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Modeling of nanostructures with complex source and drain

Jani Hakanen

Published Jan 1, 2004• 1 citation
OpenAlex

Abstract

In this thesis we report on calculations for open quantum mechanical and certain microwave systems. The models refer to a quantum point contact and an electron cavity. We model this open system with an imaginary potential as source and drain, and use the finite difference method to make our calculations. We report on general features of the model we have found, and compare our calculations with measurements made on microwave cavities.

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In this thesis we report on calculations for open quantum mechanical and certain microwave systems. The models refer to a quantum point contact and an electron cavity. We model this open system with an imaginary potential as source and drain, and use the finite difference method to make our calculations. We report on general features of the model we have found, and compare our calculations with measurements made on microwave cavities.
A basic model for particle states and current flow in open quantum dots/billiards are investigated. The model is unconventional and extends the use of complex potentials first introduced in phenomenological nuclear inelastic scattering theory (the optical model). Attached leads/source drain are represented by complex potentials. Probability densities and currents flows for open 2D quantum dots/billiards are calculated and the results are compared with microwave measurements used to emulate the dot. We also apply the model to a rectangular enclosure and report on helical flows guided by nodal lines and disc-like accumulations of flow lines. The model is of conceptual as well as practical and educational interest
A heuristic model for particle states and current flow in open ballistic two-dimensional (2D) quantum dots/wave billiards is proposed. The model makes use of complex potentials first introduced in phenomenological nuclear inelastic scattering theory (the optical model). Here we assume that external input and output leads connecting the system to the source and the drain regions may be represented by complex potentials. In this way, a current may be set up between the two 'pseudo-leads'. Probability densities and current flows for an open quantum dot are analyzed here numerically and the results are compared with the microwave measurements used to emulate the system. The model is of conceptual as well as practical interest. In addition to quantum billiards, it may be used as a tool per se to analyze transport in classical wave analogues, such as microwave resonators, acoustic resonators, effects of leakage on such systems, etc.
Devices involving bound or propagating photons are among the basic building blocks for modern quantum technologies. For example, the bound modes of open optical resonators, coupled to quantum emitters such as atoms, molecules, or quantum dots, are used for an enhanced emission in lasing applications, for increased sensitivity in quantum sensing, and as qubits in quantum computing. Meanwhile, propagating photons are crucial for the transmission of quantum states between spatially separated systems. In this thesis, we develop a rigorous theory of multiple, spatially separated, and individually addressable cavities (or plasmonic resonators) for applications in modern quantum devices. Losses are modeled via the use of quasinormal modes (QNMs), which are solutions to the source-free Helmholtz equation under open boundary conditions, making them the natural modes of open resonators. Quantum emitters are modeled as two-level systems (TLSs) which couple to the electric field via dipole coupling. The multi-cavity theory is developed in three steps: 1. We present a classical scattering theory for a system of multiple QNM cavities, where the multi-cavity Green's function is formulated in terms of the single-cavity modes. The inter-cavity scattering is frequency-dependent to account for retardation delays, and is efficiently calculated numerically, using common (commercial) solvers. 2. We formulate a quantization scheme for QNMs of spatially separated open resonators. We introduce the \textit{cavity separation parameter} as a simple measure for when QNM cavities can be quantized separately and when they have to be treated as a single system with a joint set of operators. We derive a general system-bath Hamiltonian that contains coupling between bound modes, quantum emitters, and a bath of propagating photons, expressed via rigorous, numerically calculable coupling parameters. 3. We discuss the time-dependent theory of QNMs and TLSs coupled to propagating photons. The system-bath interaction is formulated in terms of correlation functions that are again rigorously defined in terms of numerically calculable QNM parameters. The correlation functions are immediately applicable to common methods for calculating the dynamics of open quantum systems. Steps 1-3 are all formulated for general cavity shapes and materials, as well as (in principle) arbitrary background structures. Hence, the theory is applicable to a wide range of devices, including cavities or plasmonic resonators in free space, on a photonic crystal, or on a substrate. For each step, we show example calculations for one-dimensional or three-dimensional cavities.
The thesis discusses description of associative detachment of electron in the iont interaction with neutral atoms in optical lattice. This is given by combination of the model for interaction of particles in optical lattice, given by periodic potential, and of the model for associative detachment of electron, describe by imaginary component of the potential. In thesis is stated form of Schrödinger's equation for periodic potential, and subsequent solution of such equation in case of general complex and non hermitian Hamiltonian (because of imaginary component of potential). I specifically compute complex energetic levels one-dimensional model with numeric method from software package EISPACK for non hermitian Hamiltonian decomposed into finite base. Powered by TCPDF (www.tcpdf.org)
The approximate numerical method for a calculation of a quantum wave impedance in a case of a potential energy with a complicated spatial structure is considered. It was proved that the approximation of a real potential by a piesewise constant function is also reasonable in a case of using a quantum impedance approach.The dependence of an accuracy of numerical calculations on a number of cascads by which a real potential is represented was found. The method of including into a consideration of zero-range singular potentials was developed.
Interesting discoveries have recently been made in the area of solid state physics and nano technology regarding electronic systems that are confined to reduced spatial dimensions. Under these circumstances the quantum nature of the electrons begins to surface. In the one-dimensional case this class of systems is therefore called quantum- or nano wires. The conductance in such quantum wires becomes quantized and is dominated by electronic correlations. The goal of this thesis was to develop a fast and efficient procedure to describe a realistic transport measurement for such systems. The method presented here is in- spired by the work of Dan Bohr et al. who used the Density Matrix Renormalization Group algorithm(DMRG) to evaluate the Kubo formula for the linear response to an applied potential. In a similar way the procedure of this thesis also computes the Kubo formula using the dynamical DMRG in order to calculate the low frequency response to an AC source-drain voltage of finite systems. Making use of a special finite size scaling allows to extrapolate the results into the thermodynamic limit and to finally obtain the linear DC-conductance. First, the theoretical framework for the new method was developed. This was fol- lowed by testing the new approach in different model systems. The first model com- prised of a tight-binding chain that was filled with spinless, noninteracting fermions. In subsequent steps the model was expanded by introducing a homogeneous in- teraction in the Luttinger liquid regime followed by inhomogeneous interaction for different chain sections. The potential impact of impurities was assessed in the above models. Lastly, the two cases of the Hubbard chain of spin- 2 1 electrons and of the Holstein model in one dimension, where Einstein phonons interact with spinless fermions, were studied. The results of the proposed method are consistent with Luttinger liquid and Lan- dauer scattering theory. In the Luttinger liquid regime the influence of phonons to the charge structure factor was confirmed. A dependency on the length of the quantum wire in the form of dissipation effects for the conductance was not observed.