Theory Of Electron Transport Research Articles

One-dimensional transport in hybrid metal-semiconductor nanotube systems

We develop an electron transport theory for the hybrid system of a semiconducting carbon nanotube that encapsulates a one-atom-thick metallic wire. The theory predicts Fano resonances in electron transport through the system, whereby the interaction of electrons on the wire with nanotube plasmon generated near-fields blocks some of the wire transmission channels to open up the new coherent plasmon-mediated channel in the nanotube forbidden gap outside the wire transmission band. Such a channel makes the entire hybrid system transparent in the energy domain where neither wire, nor nanotube is indivudually transparent. This effect can be used to manipulate by the electron charge transfer in hybrid nanodevices built on metal-semiconductor nanotube systems.

Reprint of : Block-determinant formalism for an action of a multi-terminal scatterer

The scattering theory of electron transport allows for a compact and powerful description in terms of gˇ2=1 Green functions, the so-called circuit theory of quantum transport. A scatterer in the theory is characterized by an action, most generally a Keldysh one, that can be further used as a building bock of theories describing statistics of electron transport, superconducting correlations, time-dependent and interaction effects. The action is usually used in the form suitable for a two-terminal scatterer.Here we provide a comprehensive derivation of a more general form of the action that is especially suitable and convenient for general multi-terminal scatterers. The action is expressed as a determinant of a block of the scattering matrix obtained by projection on the positive eigenvalues of the Green functions characterizing the reservoirs. We start with traditional Green function formalism introducing gˇ2=1 matrices and give a first example of multi-terminal counting statistics. Further we consider one-dimensional channels and discuss chiral anomaly arising in this context. Generalizing on many channels and superconducting situation, we arrive at the block-determinant relation. We give the necessary elaborative examples reproducing basic results of counting statistics and super-currents in multi-terminal junctions.

Thermoelectric transport in graphene/h-BN/graphene heterostructures: A computational study

We present first principles study of thermoelectric transport properties of sandwiched heterostructure of Graphene (G)/hexagonal Boron Nitride (BN)/G, based on Boltzmann transport theory for band electrons using the bandstructure calculated from the Density Functional Theory (DFT) based plane-wave method. Calculations were carried out for three, four and five BN layers sandwiched between Graphene layers with three different arrangements to obtain the Seebeck coefficient and Power factor in T∼25–400K range. Moreover, using Molecular Dynamics (MD) simulations with very large simulation cell we obtained the thermal conductance (K) of these heterostructures and obtained finally the Figure-of-Merit (ZT). These results are in agreement with recently reported experimental measurements.

Mapping the current–current correlation function near a quantum critical point

The current–current correlation function is a useful concept in the theory of electron transport in homogeneous solids. The finite-temperature conductivity tensor as well as Anderson’s localization length can be computed entirely from this correlation function. Based on the critical behavior of these two physical quantities near the plateau–insulator or plateau–plateau transitions in the integer quantum Hall effect, we derive an asymptotic formula for the current–current correlation function, which enables us to make several theoretical predictions about its generic behavior. For the disordered Hofstadter model, we employ numerical simulations to map the current–current correlation function, obtain its asymptotic form near a critical point and confirm the theoretical predictions.

Single-electron tunneling with slow insulators

Usual paradigm in the theory of electron transport is related to the fact that the dielectric permittivity of the insulator is assumed to be constant, no time dispersion. We take into account the "slow" polarization dynamics of the dielectric layers in the tunnel barriers in the fluctuating electric fields induced by single-electron tunneling events and study transport in the single electron transistor (SET). Here "slow" dielectric implies slow compared to the characteristic time scales of the SET charging-discharging effects. We show that for strong enough polarizability, such that the induced charge on the island is comparable with the elementary charge, the transport properties of the SET substantially deviate from the known results of transport theory of SET. In particular, the coulomb blockade is more pronounced at finite temperature, the conductance peaks change their shape and the current-voltage characteristics show the memory-effect (hysteresis). However, in contrast to SETs with ferroelectric tunnel junctions, here the periodicity of the conductance in the gate voltage is not broken, instead the period strongly depends on the polarizability of the gate-dielectric. We uncover the fine structure of the hysteresis-effect where the "large" hysteresis loop may include a number of "smaller" loops. Also we predict the memory effect in the current-voltage characteristics $I(V)$, with $I(V)\neq -I(-V)$.

Collision-dominated nonlinear hydrodynamics in graphene

We present an effective hydrodynamic theory of electronic transport in graphene in the interaction-dominated regime. We derive the emergent hydrodynamic description from the microscopic Boltzmann kinetic equation taking into account dissipation due to Coulomb interaction and find the viscosity of Dirac fermions in graphene for arbitrary densities. The viscous terms have a dramatic effect on transport coefficients in clean samples at high temperatures. Within linear response, we show that viscosity manifests itself in the nonlocal conductivity as well as dispersion of hydrodynamic plasmons. Beyond linear response, we apply the derived nonlinear hydrodynamics to the problem of hot spot relaxation in graphene.

Theory for electron transport in graphene

In this pedagogical article, we address a surprising result in the graphene transport literature, namely, measurements of the classical transport indicate that charged impurities dominate the electron scattering, while quantum transport measurements suggest that mechanical deformations that break time-reversal symmetry within a valley dominate the scattering. But surely it is the same impurities that are at play for both the phase-incoherent and phase-coherent components to the electron transport. By selectively reviewing the relevant theories for the classical and quantum transport and a careful examination of available experimental data, we show that the uncertainty in the quantum transport data makes it consistent with both with ripple-scattering being completely negligible, but also with the unphysical case of ripple scattering contributing only to quantum transport but not the classical transport. We therefore conclude that the experimental uncertainty in the available quantum transport data is too large to make any definitive statements about the relevant transport mechanisms in graphene.

Fokker Planck and Krook theory of energetic electron transport in a laser produced plasma

Various laser plasma instabilities, such as the two plasma decay instability and the stimulated Raman scatter instability, produce large quantities of energetic electrons. How these electrons are transported and heat the plasma are crucial questions for laser fusion. This paper works out a Fokker Planck and Krook theory for such transport and heating. The result is a set of equations, for which one can find a simple asymptotic approximation for the solution, for the Fokker Planck case, and an exact solution for the Krook case. These solutions are evaluated and compared with one another. They give rise to expressions for the spatially dependent heating of the background plasma, as a function of the instantaneous laser and plasma parameters, in either planar or spherical geometry. These formulas are simple, universal (depending weakly only on the single parameter Z, the charge state), and can be easily be incorporated into a fluid simulation.

Block-determinant formalism for an action of a multi-terminal scatterer

The scattering theory of electron transport allows for a compact and powerful description in terms of gˇ2=1 Green functions, the so-called circuit theory of quantum transport. A scatterer in the theory is characterized by an action, most generally a Keldysh one, that can be further used as a building bock of theories describing statistics of electron transport, superconducting correlations, time-dependent and interaction effects. The action is usually used in the form suitable for a two-terminal scatterer.Here we provide a comprehensive derivation of a more general form of the action that is especially suitable and convenient for general multi-terminal scatterers. The action is expressed as a determinant of a block of the scattering matrix obtained by projection on the positive eigenvalues of the Green functions characterizing the reservoirs. We start with traditional Green function formalism introducing gˇ2=1 matrices and give a first example of multi-terminal counting statistics. Further we consider one-dimensional channels and discuss chiral anomaly arising in this context. Generalizing on many channels and superconducting situation, we arrive at the block-determinant relation. We give the necessary elaborative examples reproducing basic results of counting statistics and super-currents in multi-terminal junctions.

Electron transport in graphene/graphene side-contact junction by plane-wave multiple-scattering method

Electron transport in graphene is along the sheet but junction devices are often made by stacking different sheets together in a ``side-contact'' geometry which causes the current to flow perpendicular to the sheets within the device. Such geometry presents a challenge to first-principles transport methods. We solve this problem by implementing a plane-wave-based multiple-scattering theory for electron transport. This implementation improves the computational efficiency over the existing plane-wave transport code, scales better for parallelization over large number of nodes, and does not require the current direction to be along a lattice axis. As a first application, we calculate the tunneling current through a side-contact graphene junction formed by two separate graphene sheets with the edges overlapping each other. We find that transport properties of this junction depend strongly on the AA or AB stacking within the overlapping region as well as the vacuum gap between two graphene sheets. Such transport behaviors are explained in terms of carbon orbital orientation, hybridization, and delocalization as the geometry is varied.

Dissipative time-dependent quantum transport theory: Quantum interference and phonon induced decoherence dynamics.

A time-dependent inelastic electron transport theory for strong electron-phonon interaction is established via the equations of motion method combined with the small polaron transformation. In this work, the dissipation via electron-phonon coupling is taken into account in the strong coupling regime, which validates the small polaron transformation. The corresponding equations of motion are developed, which are used to study the quantum interference effect and phonon-induced decoherence dynamics in molecular junctions. Numerical studies show clearly quantum interference effect of the transport electrons through two quasi-degenerate states with different couplings to the leads. We also found that the quantum interference can be suppressed by the electron-phonon interaction where the phase coherence is destroyed by phonon scattering. This indicates the importance of electron-phonon interaction in systems with prominent quantum interference effect.

Theory of high-field electron transport in the heterostructures AlxGa1-xAs/GaAs/AlxGa1-x with delta-doped barriers. Effect of real-space transfer

Steady-state electric characteristics of quantum heterostructures AlxGa1–xAs/GaAs/AlxGa1–xAs with  -doped barriers have been analyzed in this work. It has been shown that at high doping the additional low-conductive channels are formed in the barrier layers. Current-voltage characteristics of the structure were obtained in the wide interval of applied electric fields up to several kV/cm being based on the solution of Boltzmann transport equation. It has been found that in the electric fields higher than 1 kV/cm the effect of exchange of the carriers between the high-conductive channel of the GaAs quantum well and the channels in the AlGaAs barriers becomes essential. This effect gives rise to the appearance of the strongly nonlinear current-voltage characteristics with a portion of negative differential conductivity. The developed model of heterostructure is adequate to those recently fabricated and studied by Prof. Sarbey’s group. The obtained results explain some observation of this paper. It has been found that the effect of electron real-space transfer takes place at both low temperatures and room temperatures, which opens perspectives to design novel type nanostructured current controlled devices.

Communication: Finding destructive interference features in molecular transport junctions.

Associating molecular structure with quantum interference features in electrode-molecule-electrode transport junctions has been difficult because existing guidelines for understanding interferences only apply to conjugated hydrocarbons. Herein we use linear algebra and the Landauer-Büttiker theory for electron transport to derive a general rule for predicting the existence and locations of interference features. Our analysis illustrates that interferences can be directly determined from the molecular Hamiltonian and the molecule-electrode couplings, and we demonstrate its utility with several examples.

Quantum dots with indirect band gap: power-law photoluminescence decay

In this work the experimental effect of a slow decay of the photoluminescence is studied theoretically in the case of quantum dots with an indirect energy band gap. The slow decay of the photoluminescence is considered as decay in time of the luminescence intensity, following the excitation of the quantum dot sample electronic system by a short optical pulse. In the presented theoretical treatment the process is studied as a single dot property. The inter-valley deformation potential interaction of the excited conduction band electrons with lattice vibrations is considered in the self-consistent Born approximation to the electronic self-energy. The theory is built on the non-equilibrium electronic quantum transport theory. The time dependence of the photoluminescence decay is estimated upon using a simple effective mass model. The numerical calculation of the considered model shows the power-law time characteristics of the photoluminescence decay in the long-time limit of the decay. We demonstrate that the nonadiabatic influence of the interaction of the conduction band electrons with the lattice vibrations provides a mechanism giving us the power-law time dependence of the photoluminescence intensity signal. This theoretical result emphasizes the role of the electron-phonon interaction in the nanostructures.

Scattering theory of electron transport in single layer graphene with a time-periodic potential

Abstract We applied the scattering approach to studying the transport properties of charge carriers through single layer graphene in the presence of a time-periodic potential. Using the method, expressions for the second-quantized current operator, conductivity and shot noise are obtained. The results obtained in this study demonstrate that the applied external field provides sidebands for charge carriers to tunnel through the graphene, and these sidebands changed the transport properties of the system. The results obtained in this study might be of interest to basic understanding of photon-assisted tunneling (PAT) and designers of electron devices based on graphene.

Theory of fast electron transport for fast ignition

Fast ignition (FI) inertial confinement fusion is a variant of inertial fusion in which DT fuel is first compressed to high density and then ignited by a relativistic electron beam generated by a fast (<20 ps) ultra-intense laser pulse, which is usually brought in to the dense plasma via the inclusion of a re-entrant cone. The transport of this beam from the cone apex into the dense fuel is a critical part of this scheme, as it can strongly influence the overall energetics. Here we review progress in the theory and numerical simulation of fast electron transport in the context of FI. Important aspects of the basic plasma physics, descriptions of the numerical methods used, a review of ignition-scale simulations, and a survey of schemes for controlling the propagation of fast electrons are included. Considerable progress has taken place in this area, but the development of a robust, high-gain FI ‘point design’ is still an ongoing challenge.

First-principles studies of the TE properties of [110]-Ge/Si core/shell nanowires with different surface structures

Based on first-principle electronic structure calculations and Boltzmann transport theory, we investigate the composition-dependent thermoelectric properties of germanium/silicon core/shell [110]-oriented nanowires, as well as the surface passivation effects. The results demonstrate that the ZT values depend on the surface structure and the Ge/Si ratio. Significantly, for n-type [110]-Ge/Si core/shell NWs (about 2.6 nm in diameter) ZT = 0.65 at 300 K can be obtained, that is 65 times that of bulk Si, and 1.8 times that of SiNW without the core/shell structure at the same temperature.

The influence of ionized impurity scattering on the thermopower of Si nanowires

The thermopower of Si nanowires was investigated on the basis of electronic transport theory, taking into account ionized impurity scattering as well as electron–phonon scattering. It was found that the enhancement of the Seebeck coefficient in nanowires arising from quantum confinement is unimportant due to the ionized impurity scattering associated with donor deactivation. Furthermore, because the electrical conductivity is degraded significantly as the nanowire size becomes smaller, despite the accompanying slightly enhanced Seebeck coefficient, the reduction of the nanowire size is not beneficial, at least for the thermopower of devices.

Electronic Structure and Thermoelectric Properties of ZnO Single-Walled Nanotubes and Nanowires

Based on ab initio electronic structure calculations and Boltzmann transport theory, the size dependence of thermoelectric properties of ZnO single-walled nanotubes (SWNTs) and nanowires was investigated. There is an optimal carrier concentration yielding the maximum value of ZT at room temperature. The optimal carrier concentration and the maximum value of ZT depend on the diameters and structure of ZnO. The maximum value of ZT for ZnO SWNTs are remarkably higher than that of ZnO nanowires. The 9.60 Å ZnO SWNT possess the highest ZT value, 0.322, which is nearly 3-fold higher than that of the best experimental samples at room temperature.

Rethinking first-principles electron transport theories with projection operators: The problems caused by partitioning the basis set

We revisit the derivation of electron transport theories with a focus on the projection operators chosen to partition the system. The prevailing choice of assigning each computational basis function to a region causes two problems. First, this choice generally results in oblique projection operators, which are non-Hermitian and violate implicit assumptions in the derivation. Second, these operators are defined with the physically insignificant basis set and, as such, preclude a well-defined basis set limit. We thus advocate for the selection of physically motivated, orthogonal projection operators (which are Hermitian) and present an operator-based derivation of electron transport theories. Unlike the conventional, matrix-based approaches, this derivation requires no knowledge of the computational basis set. In this process, we also find that common transport formalisms for nonorthogonal basis sets improperly decouple the exterior regions, leading to a short circuit through the system. We finally discuss the implications of these results for first-principles calculations of electron transport.