Electron Group Velocity Research Articles

Optimizing long-range order, band gap, and group velocities for graphene on close-packed metal surfaces

We compare different growth methods with the aim of optimizing the long-range order of a graphene layer grown on Ru(0001). Combining chemical vapor deposition with carbon loading and segregation of the surface layer leads to autocorrelation lengths of 240 Å. We present several routes to band gap and charge carrier mobility engineering for the example of graphene on Ir(111). Ir cluster superlattices self-assembled onto the graphene moiré pattern produce a strong renormalization of the electron group velocity close to the Dirac point, leading to highly anisotropic Dirac cones and the enlargement of the gap from 140 to 340 meV. This gap can further be enhanced to 740 meV by Na co-adsorption onto the Ir cluster superlattice at room temperature. This value is close to that of Ge, and the high group velocity of the charge carriers is fully preserved. We also present data for Na adsorbed without the Ir clusters. In both cases we find that the Na is on top of the graphene layer.

A graphene electron lens

An epitaxial layer of graphene was grown on a pre patterned 6H-SiC(0001) crystal. The graphene smoothly covers the hexagonal nano-holes in the substrate without the introduction of small angle grain boundaries or dislocations. This is achieved by an elastic deformation of the graphene by ≈0.3% in accordance to its large elastic strain limit. This elastic stretching of the graphene leads to a modification of the band structure and to a local lowering of the electron group velocity of the graphene. We propose to use this effect to focus two-dimensional electrons in analogy to simple optical lenses.

Anisotropic surface transport in topological insulators in proximity to a helical spin density wave

We study the effects of spatially localized breakdown of time reversal symmetry on the surface of a topological insulator (TI) due to proximity to a helical spin density wave (HSDW). The HSDW acts like an externally applied one-dimensional periodic (magnetic) potential for spins on the surface of the TI, rendering the Dirac cone on the TI surface highly anisotropic. The decrease in group velocity along the direction $\mathrm{x\ifmmode \hat{}\else \^{}\fi{}}$ of the applied spin potential is twice as great as that perpendicular to $\mathrm{x\ifmmode \hat{}\else \^{}\fi{}}$. At the Brillouin zone boundaries, it also gives rise to new semi-Dirac points that have a linear dispersion along $\mathrm{x\ifmmode \hat{}\else \^{}\fi{}}$ but a quadratic dispersion perpendicular to $\mathrm{x\ifmmode \hat{}\else \^{}\fi{}}$. The group velocity of electrons at these new semi-Dirac points is also shown to be highly anisotropic. Experiments using TI systems on multiferroic substrates should realize our predictions. We further discuss the effects of other forms of spin density waves on the surface transport property of TIs.

Highly Anisotropic Dirac Cones in Epitaxial Graphene Modulated by an Island Superlattice

We present a new method to engineer the charge carrier mobility and its directional asymmetry in epitaxial graphene by using metal cluster superlattices self-assembled onto the moiré pattern formed by graphene on Ir(111). Angle-resolved photoemission spectroscopy reveals threefold symmetry in the band structure associated with strong renormalization of the electron group velocity close to the Dirac point giving rise to highly anisotropic Dirac cones. We further find that the cluster superlattice also affects the spectral-weight distribution of the carbon bands as well as the electronic gaps between graphene states.

Electrical Transport Properties of Filled CoSb3 Skutterudites: A Theoretical Study

We present an investigation of electronic structures and electrical transport properties of some filled CoSb3 skutterudites by combining ab initio projected augmented plane-wave calculations and Boltzmann transport theory with electron group velocity evaluated by the momentum matrix method. The systems are studied in a 2 × 2 × 2 supercell of Co4Sb12 to reveal the effects induced by different filler atoms and their filling fractions. The temperature dependences of the Seebeck coefficient and power factor are studied, and they are in good agreement with experimental data. Our results reveal an optimal filling fraction for n-type filled CoSb3 skutterudites and related compounds for achieving the highest power factor values.

Spin-polarization in a 3-terminal conductor induced by Rashba spin–orbit coupling

We investigate numerically the spin polarization of the current in the presence of Rashba spin–orbit interaction (RSOI) in a 3-terminal conductor. We use equation-of-motion method to simulate the time evolution of the wave packet and focus on single-channel transport. A T-shaped conductor with uniform RSOI proposed by Kiselev and Kim and a Y-shaped conductor with nonuniform RSOI are considered. In the T-shaped conductor, the strength of RSOI is assumed to be uniform. We have found that the spin polarization becomes nearly 100% with little loss of conductance for sufficiently strong spin–orbit coupling. This is due to the spin-dependent group velocity of electrons at the junction which causes the spin separation. In the Y-shaped conductor, the strength of RSOI is modulated perpendicular to the charge current. A spatial gradient of effective magnetic field due to the nonuniform RSOI causes the Stern–Gerlach type spin separation. The direction of the polarization is perpendicular to the current and parallel to the spatial gradient. Again almost 100% spin polarization can be realized by this spin separation.

First-principles calculation of the electron inelastic mean free path in Be metal

The Be electron inelastic mean free path (IMFP) is calculated by using the GW approximation of many-body theory. It is demonstrated that the inclusion of band structure effects significantly improves the agreement between the calculated and measured IMFP in the energy range up to $\ensuremath{\sim}30\mathrm{eV}.$ We show that the main effect results from the electron group velocity obtained from ab initio band structure calculations, whereas the evaluated linewidth averaged over momenta is not significantly affected with respect to the prediction of a free electron gas model. The comparison of the IMFP computed within two models, namely, the free electron gas model and the full band structure model, supports the idea of the importance of band structure effects for the description of electron transport in this metal for energies below 30 eV, and a nearly free-electron-like behavior for excitation energies above 30 eV. The calculated plasmon dispersion is in excellent agreement with available experimental data.

Study of period number effect in the superlattice infrared photodetector

Superlattices have been demonstrated previously by our group in the design of the multicolor infrared photodetector. In general, the period number of the superlattice may be up to several dozens. In this paper, we have investigated the performance of the infrared photodetectors especially with 3, 5 and 15 periods. The detector structure contains a thick blocking barrier embedded between two superlattices with different period numbers but with the same well and barrier widths. This double-superlattice structure shows switchable spectral responses between two spectral regions by the voltage polarities. The photoresponse in each spectral region is also tunable by the magnitude of the applied voltage. The voltage-dependent behavior reveals the photoelectron relaxation and transport mechanism in the superlattice miniband. Superlattice with few periods has high electron group velocity, less relaxation effect and less collection efficiency. Therefore the superlattice with few periods may have better responsivity and narrower photoresponse range than the one with many periods. Based on the experimental results of our devices, it is observed that the superlattice with fewer periods has better detectivity, responsivity, wider range of the operational temperature, and more flexible miniband engineering than the conventional multiple quantum well infrared photodetector.

Minigaps and the quantum Hall effect in broken gap InAs/GaSb heterostructures

InAs/GaSb heterojunctions offer the unique situation in a semiconductor of overlapping conduction and valence bands. A wavevector dependent minigap occurs due to the anticrossing of the electron and hole dispersion relations. As a result the resistivity increases strongly in very pure intrinsic structures due to the reduction in the electron group velocity. Applying a magnetic field parallel to the layers shifts the conduction and valence band relative to each other in k-space and the structure turns back to an indirect semimetal. As a result we can observe a giant negative magnetoresistance. Interband absorption is observed across the minigap, and this can also be removed by the parallel field which transforms the system to an indirect band gap alignment. In high perpendicular magnetic fields strong oscillations occur in the Hall coefficient, and at low temperatures a series of zero Hall resistance states are found in which a divergence of the diagonal resistivity occurs at the same point as a zero in the Hall resistance.

Angular dependent magnetoresistance oscillations in SbCl5-intercalated graphite

Abstract We have observed angular dependent magnetoresistance oscillations (ADMRO) in the out-of-plane resistivity of low-stage SbCl 5 -intercalated graphite. This new phenomenon is a semi-classical geometric resonance effect inherent in quasi two-dimensional systems whose Fermi surface is weakly corrugated in the k z -direction. Typically, ADMRO is characterized by peak positions that are periodic in tan θ. The peaks in ϱ zz occur when the average of the k z -component of electron group velocity around its extended orbit is zero. Significant deviations from ‘standard’ behaviour are found. The implications for electronic structure are discussed.

Energy-momentum relation for polarons in quantum-well wires

The interaction of quasi-one-dimensional electrons and longitudinal-optical (LO) phonons is calculated. Results are presented for the polaron correction to the electric subbands and the polaron effective mass. Using improved Wigner-Brillouin perturbation theory, we have investigated in detail the energy-momentum relation for quasi-one-dimensional polarons. It is shown that the dispersion curves of all subbands bend over and are pinned at the phonon continuum above the renormalized ground state. This should result in a spatial oscillation of the electron group velocity in real quantum-well wires.

Edge phonoconductivity in a magnetically quantized two-dimensional electron gas.

Scattering of electrons in edge states of a magnetically quantized two-dimensional electron gas (2DEG) by nonequilibrium acoustic phonons has been studied both experimentally and theoretically. A phonoconductance imaging technique was used to probe the spatial and magnetic-field (B) dependence of the acoustic-phonon scattering of electrons in a GaAs device. It was discovered that a response was observed only when phonons were incident at the edge of the 2DEG. Giant oscillations in the phonoconductance with magnetic field were observed, these were periodic in 1/B and changed sign when the field was increased beyond 1.3 T. At low field the oscillations were negative, i.e., phonon scattering causes a decrease in conductance, whereas at high field the oscillations become positive. These results are described theoretically by considering the change in group velocity of the edge electrons upon absorption of a phonon which changes their energy and wave vector. Assuming a sharp edge potential, an important parameter in the theory turns out to be the product of the phonon momentum component parallel to the edge and the magnetic length. If this parameter is greater than unity, then interedge state transitions leading to a decrease in electron group velocity produce the dominant effect, a decrease in conductance. However, if it is less than unity, only intraedge state transitions can take place giving rise to an increase in group velocity and hence an increase in conductance. If the potential at the sample edge is considered to be smooth, which is a more realistic assumption, then the theoretical results remain qualitatively the same, except that the field at which interedge state transitions are no longer possible is reduced in line with the greater separation of the edge channels. This makes it possible to use our results to estimate both the potential gradient at the edge of the sample and the spatial separation of the edge channels. It is also demonstrated that the spatially resolved phonoconductance measurements as a function of magnetic-field strength can be used to probe the local electron concentration and the charge separation connected with the Hall voltage is determined for our sample.

On the Possibility of Describing Lattice Properties of Iridium in Terms of Pseudopotential Theory

AbstractThe possibility is discussed of describing lattice properties of iridium in terms of pseudopotential perturbation theory with allowance for second and third order. Values of pseudopotential parameters are proposed which provide a good description of the lattice properties of iridium under zero pressure, the contributions of the three‐ion forces being small. The total energy, pressure, elastic moduli, Debye temperature, low‐temperature Grüneisen parameter, pairwise potentials, and also effective solid sphere packing parameters are calculated. In addition, by invoking molecular dynamic methods, the vacancy formation and migration energies and the stacking fault energies are computed. The electron energy spectrum and group velocity calculations suggest that the electron density of states curve of Ir exhibits no van Hove singularities near the Fermi level, a fact which apparently accounts for the successful description of lattice properties in terms of the pseudopotential perturbation theory.

Surface superlattices and quasi-one-dimensional conductors in GaAs HEMTs: how best to compare theory and experiment?

The authors discuss evidence of (1) electron standing waves forming underneath a 2000-AA period Ti/Au Schottky grid or grating incorporated as a gate into a GaAs HEMT (high-electron-mobility transistor) structure, and (2) modulation of the scattering time due to intersubband scattering in an array of approximately 100 parallel wires of 400-AA width formed by laterally patterning a GaAs/GaAlAs heterostructure. The authors show how knowledge of the electron group velocity along with a scattering rate derived from Fermi's golden rule can explain the observed effects. They compare the mobility modulation from intersubband scattering to the well-known prediction of Sakaki for increased mobility in quasi-one-dimensional wire due to the finite range of the scatterers. By first solving for the density of states and conductivity in a one-dimensional periodic potential, the authors show how to incorporate energy level broadening due to elastic and inelastic scattering, temperature broadening, and an increase in the dimensionality of the device by convolving with various known functions.

De-Haas-van Alphen effect study of electronic structures of niobium-based molybdenum alloys

The electronic structures of dilute niobium-based molybdenum alloys have been studied by using the de Haas-van Alphen effect. The rate of increase of the Dingle temperature ( Delta TD*) on alloying is found to be fairly small compared with that of noble-metal alloys and to be anisotropic over the Fermi surfaces that is, 3K (at.% Mo)-1 for nu oscillations arising from the ellipsoids, and 7K (at.% Mo)-1 for alpha and eta oscillations arising from the jungle gym. The change in frequency of the nu 3456 oscillation is about 2/3 that predicted by the rigid band model. Applying the partial-wave analysis to these experimental facts, the following results are obtained. (i) The d wave phase shift dominates over s, p and f wave phase shifts in this alloy system and the anisotropy in Delta TD* results from the anisotropy in the amount of d component of the wavefunction over the Fermi surfaces. (ii) The non-rigid band-like behaviour of the nu 3456 oscillation arises from the same origin as Delta TD*. (iii) The significantly small Delta TD* found in the present experiment is related to a small electron group velocity on the Fermi surfaces in niobium.

Erratum: Experimental study of quantum size effects in thin metal films by electron tunneling

Periodic structure in the electron tunneling spectra of Pb, Mg, Au, and Ag has been observed. Such spectra represent in fact a direct observation of size-dependent electronic states in thin metal films. Films with thicknesses from 100 to 1000 \AA{} were studied and the effect on the electronic standing-wave energies was measured. The physical model for these effects and their observability involve the existence of so-called commensurate states. The spacing of the quantized energy levels provides a direct measurement of the electron group velocity while their location in energy determines the position of band edges and other critical energy states in the band structure of the metals. In some cases, the effective mass can also be determined. A qualitative theoretical picture is sufficient to understand all of the sailient features of the observations. A number of experiments including alloying, strain, and electric field modulation are also described.

Experimental study of quantum size effects in thin metal films by electron tunneling

Periodic structure in the electron tunneling spectra of Pb, Mg, Au, and Ag has been observed. Such spectra represent in fact a direct observation of size-dependent electronic states in thin metal films. Films with thicknesses from 100 to 1000 \AA{} were studied and the effect on the electronic standing-wave energies was measured. The physical model for these effects and their observability involve the existence of so-called commensurate states. The spacing of the quantized energy levels provides a direct measurement of the electron group velocity while their location in energy determines the position of band edges and other critical energy states in the band structure of the metals. In some cases, the effective mass can also be determined. A qualitative theoretical picture is sufficient to understand all of the sailient features of the observations. A number of experiments including alloying, strain, and electric field modulation are also described.

Investigation of static skin effect on atomic pure (100) and (110) faces of tungsten single crystal

When a Bloch wave is specularly reflected from the metal boundary, several states may appear on different isoenergetic surface sheets. Depending on the shape, Gauss curvature sign and arrangement of separate sheets of the isoenergetic surface as well as orientation of the crystal physical boundary, such reflections may cause to reverse the tangential components of the electron group velocity after the “mirror” reflection. In W crystals such reflections are realized on the faces (100) and (111) and cannot occur on the (110) face. A comparative investigation of the character of the conduction electron reflection from the atomic pure and oxidized faces (100) and (110) of the tungsten single crystal has been made. The method of static skin effect is used.

Observation of electron standing waves in Mg by tunneling

Electron standing wave states in Mg films are observed by electron tunneling measurements. An electron group velocity is determined by this experiment.

Electronic Attenuation of Longitudinal Soundwaves in Aluminium

AbstractThe frequency dependence of the difference between the attenuation of longitudinal soundwaves in a perpendicular magnetic field and in zero field is used in an experimental analysis of three parameters in the electron‐phonon interaction. The parameters are the electron mean free path and the magnitude of the interaction in zero and infinite field. The first parameter is compared with the mean free path deduced from electrical size effects. The interaction parameter in zero field is found to be in fair agreement with theoretical estimates. In high fields the interaction is not localized at the fermi surface, and it is found that symmetrically shaped orbits having an electron group velocity normal to the magnetic field, contribute most strongly to the attenuation.