Interacting Electron Wave Packet Dynamics in a Two-Dimensional Nanochannel

Abstract

Classical and quantum dynamics are important limits for the understanding of the transport characteristics of interacting electrons in nanodevices. Here, we apply an intermediate semiclassical approach to investigate the dynamics of two interacting electrons in a planar nanochannel as a function of Coulomb repulsion and electric field. We find that charge is mostly redistributed to the channel edges and that an electric field enhances the particle-like character of electrons. These results may have significant implications for the design and study of future nanodevices.Ideal ultrasmall logic nanodevices feature high switching speeds, low power consumption, excellent on-off current ratios and high scalability and integrability. Electron transport in ultrasmall nanodevices approaching channel lengths of approximately 10 nm, [1] however, turns out to be quasi-ballistic and intricate [2,3] due to Brownian motion (thermal noise caused by scattering and diffusion) and the discreteness of the electric charge (leading to shot noise enhanced by unscreened trapped charges). These effects give rise to significant current fluctuations at high clock speeds and low voltages, [4,5] which are detrimental to efficient device operation. This indicates that high-speed electrons in nanoscale regions cannot be described by conventional statistical frameworks such as Maxwell-Boltzmann approaches. Highly doped drain and source regions can further impact channel electrons, e.g., due to the build-up of mirror charges, suggesting that Coulomb interaction is a paramount ingredient in describing transport, dissipation, and equilibration in nanostructures. [2,3,6] A comprehensive understanding of electron dynamics on small time and length scales therefore is desirable to improve the device performance.Various approaches to electron transport in nanodevices have been taken so far, ranging from classical Monte Carlo and molecular dynamics methods to quantum nonequilibrium Green function calculations. [2,4,5,7,8] Here, we address the charge transport from an intermediate, semiclassical perspective, [9,10] by solving the Schrödinger equation numerically for a pair of interacting electron wave packets that propagate in a planar nanochannel. This approach interpolates between the classical, particle-like and the quantum, wavelike nature of electrons (Fig. 1) and approximately preserves the discreteness of the transported electron charge over appropriate (not too short) time scales. Wave packet approaches have been considered previously, but relied on strictly one-dimensional structures and/or on noninteracting electrons, or were based on approximate schemes such as the time-dependent Hartree-Fock theory. [11][12][13][14][15][16][17] Below, we study in detail the effect of Coulomb repulsion and an external electric field on wave packet propagation in a two-dimensional nanochannel. A main finding is that Coulomb repulsion redistributes the charge density to the channel walls, which makes electron transport more sensitive to perturbations at the in...

Manifestation of the Berry curvature in geophysical ray tracing

“…The set of equations (3.13) is different from the ones obtained with the traditional scalar derivation (see §4.c) as it accounts for both the corrected ray Hamiltonian Ω ( n ) and the geometry of the wave packet’s polarization relations in ray phase space through the Berry curvature. Such a form of ray-tracing equations has already been derived for different purposes such as the study of the time-dependent Schrödinger equation in the adiabatic limit [19], the theory of Bohr–Sommerfeld quantization [37] and semiclassical analyses of wave packet trajectories in slowly perturbed crystals [6,14,40,41], optical lattices [18,42] and ultracold atoms [17]. Formal expressions for first-order corrections to transport equations in multi-component fluid wave problems with inhomogeneous media were proposed by Onuki [22], with concrete applications to shallow-water waves.…”

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Effect of long-range Coulomb interactions on electron transport in a nanoscale one-dimensional ring

“…However, a previous study, which was carried out with a wave packet picture, showed that with high electric fields the particle nature of the electrons emerges. 8) Because the source-drain bias does not scale as severely as the channel length, 2) the electric field in the channel can be as high as 10 MV cm −1 . All things considered, electrons in a nanoscale channel are in the intermediate region between quantum waves and classical particles.…”