This book presents the most important advances in the class of topological materials and
discusses the topological characterization modeling and metrology of materials. Further it
addresses currently emerging characterization techniques such as optical and acoustic
vibrational spectroscopy (Brillouin infrared Raman) electronic magnetic fluorescence
correlation imaging laser lithography small angle X-ray and neutron scattering and other
techniques including site-selective nanoprobes. The book analyzes the topological aspects to
identify and quantify these effects in terms of topology metrics. The topological materials are
ubiquitous and range from (i) de novo nanoscale allotropes of carbons in various forms such as
nanotubes nanorings nanohorns nanowalls peapods graphene etc. to (ii) metallo-organic
frameworks (iii) helical gold nanotubes (iv) Möbius conjugated polymers (v) block
co-polymers (vi) supramolecular assemblies to (vii) a variety of biological and soft-matter
systems e.g. foams and cellular materials vesicles of different shapes and genera biomimetic
membranes and filaments (viii) topological insulators and topological superconductors (ix) a
variety of Dirac materials including Dirac and Weyl semimetals as well as (x) knots and
network structures. Topological databases and algorithms to model such materials have been also
established in this book. In order to understand and properly characterize these important
emergent materials it is necessary to go far beyond the traditional paradigm of microscopic
structure-property-function relationships to a paradigm that explicitly incorporates
topological aspects from the outset to characterize and or predict the physical properties and
currently untapped functionalities of these advanced materials. Simulation and modeling tools
including quantum chemistry molecular dynamics 3D visualization and tomography are also
indispensable. These concepts have found applications in condensed matter physics materials
science and engineering physical chemistry and biophysics and the various topics covered in
the book have potential applications in connection with novel synthesis techniques sensing and
catalysis. As such the book offers a unique resource for graduate students and researchers
alike.
