Saddle-point Potential Research Articles

Electronic transport and spatial current patterns of 2D electronic system: A recursive Green’s function method study

Based on the scanned probe microscopes, the local current properties in a nanodevice can be clearly exposed. However, it is still a big challenge to experimentally observe the atomic scale varying current pattern. A numerical-aided method is therefore very important for getting the local current information in a microsystem. In this study, we show the nonequilibrium Green’s function method to calculate the transport properties of two-terminal devices. For applying this method to larger systems, a recursive procedure is present in detail. The correctness of this method is confirmed by calculating the transport properties of a clean 2DEG. The conductance steps in such a sample match the corresponding band structure very well. Then, we calculate the current patterns in quantum point contact under a saddle-point potential. Several current jets can be clearly spotted which correspond to transport channels in quantum point contact. Meanwhile, the interference streaks are spotted near the edges of the device due to the reflection of electrons at the edges.

Thermal Conductance and Seebeck Effect in Mesoscopic Systems

In this work, thermoelectric transport through a saddle-point potential is discussed with an emphasis on the effects of the chemical potential and temperature. In particular, the thermal conductance and the Seebeck coefficient are calculated for two-dimensional systems of a constriction defined by a saddle-point potential. The solution as a function of temperature and chemical potential has been investigated. The Peltier coefficient and thermal transport in a quantum point contact (QPC), under the influence of external fields and different temperatures, are presented. Also, the oscillations of the Peltier coefficient in external fields are obtained. Numerical calculations of the Peltier coefficient are performed at different applied voltages, amplitudes, and temperatures. Moreover, a method is proposed for measuring the sub-band energies and spin-splitting energies in a bottle-neck of the constriction. For weak non-linearities, the charge and entropy currents across a QPC are expanded as a series in powers of the applied bias voltage and the temperature difference. Expansions of the Seebeck voltage in terms of the temperature difference and the Peltier heat in terms of the current are obtained.

Nonlinear Transport of the Wigner Crystal on Superfluid 4He in a Quasi-One-Dimensional Channel

We study transport properties of a Wigner crystal driven by an external force on the surface of superfluid 4 He , in the "quantum wire" regime, i.e. in the quasi-one-dimensional (quasi-1D) case when a typical width of the channel is comparable to the inter-electron separation. Utilizing molecular dynamics simulations, we investigate the electronic transport through the channels with different constrictions: (i) geometrical constrictions with varying shape and size, and (ii) a saddle-point potential with varying gate voltage. The average particle velocity has been calculated as a function of the driving force or gate voltage. We have revealed a significant difference in the dynamical behavior for long and short constrictions. In particular, we found that the oscillations of the average particle velocity in channels with short constrictions exhibit a clear correlation with the transitions between the states with different numbers of rows of particles in the constriction, while for channels with longer constrictions these oscillations are suppressed. The obtained results are in agreement with the recent experimental observations,1 and thus bring new important insights into the dynamics of electrons floating on the surface of superfluid 4 He in channels with constrictions. [Formula: see text] Special Issue Comments: This article presents results on the dynamics of electrons moving on the surface of liquid helium in narrow channels with constrictions, with a focus on the "quantum wire", i.e. single file, regime. This article is connected to the Special Issue articles about advanced statistical properties in single file dynamics39 and the experiments on liquid helium.40

Coulomb imaging of the concerted and stepwise break up processes of OCS ions in intense femtosecond laser radiation

We study the break up of OCS in intense femtosecond laser radiation using the FEMPULS technique to vary the laser pulse duration from 7fs to 200fs. Newton and Dalitz plots show the progression of molecular deformation and break up for OCS3+ and OCS4+. For increasing pulse length, the concerted three body dissociation exhibits increasing bending, and the amount of stepwise dissociation decreases. For the longest pulses however the stepwise process increases again. Both phenomena can be interpreted in terms of the effect of the laser field on lower charge states and the behaviour of a wave packet on a saddle point potential. The experiment illustrates the ability of the Coulomb imaging method to track molecular geometry and dynamics and indicates a new path to laser control of molecular parameters.

0.7 structure of conductance quantization in quantum point contact

In the paper, we study electronic transport property through a quantum point contact with the saddle-point potential. Our numerical approach is based on the Green's function technique which is evaluated at the Hartree-Fork level. We reproduce relevant features of 0.7 structure when the strength of electron-electron interaction has changed. Besides, we calculate spin accumulation and noise factor at zero temperature. We deepen the understanding of the effect of strong correlation interaction on spin transport in nanometer semiconductor device.

Exact propagator for an electron in a quadratic saddle-point potential and a magnetic field

We study the propagator for an electron moving in a two-dimensional (2D) quadratic saddle-point potential, in the presence of a perpendicular uniform magnetic field. A closed-form expression for the propagator is derived using the Feynmann path integrals.

Transmission coefficient through a saddle-point electrostatic potential for graphene in the quantum Hall regime

From the scattering of semicoherent-state wavepackets at high magnetic field, we derive analytically the transmission coefficient of electrons in graphene in the quantum Hall regime through a smooth constriction described by a quadratic saddle-point electrostatic potential. We find anomalous half-quantized conductance steps that are rounded by a backscattering amplitude related to the curvature of the potential. Furthermore, the conductance in graphene breaks particle-hole symmetry in cases where the saddle-point potential is itself asymmetric in space. These results have implications both for the interpretation of split-gate transport experiments, and for the derivation of quantum percolation models for graphene.

Spin-current quantization in a quantum point contact with spin-orbit interaction

We develop a realistic and analytically tractable model to describe the spin current which arises in a quantum point contact (QPC) with spin-orbit interaction (SOI) upon a small voltage is applied. In the model, the QPC is considered as a saddle point of two-dimensional potential landscape. The SOI acts within a finite region and is absent deep in the reservoirs. The SOI strength is not supposed to be strong. It is shown that the spin polarization appears in the third order of the perturbation theory as a result of definite combinations of electron transitions. They include two intersubband transitions to nearest subbands and one intrasubband transition. The spin current is proportional to the cube of the SOI strength and strongly depends on geometric parameters of the saddle point. The spin is polarized in the plane of the QPC and directed normally to the electron current if the SOI is of Rashba type. As a function of the saddle-point potential (i.e., the height of the QPC barrier), the spin conductance and especially the spin polarization have characteristic features (specifically, peaks) correlated with the charge conductance quantization steps. The peak shape depends on the length of the region where the SOI acts. In QPCs with sharp potential landscape, this picture is distorted by interference processes.

Electron–electron interaction effects in quantum point contacts

We consider electron–electron interaction effects in quantum point contacts on the first quantization plateau, taking into account all scattering processes. We compute the low-temperature linear and nonlinear conductance, shot noise and thermopower, by perturbation theory and a self-consistent nonperturbative method. On the conductance plateau, the low-temperature corrections are solely due to momentum-nonconserving processes that change the relative number of left- and right-moving electrons. This leads to a suppression of the conductance for increasing temperature or voltage. The size of the suppression is estimated for a realistic saddle-point potential, and is largest in the beginning of the conductance plateau. For large magnetic field, interaction effects are strongly suppressed by the Pauli principle, and hence the first spin-split conductance plateau has a much weaker interaction correction. For the nonperturbative calculations, we use a self-consistent nonequilibrium Green's function approach, which suggests that the conductance saturates at elevated temperatures. These results are consistent with many experimental observations related to the so-called 0.7 anomaly.

Single-Electron Tunneling through Individual InAs Quantum Dots within a Saddle Point Potential

Single-Electron Tunneling through Individual InAs Quantum Dots within a Saddle Point Potential

Single-Electron Tunneling through Individual InAs Quantum Dots within a Saddle Point Potential

InAs quantum dots were embedded in a two-dimensional electron gas of a modulation doped heterostructure. A constriction was lithographically defined to allow electron transport through at maximum three quantum dots. Sharp resonances appear at the onset of the conductance which are attributed to electron tunneling through the first excited state of a single dot within the constriction. A Coulomb blockade energy of 12 meV was estimated for this energy level which is in good agreement with capacitance data measured on a dot ensemble. When the source bias is varied Coulomb blocked regimes can be observed which are typical for single electron devices.

Two-terminal conductance fluctuations in the integer quantum Hall regime

Motivated by recent experiments on the conductance fluctuations in mesoscopic integr quantum Hall systems, we consider a model in which the Coulomb interactions are incorporated into the picture of edge-state transport through a single saddle-point. The occupancies of `classical' localised states in the two-dimensional electron system change due to the interactions between electrons when the gate voltage on top of the device is varied. The electrostatic potential between the localised states and the saddle-point causes fluctuations of the saddle-point potential and thus fluctuations of the transmission probability of edge states. This simple model is studied numerically and compared with the observation.

Differential conductance of a saddle-point constriction with a time-modulated gate-voltage

This work investigates how a time-modulated gate-voltage influences the differential conductance G of a saddle-point constriction. The constriction is modeled by a symmetric saddle-point potential and the time-modulated gate-voltage is represented by a potential of the form V 0 Θ(a/2−|x−x c |) cos(ωt) . For ℏ ω less than half of the transverse subband energy level spacing, gate-voltage-assisted (suppressed) feature occurs when the chemical potential μ is less (greater) than but close to the threshold energy of a subband. Our results indicate that as μ increases, G exhibits, alternatively, the assisted and the suppressed feature. For a larger ℏ ω, these two features may overlap. In addition, dip structures are found in the suppressed regime, and mini-steps are found in the assisted regime only when the gate-voltage covers a region sufficiently distant from the center of the constriction.

Short-range impurity in the vicinity of a saddle point and the levitation of the two-dimensional delocalized states in a magnetic field.

The effect of a short-range impurity on the transmission through a saddle-point potential for an electron, moving in a strong magnetic field, is studied. It is demonstrated that for a random position of an impurity and random sign of its potential, the impurity-induced mixing of the Landau levels diminishes on average the transmission coefficient. This results in an upward shift (levitation) of the energy position of the delocalized state in a smooth potential. The magnitude of the shift is estimated. It increases with decreasing magnetic field B as ${\mathit{B}}^{\mathrm{\ensuremath{-}}4}$. \textcopyright{} 1996 The American Physical Society.

Exact propagators for a two-dimensional electron in quadratic potentials and a transverse magnetic field.

The propagator for an electron moving in a two-dimensional (2D) saddle-point potential under the influence of a transverse magnetic field is evaluated exactly using the Feynmann path integrals. The applications of this result for the calculation of tunneling through a saddle point are discussed. We also investigate tunneling a 2D electron at finite temperature in the presence of a transverse magnetic field, dissipation, and random scatterers by the use of a nonlocal harmonic oscillator model and find a crossover temperature ${\mathit{T}}_{1}$. The application of the same model at zero temperature for a quantum Hall system is shown to be incorrect. \textcopyright{} 1996 The American Physical Society.

Analytic modeling of the conductance in quantum point contacts with large bias.

We have developed a model for calculating differential conductance that accounts for the effects observed at high source-drain voltage. The model uses a linear potential drop over a saddle-point potential. If the region of the potential drop is wide enough, only that region is contributing to the transmission and a simple expression is obtained. The temperature is assumed to increase linearly with the source-drain voltage and a model for an equipotential region in the saddle-point potential corresponding to the channel width is made. The result from the calculations of the conductance with this model is in good agreement with experimental results.

Analytical model of a one-dimensional constriction with many occupied subbands: Calculation and experiment.

We have measured the differential conductance of two different one-dimensional (1D) constrictions with several occupied subbands at low temperature under conditions of high dc source-drain bias relative to the 1D subband spacing. The results are compared with a simulation based on a saddle-point potential with and without a thin equipotential strip at the center. We fit the experimental results at high conductance by increasing the width of the equipotential strip with an increase in number of conducting subbands. For a split gate where the depth of the electron gas is 70 nm and where there are at most three occupied 1D subbands, a simple parabolic saddle-point model is sufficient. For a device where the depth of the electron gas is 27 nm and there are eight occupied 1D subbands, the modified potential model is needed to give good agreement with experimental data.

Short-range impurity in a saddle-point potential: Conductance of a microjunction.

The conductance G of the two-dimensional electron gas in the presence of an impurity in the central cross section of the split-gate constriction is calculated. The confining potential of the constriction is assumed to be a saddle-point potential, and the impurity is assumed to be short range. It is found that for attractive impurity potentials a quasibound state exist below the band bottom of each transverse subband. If the energy of this bound state is far from the threshold energy, then one observes resonant reflection and a narrow downward dip in G vs the Fermi energy E. When the bound state is near the threshold, one observes resonant transmission and a narrow peak in G vs E.

Non-linear conductance of a saddle-point constriction

The authors present calculations of the differential conductance, G, of a constriction, defined by a saddle-point potential in a two-dimensional electron gas, in the non-linear regime of transport as a function of Fermi energy, source-drain voltage and magnetic field. The manner in which the potential is dropped along the device is considered phenomenologically. The dependence of G on the parameters that define the potential drop is investigated, extending the model proposed by Glazman and Khaetskii. A method for measuring the sub-band energies and spin-splitting energies in a bottle-neck of the constriction is also proposed. Finally, a comparison between experimental data and theoretical calculations is presented.

Quantisation of the conductance in units of e 2/2h in a ballistic quasi-one-dimensional channel, produced by strong electric and magnetic fields

We present data for the differential conductance of a quantum point contact under both strong electric and magnetic fields that shows quantisation in units of e 2/2h, proving that the spin-splitting and the bias-induced-splitting of the plateaux are two independent effects. Calculations of the non-linear differential conductance, using a saddle-point potential to model (1) the one-dimensional channel and assuming that half of the applied source-drain voltage is dropped between each of the contacts and the centre of the channel (2), show excellent agreement with the experimental data.