Electron Dispersion Relation Research Articles

Paramagnetic-ferromagnetic transition in a double-exchange model

We study paramagnetic - ferromagnetic transition due to exchange interaction between classical localized magnetic moments and conduction electrons. We formulate the Dynamical Mean Field Approximation equations for arbitrary electron dispersion law, concentration and relation between exchange coupling and the electron band width. Solving these equations we find explicit formula for the transition temperature $T_c$. We present the results of calculations of the $T_c$ for the semi-circular electron density of states.

Ballistic and quasiballistic tunnel transit time oscillators for the terahertz range: Linear admittance

We have considered interactions between ballistic (or quasiballistic) electrons accelerated by a dc electric field in an undoped transit space (T space) and a small ultrahigh frequency ac electric field and have calculated the linear admittance of the T space. Electrons in the T space have a conventional, nonparabolic dispersion relation. After consideration of the simplest specific case when the current is limited by the space charge of the emitted electrons, we turned to an actual case when the current is limited by a heterostructural tunnel barrier (B barrier) separating the heavily doped cathode contact and the T space. We assumed that the B barrier is much thinner than the T space and both dc and ac voltages drop mainly across the T space. The emission tunnel current through the B barrier is determined by the electric field E(0) in the T space at the boundary B barrier/T space. The more substantial is, the tunnel current limitation the higher the electric field E(0) becomes. We have shown that for a space-charge limited current the change from parabolic dispersion to the nonparabolic branch induces narrowing and closing of the frequency windows of transit-time negative conductance starting with the lowest-frequency windows. These narrowing and closing frequency windows become effective only for very high voltages U across the T space: U≫mVS2/2e, where m is the effective mass for the parabolic branch and VS is the saturated velocity for the nonparabolic branch. For moderate voltages U, the effects of nonparabolicity are not very substantial. The tunnel current limitation decreases the space-charge effects in the T space and diminishes the role of the detailed electron dispersion relation. As a result, restoration of the frequency windows of transit-time negative conductance and an increase in the value of this negative conductance occur. The implementation of the considered tunnel injection transit time oscillator diode promises to lead to efficient and powerful sources of terahertz range radiation.

Negative Effective Mass Terahertz Range Oscillators on a Cleaved Edge of a Superlattice

We consider electron dispersion relations in a quantum well overgrown on a cleaved edge of a superlattice and covered by a top barrier containing a donor modulation-doping sheet. Parameters of this structure are selected so that the electron wave function, which is localized inside of the quantum well at kZ = 0 (kZ is a wave vector component along the superlattice vector), enters the superlattice deeper and deeper with increasing kZ. As a result of this penetration, electrons become heavier and heavier. Such a dynamic (quantum) real-space transfer (without any scattering) leads to the appearance of a negative effective mass section in the lowest quantization subband. The position of this section as well as the width of the subband itself and its distance from the next subbands are regulated by both the quantum well parameters and parameters of the superlattice. The latter has to be with maximally high barriers and a small spatial period. The limitation of transverse motion of electrons in the superlattice layers is accomplished by an electric field of a pn-heterojunction formed as a result of an acceptor doping of the superlattice barriers and the above-mentioned donor modulation doping of the top barrier. This field also effectively controls the dispersion relations. Diodes with negative effective mass sections in the dispersion relation promise to be efficient terahertz range oscillators.

Influence of the electronic structure on the field electron emission from carbon nanotubes

The classical statistical-tunneling approach for the electron field emission is applied for carbon nanotubes. Detailed computations for differential emission currents reveal very close peak shapes for the armchair and zigzag geometries, thus suggesting there is very little influence of the form of the electronic energy dispersion relations on the bulk field emission currents. For carbon nanotubes of practical width, an approximate semianalytical procedure is developed to compute the differential and total emission currents for virtually any type of dispersion relations. After validation for the armchair and zigzag geometries, this procedure may be further simplified into the frame of a fictitious confined two-dimensional free electron model. Some conclusions are drawn from the comparison of the computed field emission currents (through the simplified procedure) with present experimental data and a fully analytical expression for the total bulk field emission current is obtained for practical use.

Linewidth of the Raman features of individual single-wall carbon nanotubes

In this work we analyze the room-temperature linewidth for several Raman features (i.e., the radial breathing mode, the G band, the D band, and the ${G}^{\ensuremath{'}}$ band) observed for individual isolated single-wall carbon nanotubes (SWNTs). Temperature-dependent measurements on SWNT bundles and isolated SWNTs show that anharmonic effects are not important for linewidth broadening at room temperature. Measurements on a large number of samples (170 isolated SWNTs) allow us to filter out the effect from extrinsic SWNT properties (e.g., defects, tube deformations, substrate roughness) and to obtain information about intrinsic properties related to phonon and electron dispersion relations, curvature and Breit-Wigner-Fano effects, single- vs double-resonance Raman scattering processes, and the resonance condition itself through a linewidth analysis. We also use observations at the single-nanotube level to understand linewidth effects in SWNT bundles.

Strain-induced semimetal-semiconductor transition in InAs/GaSb broken-gap quantum wells

We investigate the hybridization of the electron, heavy-hole and/or light-hole dispersion relations in strained InAs/GaSb quantum wells. In the considered structures, the lowest electron level lies below several hole levels at zero in-plane wave vector k(parallel to), so that the anticrossings of subbands produce gaps in the in-plane dispersions. To calculate the electronic band structures of such quantum wells grown on different substrates, we use the eight-band k.p model and the scattering matrix method. We have found that the order of levels at the zone center (k(parallel to)=0), gap positions and magnitudes can change due to the lattice-mismatched strain. Strain can also enhance the hybridization of electron and light-hole states at k(parallel to)=0 considerably. In the structure with a thick InAs layer grown on GaSb, we have obtained a negative indirect gap in the in-plane dispersion resulting from the anticrossing of electronlike and highest heavy-hole-like subbands. If the substrate is InAs, the gap becomes direct and positive. This phenomenon can be treated as strain-induced semimetal-semiconductor phase transition. (Less)

Low-temperature magnetoresistance of individual single-walled carbon nanotubes: A numerical study

The low-temperature magnetoresistance induced by an axial magnetic field in individual single-walled carbon nanotubes (SWNTs) is studied numerically based on Boltzmann transport equation and \ensuremath{\pi} electronic energy dispersion relations for individual SWNTs as well as taking one-dimensional weak localization (WL) into account. It is shown that the Altshuler-Aronov-Spivak effect related to WL is much weaker in individual SWNTs than in individual multiwalled carbon nanotubes, whereas the Aharonov-Bohm (AB) effect related to tubular energy band structure is stronger in individual SWNTs when the conducting electrons occupy lower energy levels, but this effect weakens rapidly as conducting electron energy increases. This suggests that only the AB effect can be observed remarkably in the states of the conducting electrons with lower energy.

The Influence of Many-Body and Bandstructure Effects in the Design of High Power Diode Lasers

A microscopic many-body theory is used to compute the dielectric constant of single quantum wells. The nonparabolic electron and hole subband dispersion relations and dipole transition moments of the free propagators stem from the numerical solutions of an 8 × 8 k · p Hamiltonian. The resulting local optical response and carrier recombination rates are used as input for realistic device simulators. Absorption, gain as well as threshold currents of distributed Bragg reflector lasers are presented.

Overshoot velocity in ultra-broadband THz studies in GaAs and InP

We model velocity overshoot in GaAs and InP using a fullband, particle-based device simulator based on the so-called cellular automaton method. This study has been motivated by the recent availability of experimental measures of the THz radiation generated by transient acceleration of photogenerated charge carriers in pin diode structures. The fullband code used in this study includes the full energy-momentum dispersion relation of electrons and holes as well as the full dispersion for the relevant phonons. Here we use this code for the simulation of high-field transient transport in bulk GaAs, InP, and for the experimental pin structure, where favorable comparison is found with the velocities measured from the transient THz radiation after ultrafast excitation.

Electron dispersion relations with negative effective masses in quantum wells grown on the cleaved edge of a superlattice

Engineered energy-wave-vector dispersion relations of either electrons or holes hold great promise for realizing fundamental oscillators at terahertz frequencies if they contain sections with a negative effective mass (NEM) at appropriate energy levels. However, neither bulk semiconductor materials nor quantum wells or quantum wires exhibit such NEM sections in the dispersion relations at favorable energy levels. Therefore, the novel use of a nanostructure is proposed to create an NEM section of electrons at suitable energy levels. This structure utilizes a heterojunction with a quantum well (QW) channel grown perpendicular to a superlattice. At small values of the wave-vector k, the electron wave function Ψ resides mostly in the QW channel and, as k increases, Ψ extends further into the superlattice. This spread of Ψ induces an NEM section in the energy dispersion relation E( k). Several combinations of suitable material systems are considered.

Two-dimensional imaging of electronic wavefunctions in carbon nanotubes.

The drive towards the development of molecular electronics is placing increasing demands on the level of control that must be exerted on the electronic structure of materials. Proposed device architectures ultimately rely on tuning the interactions between individual electronic states, which amounts to controlling the detailed spatial structure of the electronic wavefunctions in the constituent molecules. Few experimental tools are available to probe this spatial structure directly, and the shapes of molecular wavefunctions are usually only known from theoretical investigations. Here we present scanning tunnelling spectroscopy measurements of the two-dimensional structure of individual wavefunctions in metallic single-walled carbon nanotubes; these measurements reveal spatial patterns that can be directly understood from the electronic structure of a single graphite sheet, and which represent an elegant illustration of Bloch's theorem at the level of individual wavefunctions. We also observe energy-dependent interference patterns in the wavefunctions and exploit these to directly measure the linear electronic dispersion relation of the metallic single-walled carbon nanotube.

Negative effective mass mechanism of negative differential drift velocity and terahertz generation

The negative-differential-drift-velocity instability, which forms the basis of Gunn high-frequency generators, can originate from Ridley-Watkins-Hilsum or negative effective mass (NEM) mechanisms. The first mechanism is dissipative by nature. The second is mainly drift-related. Therefore, the second mechanism promises to be more effective. We show the existence of stationary oscillatory regimes in the ballistic NEM p/sup +/ p p/sup +/-diodes, which have a base in the form of a periodic system of parallel p-type quantum-well channels with base length up to 30 nm. An oscillation frequency, which depends on the base length, doping, and spatial period, as well as loads and voltage across the diode, ranges from /spl les/1 to 5 THz. We propose an additional combined quantum GaAs-AlGaAs-heterostructure, which can be overgrown on a cleaved edge of a specially grown wafer. This structure is intended to obtain electron dispersion relations with NEM sections in the useful energy range of 0.1-0.25 eV.

Gauge independence of the limiting cases of the one-loop electron dispersion relation in high-temperature QED

Assuming high temperature and taking subleading temperature dependence into account, the gauge dependence of one-loop electron dispersion relation is investigated in massless quantum electrodynamics (QED) at zero chemical potential. The analysis is carried out using a general linear covariant gauge. The equation governing the gauge dependence of the dispersion relation is obtained and used to prove that the dispersion relation is gauge independent in the limiting case of momenta much larger than $\mathrm{eT}.$ It is also shown that the effective mass is not influenced by the leading temperature dependence of the gauge dependent part of the effective self-energy. As a result, the effective mass, which is of order $eT,$ does not receive a correction of order ${e}^{2}T$ from one-loop, independent of the gauge parameter.

Isotopic Effects in the Phonon and Electron Dispersion Relations of Crystals

Isotopic Effects in the Phonon and Electron Dispersion Relations of Crystals

Isotopic Effects in the Phonon and Electron Dispersion Relations of Crystals

Isotopic Effects in the Phonon and Electron Dispersion Relations of Crystals

Metal–insulator transition in the half-filled Kondo lattice

The metal–insulator transition within the Kondo lattice model is studied. We show that the ground state at half-filling depends on the conduction electron dispersion relation; metallic Kondo states can be obtained. We also calculate the temperature of the metal–insulator transition; this temperature can be equal or smaller than the Kondo temperature depending on the model parameters.

Asymmetric doping effects on electronic properties of coupled quantum wells in an in-plane magnetic field

The purpose of this work is to study the influence of asymmetric doping positions on the electronic properties of tunnel-coupled double quantum wells (DQWs) in an in-plane magnetic field. The doping asymmetry introduces peculiarities in the gap due to the anticrossing of the two branches of the electronic dispersion relations. The built-in potential caused by the doping dramatically affects the self-consistent Fermi energy renormalization and strongly opposes an applied bias. As a result, the magnetization shows an abrupt jump when the transition from vertical to horizontal anticrossing occurs. The absolute value of the magnetoinduced voltage of two dimensional electrons in DQWs increases if the Fermi level is localized near such peculiarities and shows additional features in comparison with the symmetric-doping case. We suggest that the transverse voltage induced by a magnetic field and the magnetization are powerful tools for the experimental study of doping characteristics and equilibrium magnetic properties of quantum heterostructures.

Tunnelling between the edges of two lateral quantum Hall systems

The edge of a two-dimensional electron system in a magnetic field consists of one-dimensional channels that arise from the confining electric field at the edge of the system. The crossed electric and magnetic fields cause electrons to drift parallel to the sample boundary, creating a chiral current that travels along the edge in only one direction. In an ideal two-dimensional electron system in the quantum Hall regime, all the current flows along the edge. Quantization of the Hall resistance arises from occupation of N one-dimensional edge channels, each contributing a conductance of e2/h. Here we report differential conductance measurements, in the integer quantum Hall regime, of tunnelling between the edges of a pair of two-dimensional electron systems that are separated by an atomically precise, high-quality, tunnel barrier. The resultant interaction between the edge states leads to the formation of new energy gaps and an intriguing dispersion relation for electrons travelling along the barrier: for example, we see a persistent conductance peak at zero bias voltage and an absence of tunnelling features due to electron spin. These features are unexpected and are not consistent with a model of weakly interacting edge states. Remnant disorder along the barrier and charge screening may each play a role, although detailed numerical studies will be required to elucidate these effects.

An asymptotic approximation of multiple-scattering theory in very-low-energy electron diffraction from a metal surface

An asymptotic approximation of multiple-scattering theory has been used to analyze the intensity of very-low-energy-electron diffraction (VLEED). An analytic expression relating the amplitudes of the Bloch waves excited in a crystal (and, hence, the VLEED intensities) to the critical zone points of an infinite crystal has been obtained. The possibilities of the new approach are compared with a calculation of partial electron-transmission coefficients made by the matching method employed conventionally in interpretation of VLEED data. While providing a comparable accuracy, the proposed approach is fairly simple and free of the instabilities inherent in matching-method calculations. The explicit connection of the quantities obtained by this method with the electron dispersion relation for an infinite crystal makes it promising for analysis of band-structure effects in VLEED and photoemission experiments.

Spin-dependent tunneling in double-barrier semiconductor heterostructures

Spin-dependent tunneling in symmetric and asymmetric double-barrier semiconductor heterostructures is studied. The effective one-band Hamiltonian approximation and spin-dependent boundary conditions approach are used for a theoretical investigation of the influence of electron spin on the tunneling probability. It is shown that spin-orbit splitting in the dispersion relation for electrons in ${A}_{\mathrm{III}}{B}_{\mathrm{V}}$ semiconductors can provide the dependence of the tunneling transmission probability on the electron-spin polarization without additional magnetic field. The dependence can be controlled by an external electric field, and may be significant for realistic models of double-barrier semiconductor heterostructures.