etched into it. Atomic resolution was obtained on the freestanding portions of the nanotubes. Spatially resolved spectroscopy on the suspended portion of both metallic and semiconducting nanotubes was also achieved, showing a Coulomb-staircase behavior superimposed on the local density of states. The spacing of the Coulomb blockade peaks changed with tip position reflecting a changing tip-tube capacitance.

We measure the energy distribution of electrons passing through a two-dimensional electron gas using a scanning probe microscope. We present direct spatial images of coherent electron wave flow from a quantum point contact formed in a GaAs/AlGaAs two-dimensional electron gas using a liquid He cooled SPM. A negative voltage is placed on the tip, which creates a small region of depleted electrons that backscatters electron waves. Oscillating the voltage on the tip and locking into this frequency gives the spatial derivative of electron flow perpendicular to the direction of current flow. We show images of electron flow using this method. By measuring the amount of electrons backscattered as a function of the voltage applied to the tip, the energy distribution of electrons is measured., Comment: 2 pages, 3 figures; submitted to LT23 proceedings

Images of electron flow through a two-dimensional electron gas from a quantum point contact (QPC) can be obtained at liquid He temperatures using scanning probe microscopy (SPM). A negatively charged SPM tip depletes the electron gas immediately below it and decreases the conductance by backscattering electrons. Images of electron flow are obtained by recording the conductance as the tip is scanned over the sample. These images show angular patterns that are characteristic of electron flow through individual modes of the QPC, as well as well-defined branches at longer distances. The addition of a prism formed by a triangular gate bends electron paths as the electron density is reduced under the prism by an applied gate voltage. Under the conditions of the experiment, electron-electron scattering is the dominant inelastic process. By observing how the amplitude of backscattered electrons in images of electron flow decreases with added electron energy, we are able to determine the average length and time necessary for inelastic scattering. A dc voltage Vo applied across the QPC accelerates electrons so that their energy is greater than the Fermi energy before inelastic scattering occurs. The signal is observed to decrease in amplitude and eventually disappear at distances from the QPC that decrease progressively as Vo is increased., Comment: 8 pages, 9 figures; to appear in Proceedings of the International Conference on the Physics of Semiconductors (ICPS 2002)

Semiconductor nanostructures based on two dimensional electron gases (2DEGs) have the potential to provide new approaches to sensing, information processing, and quantum computation. Much is known about electron transport in 2DEG nanostructures and many remarkable phenomena have been discovered (e.g. weak localization, quantum chaos, universal conductance fluctuations)1,2 - yet a fundamental aspect of these devices, namely how electrons move through them, has never been clarified. Important details about the actual pattern of electron flow are not specified by statistical measures such as the mean free path. Scanned probe microscope (SPM) measurements allow spatial investigations of nanostructures, and it has recently become possible to directly image electron flow through 2DEG devices using newly developed SPM techniques3-13. Here we present SPM images of electron flow from a quantum point contact (QPC) which show unexpected dynamical channeling - the electron flow forms persistent, narrow, branching channels rather than smoothly spreading fans. Theoretical study of this flow, including electron scattering by impurities and donor atoms, shows that the channels are not due to deep valleys in the potential, but rather are caused by the indirect cumulative effect of small angle scattering. Surprisingly, the channels are decorated by interference fringes well beyond where the simplest thermal averaging arguments suggest they should be found. These findings may have important implications for 2DEG physics and for the design of future nanostructure devices., Comment: 14pages, 4 figures, Submitted to Nature