Symmetry Spin Dynamics And The Properties Of Nanostructures Lecture Notes Of The 11th International School On Theoretical Physics

"This book is a collection of lecture notes which were presented by invited speakers at the Eleventh School on Theoretical Physics "Symmetry and Structural Properties of Condensed Matter SSPCM 2014" in Rzeszów (Poland) in September 2014. The main challenge for the lecturers was the objective to present their subject as a review as well as in the form of introduction for beginners. Topics considered in the volume concentrate on: spin dynamics and spin transport in magnetic and non-magnetic structures, spin-orbit interaction in two-dimensional systems and graphene, and new mathematical method used in the condensed matter physics."--

This volume presents lecture notes of the 12th International School of Theoretical Physics held in 2016 in Rzeszów, Poland. The lectures serve as an introduction for young physicists starting their career in condensed matter theoretical physics. The book provides a comprehensive overview of modern ideas and advances in theories and experiments of new materials, quantum nanostructures as well as new mathematical methods.This lecture note is an essential source of reference for physicists and materials scientists. It is also a suitable reading for graduate students.

Over last decades low-dimensional materials are in focus of physics and chemistry as well as of material and other natural sciences. Like Vitaly Ginzburg has foreseen 30 years ago, low dimensionality offers physical phenomena and properties unseen in three-dimensional world. To see how thin ?lms and monomolecular layers realize such a prediction it suf?ces only to observe intensity of research devoted to recently synthesized graphene. Still, quasi-one-dimensional compounds are over long period established as the origin of the most important and most interesting discoveries of material science and solid state physics. To mention only deoxyribonucleic acid, the most important molecule in nature, and diversity of nanotubes and nanowires, the cornerstones of the present and future nanotechnology. Line groups, describing symmetry of quasi-one-dimensional materials, offer the deepest insight to their characteristic properties. Underlying many of the laws, they are very useful, but far from simple. This book is intended to explain them, their properties, and their most common applications. In particular, it is important to understand that the line groups are much wider class of symmetries than the well-known rod groups. While the latter describe only translationally periodical objects, line groups include symmetries of incommensurate periodical structures.

Group theoretical concepts elucidate fundamental physical phenomena, including excitation spectra of quantum systems and complex geometrical structures such as molecules and crystals. These concepts are extensively covered in numerous textbooks. The aim of the present monograph is to illuminate more subtle aspects featuring group theory for quantum mechanics, that is, the concept of dynamical symmetry. Dynamical symmetry groups complement the conventional groups: their elements induce transitions between states belonging to different representations of the symmetry group of the Hamiltonian. Dynamical symmetry appears as a hidden symmetry in the hydrogen atom and quantum rotator problem, but its main role is manifested in nano and meso systems. Such systems include atomic clusters, large molecules, quantum dots attached to metallic electrodes, etc. They are expected to be the building blocks of future quantum electronic devices and information transmitting algorithms. Elucidation of the electronic properties of such systems is greatly facilitated by applying concepts of dynamical group theory.

The aim of this book is to present a formulation of the non-equilibrium physics in nanoscale systems in terms of many-body states and operators and, in addition, discuss a diagrammatic approach to Green functions expressed by many-body states. The intention is not to give an account of strongly correlated systems as such. Thus, the focus of this book ensues from the typical questions that arise when addressing nanoscale systems from a practical point of view, e.g. current-voltage asymmetries, negative differential conductance, spin-dependent tunneling. The focus is on nanoscale systems constituted of complexes of subsystems interacting with one another, under non-equilibrium conditions, in which the local properties of the subsystems are preferably being described in terms of its (many-body) eigenstates.

This book deals with the theoretical and computational simulation of monoperiodic nanostructures for different classes of inorganic substances. These simulations are related to their synthesis and experimental studies. A theoretical formalism is developed to describe 1D nanostructures with symmetric shapes and morphologies. Three types of models are considered for this aim: (i) nanotubes (rolled from 2D nanolayers and described within the formalism of line symmetry groups); (ii) nanoribbons (obtained from 2D nanolayers by their cutting along the chosen direction of translation); (iii) nanowires (obtained from 3D lattice by its sectioning along the crystalline planes parallel to the chosen direction of translation). Quantum chemistry ab-initio methods applied for LCAO calculations on electronic and vibrational properties of 1D nanostructures are thoroughly described. Understanding of theoretical aspects presented here enlarges the possibilities for synthesis of monoperiodic nanostructures with predictable morphology and better interpretation of their properties.

This book focuses on complex shaped micro- and nanostructures for future biomedical and sensing applications that were investigated by both theory and experiments. The first part of the book explores rotation-translation coupling of artificial microswimmers at low Reynolds numbers. Usually corkscrew shapes, i.e chiral shapes, are considered in such experiments, due to their inspiration from nature. However, the analysis of the relevant symmetries shows that achiral objects can also be propulsive, which is experimentally demonstrated for the first time. In the second part, a new single-particle spectroscopy technique was developed and the role of symmetry in such measurements is carefully examined. Spectra stemming from one individual nanoparticle that is moving freely in bulk solution, away from a surface, and only due to Brownian motion, are presented. On that basis, the rotationally averaged chiroptical spectrum of a single nanoparticle is measured - a novel observable that has not been accessible before.