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Australian Journal of Physics

Time-dependent Quantum Waveguide Theory: A Study of Nano Ring Structures

S. Midgley, Jingbo B. Wang

Published Feb 2, 2000• 12 citations
Publisher

Abstract

As electronic circuits get progressingly smaller to the nanometre scale, the quantum wave nature of the electrons starts to play a dominant role. It is thus possible for the devices to operate by controlling the phase of the quantum electron waves rather than the electron density as in present-day devices. This paper presents a highly accurate numerical method to treat quantum waveguides with arbitrarily complex geometry. Based on this model, a variety of quantum effects can be studied and quantified.

DOI
10.1071/ph99043

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As electronic circuits get progressingly smaller to the nanometre scale, the quantum wave nature of the electrons starts to play a dominant role. It is thus possible for the devices to operate by controlling the phase of the quantum electron waves rather than the electron density as in present-day devices. This paper presents a highly accurate numerical method to treat quantum waveguides with arbitrarily complex geometry. Based on this model, a variety of quantum effects can be studied and quantified.
With the aim of manufacturing faster and smaller devices, the electronic industry is today approaching both the nano and the picosecond scales. In this particular scenario, electron dynamics becomes strongly correlated both in space and time. We have recently shown that Bohmian trajectories allow a direct treatment of the time-dependent many-particle interaction among electrons with accuracy comparable to Density Functional Theory techniques. In this work we present a general purpose time-dependent 3D quantum electron transport simulator based on Bohmian trajectories that we call BITLLES. As a numerical example of its capabilities, we compute the full electrical characteristics (DC, High frequency and fluctuations) of a Resonant Tunneling Diode.
Electron-phonon interactions play a central role in the behaviour of matter in the condensed phase. Physicists’ interest in this subject can be traced back to the early days of quantum mechanics, when key concepts like vibration quanta in the theory of specific heat or the Born-Oppenheimer approximation in molecular electronic structure, to mention a few, were first introduced. The controlled manufacturing of nanoscale systems has ushered a renewed interest in the basic aspects of electron-phonon interactions since the spatial confinement in nano-structures can enhance the effect of specific vibrational modes, leading to concrete manifestations of interesting concepts such as, local temperature and heating. It is also expected that in an another area of physics, namely ultracold-atoms, the study of the interaction between itinerant fermions and phonon-like excitations can be successfully undertaken due to the possibility of controlled and accurate manipulation of experimental setups and selective inclusion of physical effects. This thesis investigates some elementary aspects of the electron-phonon interactions in small open and closed 1D chains. Using an exact numerical method, the time-behaviour of 1) quantum rings in magnetic fields, and 2) parabolically trapped systems has been addressed when electron-phonon and/or electron-electron interaction are present. A first outcome of this thesis is the implementation ex-novo of a computer code to describe the non-equilibrium dynamics of these aforementioned model systems. Using such numerical capability, we performed several numerical simulations. As a second outcome of our work, we have obtained a set of results which illustrates the complex interplay among fermion-fermion and fermion-phonon interactions in the presence of magnetic time-varying fields, and how such interplay depends on the i) non/adiabatic and ii) non/resonant character of the external perturbation. Our work only touches the very superficial aspects of these very interesting topics, and we hope it will provide inspiration for further investigations.
Modern electronic devices and novel materials often derive their extraordinary properties from the intriguing, complex behavior of large numbers of electrons forming what is known as an electron liquid. This book provides an in-depth introduction to the physics of the interacting electron liquid in a broad variety of systems, including metals, semiconductors, artificial nano-structures, atoms and molecules. One, two and three dimensional systems are treated separately and in parallel. Different phases of the electron liquid, from the Landau Fermi liquid to the Wigner crystal, from the Luttinger liquid to the quantum Hall liquid are extensively discussed. Both static and time-dependent density functional theory are presented in detail. Although the emphasis is on the development of the basic physical ideas and on a critical discussion of the most useful approximations, the formal derivation of the results is highly detailed and based on the simplest, most direct methods.
The last several decades have seen significant advances in the theoretical modeling of materials within the fields of solid-state physics and materials science, but many methods commonly applied to this problem struggle to capture strong electron correlation accurately. Recent widespread interest in quantum materials---where strong correlation plays a crucial role in the quantum effects governing their behavior---further highlights the need for theoretical methods capable of rigorously treating such correlation. Here, we present a periodic generalization of variational two-electron reduced density matrix (2-RDM) theory, a bootstrapping-type method that minimizes the ground-state energy as a functional of the 2-RDM without relying on the wave function. The 2-RDM is computed directly by semidefinite programming with NNN-representability conditions, ensuring accurate treatment of strongly correlated electronic systems. By exploiting translational symmetry, we significantly reduce computational scaling, enabling applications to realistic materials-scale systems. Additionally, we introduce an alternative to conventional energy band structures: natural-orbital occupation-number bands, which, being independent of mean-field assumptions, offer deeper insights into electron correlation effects. We demonstrate the effectiveness of this approach by applying the theory to hydrogen chains, molybdenum disulfide, and nickel oxide, showing that natural-orbital occupation bands correctly capture electronic character in regimes where density functional theory fails. This work represents a major step toward accurately describing the electronic structure of quantum materials using reduced density matrices rather than wave functions.