Interference Of Electron Waves Research Articles

Kagome Quantum Oscillations in Graphene Superlattices.

Electronic spectra of solids subjected to a magnetic field are often discussed in terms of Landau levels and Hofstadter-butterfly-style Brown-Zak minibands manifested by magneto-oscillations in two-dimensional electron systems. Here, we present the semiclassical precursors of these quantum magneto-oscillations which appear in graphene superlattices at low magnetic field near the Lifshitz transitions and persist at elevated temperatures. These oscillations originate from Aharonov-Bohm interference of electron waves following open trajectories that belong to a kagome-shaped network of paths characteristic for Lifshitz transitions in the moire superlattice minibands of twistronic graphenes.

Controlled crossover of electron transport in graphene nanoconstriction: From Coulomb blockade to electron interference

The ability to control transport behaviors in nanostructure is crucial for usage as a fundamental research platform as well as a practical device. In this study, we report a gate-controlled crossover of electron transport behaviors using graphene nanoconstrictions as a platform. The observed transport properties span from Coulomb blockade-dominated single electron transmission to electron–wave interference-dominated quantum behavior. Such drastic modulation is achieved by utilizing a single back gate on a graphene nanoconstriction structure, where the size of nanostructure in the constriction and coupling strength of it to the electrodes can be tuned electrically. Our results indicate that electrostatic field by gate voltage upon the confined nanostructure defines both the size of the nanoconstriction as well as its interaction to electrodes. Increasing gate voltage raises Fermi level to cross the energy profile in the nanoconstriction, resulting in decreased energy barriers which affect the size of nanoconstriction and transmissivity of electrons. The gate-tunable nanoconstriction device can therefore become a potential platform to study quantum critical behaviors and enrich electronic and spintronic devices.

RESTRUCTURING RESONANCE TUNNEL LEV-ELS DURING THE SUPERLATTICE FORMATION

Reducing the active dimensions of semiconductor structures leads to the manifestation of new edge-mechanical phenomena. The characteristic sizes of structures at which these effects appear are 1…100 nm. In this range, quantum effects begin to fully manifest themselves, and the physics of conductivity is determined by the quantum mechanical interference of electron waves. It has been established that during the formation of a superlattice consisting of a sequence of potential wells and barriers, resonant levels arise, the energy of which is determined by the number of de Broglie waves that fit across the width of the well. For particles with energy equal to the energy of the levels, the transparency of the structure is equal to unity. As the number of units increases, these levels split into similar sublevels. The scheme and mechanism for rearranging levels in the chain are considered. This mechanism is based on ideas about the points of change in the phases of oscillator oscillations during the formation of a chain. It has been established that the parameters of these sublevels (energy, half-width and wave function) depend on the parameters of the barriers and the number of cells in the chain. A model is proposed that makes it possible to determine the characteristics of these sublevels, in particular their energy and wave functions.

Volume imaging by tracking sparse topological features in electron micrograph tilt series

The sensitive coherent interference of electron waves arising from a specimen is useful for revealing subtle structural information in electron micrographs, which can be important for minimising dose and for rapid imaging. In general, dynamical diffraction is expected due to the useful strong interactions of electrons with matter, which can create phase contrast that violates the requisite Radon projection assumption for tomography. It is for these reasons that incoherent imaging modalities such as high angle annular dark field have been favoured to date in electron tomography of crystalline specimens, to access a monotonic relationship between specimen thickness and micrograph intensity. Here we use a geometric approach to track topological features that are robust to perturbation of the imaging conditions, to enable 3D reconstructions from electron microscope tilt series under imaging conditions that violate the Radon projection assumption, with an emphasis on phase contrast. Invoking a sparsity assumption, we demonstrate that topological features can be reliably tracked in 3D using a differential geometric form of stereoscopy, to circumvent departures from the projection approximation and reduce noise by effecting segmentation of interest points from the outset. We demonstrate this approach on a variety of different specimen and data types, from polyhedral nanoparticles, to steel dislocation networks, cryo-EM cellular structures and 3D diffuse diffraction of a relaxor ferroelectric.

Theory of laser-induced photoemission from a metal surface with nanoscale dielectric coating

This paper presents an analytical quantum model for photoemission from metal surfaces coated with an ultrathin dielectric, by solving the 1D time-dependent Schrödinger equation subject to an oscillating double-triangular potential barrier. The model is valid for an arbitrary combination of metal (of any work function and Fermi level), dielectric (of any thickness, relative permittivity, and electron affinity), laser field (strength and wavelength), and dc field. The effects of dielectric properties on photoemission are systematically investigated. It is found that a flat metal surface with dielectric coating can photoemit a larger current density than the uncoated case when the dielectric has smaller relative permittivity and larger electron affinity. Resonant peaks in the photoemission probability and emission current are observed as a function of dielectric thickness or electron affinity due to the quantum interference of electron waves inside the dielectric. Our model is compared with the effective single-barrier quantum model and modified Fowler–Nordheim equation, for both 1D flat cathodes and pyramid-shaped nanoemitters. While the three models show quantitatively good agreement in the optical field tunneling regime, the present model may be used to give a more accurate evaluation of photoemission from coated emitters in the multiphoton absorption regime.

Ultrafast optical-field-induced photoelectron emission in a vacuum nanoscale gap: An exact analytical formulation

By exactly solving the one-dimensional time-dependent Schrödinger equation, we construct an analytical solution for nonlinear photoelectron emission in a nanoscale metal–vacuum–metal junction driven by a single-frequency laser field, where the impact of image and space charges is neglected. Based on the analytical formulation, we examine the photoelectron energy spectra and emission current under various laser fields and vacuum gap distances. Our calculation shows the transition from direct tunneling to multiphoton induced electron emission as gap distance increases. In the multiphoton regime, the photoemission current density oscillatorily varies with the gap distance, due to the interference of electron waves inside the gap. Our model reveals the energy redistribution of photoelectrons across the two interfaces between the gap and the metals. Additionally, we find that decreasing the gap distance (before entering the direct tunneling regime) tends to extend the multiphoton regime to higher laser intensity. This work provides clear insights into the underlying photoemission mechanisms and spatiotemporal electron dynamics of ultrafast electron transport in nanogaps and may guide the future design of advanced ultrafast nanodevices, such as photoelectron emitters, photodetectors, and quantum plasmonic nanoantennas.

Substitution Pattern Controlled Quantum Interference in [2.2]Paracyclophane-Based Single-Molecule Junctions.

Quantum interference (QI) of electron waves passing through a single-molecule junction provides a powerful means to influence its electrical properties. Here, we investigate the correlation between substitution pattern, conductance, and mechanosensitivity in [2.2]paracyclophane (PCP)-based molecular wires in a mechanically controlled break junction experiment. The effect of the meta versus para connectivity in both the central PCP core and the phenyl ring connecting the terminal anchoring group is studied. We find that the meta-phenyl-anchored PCP yields such low conductance levels that molecular features cannot be resolved; in the case of para-phenyl-coupled anchoring, however, large variations in conductance values for modulations of the electrode separation occur for the pseudo-para-coupled PCP core, while this mechanosensitivity is absent for the pseudo-meta-PCP core. The experimental findings are interpreted in terms of QI effects between molecular frontier orbitals by theoretical calculations based on density functional theory and the Landauer formalism.

Spatially Inhomogeneous Distribution of the Quantum Mechanical Current Density at the Sub-Barrier Reflection of the Electron Wave from the Potential Step in the 2D Nanostructure

In this paper, the influence of the interference of electron waves during their reflection from a rectangular semi-infinite potential barrier to the spatial distribution of quantum mechanical current density еjx(x, z) (e is the electron charge and jx(x, z) is the flow of probability density) in a semiconductor 2D nanostructure is theoretically studied. The structure consists of narrow and wide rectangular quantum wells (QWs) arranged successively along the direction of electron wave propagation. It is assumed that the wave falls from narrow QW1 on a potential barrier of height V0 in wide QW2. It is shown that when a wave with energy less than V0 falls on the barrier, then, in certain conditions, spatially inhomogeneous distribution $$ej_{x}^{{\left( 1 \right)}}(x,z)$$ oscillating in a complicated way exists in QW1. An exponential attenuation and coordinate dependent leakage $$ej_{x}^{{\left( 2 \right)}}(x,z)$$ under the barrier may occur in QW2. It is shown that this behavior of $$ej_{x}^{{\left( 1 \right)}}(x,z)$$ and $$ej_{x}^{{\left( 2 \right)}}(x,z)$$ is caused by the interference of electron waves propagating through different quantum-dimensional subbands in the considered nanostructure.

Quantum transport in three-dimensional metalattices of platinum featuring an unprecedentedly large surface area to volume ratio

Three-dimensional (3D) electronic nanomaterials are less explored than their counterparts in the lower dimensions because of the limited techniques for the preparation of high-quality materials. Here we report characterization of and quantum transport measurement on 3D metalattices of Pt grown in the voids of self-assembled templates of silica nanospheres by confined chemical fluid deposition. These Pt metalattices featuring an unprecedentedly large surface area to volume ratio were found to show positive magnetoresistance (MR) at low temperatures, changing from positive to negative in low magnetic fields within a narrow temperature window as the temperature was raised. The low-field MR was attributed to the effect of quantum interference of electronic waves in the diffusive regime in three dimensions, processes known as weak localization and antilocalization. We argue that the presence of the large surface area to volume ratio results in such a strong enhancement in the electron-phonon scatterings that a change in the sign in the MR is enabled.

Temperature dependent switching of magnetoresistance in multiwall carbon nanotube-polypyrrole composite fibrils

Carbon nanotubes (CNT) are considered one of the most significant materials in nanoelectronic device applications because they can be used in the fabrication of both CNT-inorganic hybrid structures and CNT-organic composite materials. Also, the study of the electrical properties of these materials has its own fundamental and technological significance. Here, we report on low temperature charge transport characteristics (down to 4.2 K in the magnetic fields up to 11 T) of multiwall carbon nanotube (MWCNT)-polypyrrole (PPy) coaxial composite fibrils synthesized by a facile electrochemical polymerization method. Two types of samples were synthesized by carrying out electrochemical polymerization at room temperature (RT) for different durations of 90 and 45 min, respectively. Scanning electron microscopy studies indicated that the diameters of as-prepared MWCNT-PPy fibril samples were ∼1.5 μm and 0.5 μm, respectively. The dc electrical resistance of the two samples was ∼103 and 102 Ω at RT and exhibited a pronounced temperature dependence, which is indicative of the hopping process being dominant. Furthermore, a large positive magnetoresistance (MR) of ∼29% and ∼18% is displayed at 4.2 K, which switched to negative MR with a maximum magnitude of ∼11% and ∼15% at 10 K for the two samples, respectively. The switching of MR as a function of temperature showed the dominance of two important competing phenomena, namely, wave function shrinkage and forward interference of electron waves.

Current Correlations in a Quantum Dot Ring: A Role of Quantum Interference.

We present studies of the electron transport and circular currents induced by the bias voltage and the magnetic flux threading a ring of three quantum dots coupled with two electrodes. Quantum interference of electron waves passing through the states with opposite chirality plays a relevant role in transport, where one can observe Fano resonance with destructive interference. The quantum interference effect is quantitatively described by local bond currents and their correlation functions. Fluctuations of the transport current are characterized by the Lesovik formula for the shot noise, which is a composition of the bond current correlation functions. In the presence of circular currents, the cross-correlation of the bond currents can be very large, but it is negative and compensates for the large positive auto-correlation functions.

Electron Transport in Nanoporous Graphene: Probing the Talbot Effect.

Electrons in graphene can show diffraction and interference phenomena fully analogous to light thanks to their Dirac-like energy dispersion. However, it is not clear how this optical analogy persists in nanostructured graphene, for example, with pores. Nanoporous graphene (NPG) consisting of linked graphene nanoribbons has recently been fabricated using molecular precursors and bottom-up assembly (Moreno et al. Science 2018, 360, 199). We predict that electrons propagating in NPG exhibit the interference Talbot effect, analogous to photons in coupled waveguides. Our results are obtained by parameter-free atomistic calculations of real-sized NPG samples based on seamlessly integrated density functional theory and tight-binding regions. We link the origins of this interference phenomenon to the band structure of the NPG. Most importantly, we demonstrate how the Talbot effect may be detected experimentally using dual-probe scanning tunneling microscopy. Talbot interference of electron waves in NPG or other related materials may open up new opportunities for future quantum electronics, computing, or sensing.

Friedel oscillations in 2D electron gas from spin-orbit interaction in a parallel magnetic field

Effects associated with the interference of electron waves around a magnetic point defect in two-dimensional electron gas with combined Rashba-Dresselhaus spin-orbit interaction in the presence of a parallel magnetic field are theoretically investigated. The effect of a magnetic field on the anisotropic spatial distribution of the local density of states and the local density of magnetization is analyzed. The existence of oscillations of the density of magnetization with scattering by a non-magnetic defect and the contribution of magnetic scattering (accompanied by spin-flip) in the local density of electron states are predicted.

Mechanically controlled quantum interference in graphene break junctions.

The ability to detect and distinguish quantum interference signatures is important for both fundamental research and for the realization of devices such as electron resonators1, interferometers2 and interference-based spin filters3. Consistent with the principles of subwavelength optics, the wave nature of electrons can give rise to various types of interference effects4, such as Fabry-Pérot resonances5, Fano resonances6 and the Aharonov-Bohm effect7. Quantum interference conductance oscillations8 have, indeed, been predicted for multiwall carbon nanotube shuttles and telescopes, and arise from atomic-scale displacements between the inner and outer tubes9,10. Previous theoretical work on graphene bilayers indicates that these systems may display similar interference features as a function of the relative position of the two sheets11,12. Experimental verification is, however, still lacking. Graphene nanoconstrictions represent an ideal model system to study quantum transport phenomena13-15 due to the electronic coherence16 and the transverse confinement of the carriers17. Here, we demonstrate the fabrication of bowtie-shaped nanoconstrictions with mechanically controlled break junctions made from a single layer of graphene. Their electrical conductance displays pronounced oscillations at room temperature, with amplitudes that modulate over an order of magnitude as a function of subnanometre displacements. Surprisingly, the oscillations exhibit a period larger than the graphene lattice constant. Charge-transport calculations show that the periodicity originates from a combination of the quantum interference and lattice commensuration effects of two graphene layers that slide across each other. Our results provide direct experimental observation of a Fabry-Pérot-like interference of electron waves that are partially reflected and/or transmitted at the edges of the graphene bilayer overlap region.

Anomalous Nonlinear Shot Noise at High Voltage Bias.

Since the work of Walter Schottky, it is known that the shot-noise power for a completely uncorrelated set of electrons increases linearly with the time-averaged current. At zero temperature and in the absence of inelastic scattering, the linearity relation between noise power and average current is quite robust, in many cases even for correlated electrons. Through high-bias shot-noise measurements on single Au atom point contacts, we find that the noise power in the high-bias regime shows highly nonlinear behavior even leading to a decrease in shot noise with voltage. We explain this nonlinearity using a model based on quantum interference of electron waves with varying path difference due to scattering from randomly distributed defect sites in the leads, which makes the transmission probability for these electrons both energy and voltage dependent.

Observation of Electron Coherence and Fabry–Perot Standing Waves at a Graphene Edge

Electron surface states in solids are typically confined to the outermost atomic layers and, due to surface disorder, have negligible impact on electronic transport. Here, we demonstrate a very different behavior for surface states in graphene. We probe the wavelike character of these states by Fabry-Perot (FP) interferometry and find that, in contrast to theoretical predictions, these states can propagate ballistically over micron-scale distances. This is achieved by embedding a graphene resonator formed by gate-defined p-n junctions within a graphene superconductor-normal-superconductor structure. By combining superconducting Aharanov-Bohm interferometry with Fourier methods, we visualize spatially resolved current flow and image FP resonances due to p-n-p cavity modes. The coherence of the standing-wave edge states is revealed by observing a new family of FP resonances, which coexist with the bulk resonances. The edge resonances have periodicity distinct from that of the bulk states manifest in a repeated spatial redistribution of current on and off the FP resonances. This behavior is accompanied by a modulation of the multiple Andreev reflection amplitude on-and-off resonance, indicating that electrons propagate ballistically in a fully coherent fashion. These results, which were not anticipated by theory, provide a practical route to developing electron analog of optical FP resonators at the graphene edge.

Imaging electrostatically confined Dirac fermions in graphene quantum dots

Electrostatic confinement of charge carriers in graphene is governed by Klein tunneling, a relativistic quantum process in which particle-hole transmutation leads to unusual anisotropic transmission at pn junction boundaries. Reflection and transmission at these novel potential barriers should affect the quantum interference of electronic wavefunctions near these boundaries. Here we report the use of scanning tunneling microscopy (STM) to map the electronic structure of Dirac fermions confined by circular graphene pn junctions. These effective quantum dots were fabricated using a new technique involving local manipulation of defect charge within the insulating substrate beneath a graphene monolayer. Inside such graphene quantum dots we observe energy levels corresponding to quasi-bound states and we spatially visualize the quantum interference patterns of confined electrons. Dirac fermions outside these quantum dots exhibit Friedel oscillation-like behavior. Bolstered with a theoretical model describing relativistic particles in a harmonic oscillator potential, our findings yield new insight into the spatial behavior of electrostatically confined Dirac fermions.

Tunable thermoelectric properties in bended graphene nanoribbons**Project supported by the National Natural Science Foundation of China (Grant No. 61401153) and the Natural Science Foundation of Hunan Province, China (Grant Nos. 2015JJ2050 and 14JJ3126).

The ballistic thermoelectric properties in bended graphene nanoribbons (GNRs) are systematically investigated by using atomistic simulation of electron and phonon transport. We find that the electron resonant tunneling effect occurs in the metallic–semiconducting linked ZZ-GNRs (the bended GNRs with zigzag edge leads). The electron-wave quantum interference effect occurs in the metallic–metallic linked AA-GNRs (the bended GNRs with armchair edge leads). These different physical mechanisms lead to the large Seebeck coefficient S and high electron conductance in bended ZZ-GNRs/AA-GNRs. Combined with the reduced lattice thermal conduction, the significant enhancement of the figure of merit ZT is predicted. Moreover, we find that the ZTmax (the maximum peak of ZT) is sensitive to the structural parameters. It can be conveniently tuned by changing the interbend length of bended GNRs. The magnitude of ZT ranges from the 0.15 to 0.72. Geometry-controlled ballistic thermoelectric effect offers an effective way to design thermoelectric devices such as thermocouples based on graphene.

Electron transport through a two-terminal Aharonov-Bohm interferometer coupled with linear di-quantum dot molecules

A two-terminal Aharonov-Bohm (A-B) interferometer coupled with linear di-quantum dot molecules is presented. By employing Keldysh non-equilibrium Green's function technique, the conductance without introducing time-dependent external field and the average current with applying time-dependent external field are theoretically studied. In the absence of time-dependent external field, two identical linear diquantum dot molecules embedded respectively in the two arms of A-B interferometer lead to degeneracy energy levels. The central resonance peak at εd = 0 in the conductance spectrum splits into two resonance peaks as the inter-coupling strength of di-quamtum dot increases over a threshold. In the case that the two linear di-quantum dot molecules are different, three or four resonance peaks appear in the conductance spectrum. When tuning magnetic flux ψ= π, the destructive quantum interference of electron waves in the A-B interferometer takes place. The conversion between 0 and 1 for conductance is performed by switching on/off the magnetic flux, which suggests a new physical scheme of quantum switches. The effect of Rashba spin-orbit interaction on the conductance is discussed. The functionality of spin filter is suggested through adjusting the Rashba spin-orbit coupling strength and the external magnetic flux. When time-dependent external field is applied, the notable side-band effect appears in the average current curve. A series of resonance peaks is produced, with the peak-peak separation of ħω. Two main peaks become reduced as the amplitude of time-dependent external field increases, however, the sideband peaks grow gradually. This indicates that both the magnitude and the position of average current resonance peak are controllable by adjusting the amplitude of time-dependent external field. The sideband effect remains always in the average current curve no matter how much the frequency of time-dependent external field changes. But the increase in the frequency of external field leads to the growth of two main peaks at the bonding and anti-bonding energy respectively, and the decay of the corresponding sideband peaks as well. The conversion between the current peak and valley can be realized by tuning the frequency of time-dependent field. Moreover, the dependence of A-B effect of the average current on the magnetic flux is found. As the magnetic flux is ψ≠nπ, each peak in average current curves splits into two peaks. But under the condition of ψ=2nπ, the splitting phenomenon disappears. The spin-dependent average current shows effective controllability by tuning the magnetic flux and Rashba spin-orbit coupling. The results would be useful for gaining a physical insight into electron transport in the multi-quantum-dot molecules coupled A-B interferometer and for designing the quantum devices.

Single-mode and multimode Fabry-Pérot interference in suspended graphene

Phase coherence of charge carriers leads to electron-wave interference in ballistic mesoscopic conductors. In graphene, such Fabry-P\'erot-like interference has been observed, but a detailed analysis has been complicated by the two-dimensional nature of conduction, which allows for complex interference patterns. In this work, we have achieved high-quality Fabry-P\'erot interference in a suspended graphene device, both in conductance and in shot noise, and analyzed their structure using Fourier transform techniques. The Fourier analysis reveals two sets of overlapping, coexisting interferences, with the ratios of the diamonds being equal to the width to length ratio of the device. We attribute these sets to a unique coexistence of longitudinal and transverse resonances, with the longitudinal resonances originating from the bunching of modes with low transverse momentum. Furthermore, our results give insight into the renormalization of the Fermi velocity in suspended graphene samples, caused by unscreened many-body interactions.