Topological vectors as a fingerprinting system for 2D-material flake distributions

Topological feature vectors for exploring topological relationships

Topological relationships between spatial objects such as overlap, disjoint, and inside have for a long time been a focus of research in a number of disciplines like cognitive science, robotics, linguistics, artificial intelligence, and spatial reasoning. In particular as predicates, they support the design of suitable query languages for spatial data retrieval and analysis in spatial database ...

Measurement of topological invariants in a 2D photonic system

A hallmark feature of topological physics is the presence of one-way propagating chiral modes at the system boundary1,2. The chirality of edge modes is a consequence of the topological character of the bulk. For example, in a non-interacting quantum Hall model, edge modes manifest as mid-gap states between two topologically distinct bulk bands. The bulk– boundary correspondence dictates that th...

Admissible Vectors of a Covariant Representation of a Dynamical System

In this paper, we introduce admissible vectors of covariant representations of a dynamical system which are extensions of the usual ones, and compare them with each other. Also, we give some sufficient conditions for a vector to be admissible vector of a covariant pair of a dynamical system.  In addition, we show the existence of Parseval frames for some special subspaces of $L^2(G)$ related to...

A Framework for System Fingerprinting

Metal-Graphene hybrids as a model system for 2D Superconductivity

Graphene provides a ideal 2D gas of Dirac Fermions which is directly exposed to the environment. Therefore it provides an ideal platform on which to tune, via application of an electrostatic gate, the coupling between electronically ordered adsorbates deposited on its surface. This situation is particularly interesting when the network of adsorbates can induce some electronic order within the u...