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This paper explores the geometry of the space of codimension-2 submanifolds. We implicitly represent these submanifolds by a class of complex-valued functions. We show that the space of all these implicit representations admits a prequantum…

Symplectic Geometry · Mathematics 2026-04-20 Albert Chern , Sadashige Ishida

We use the maximally-localized Wannier function method to study bonding properties in amorphous silicon. This study represents, to our knowledge, the first application of the Wannier-function analysis to a disordered system. Our results…

Materials Science · Physics 2009-10-31 Pier Luigi Silvestrelli , Nicola Marzari , David Vanderbilt , Michele Parrinello

It is shown that Paley-Wiener functions on Riemannian manifolds of bounded geometry can be reconstructed in a stable way from some countable sets of their inner products with certain distributions of compact support. A reconstruction method…

Functional Analysis · Mathematics 2011-04-12 Isaac Pesenson

The intense theoretical and experimental interest in topological insulators and semimetals has established band structure topology as a fundamental material property. Consequently, identifying band topologies has become an important, but…

Electronic flat bands have localized Wannier-like orbitals as zero modes. In the Lieb or the kagome models, the localized orbitals satisfy a topological condition that entails two non-contractible loop eigenstates along $x/y$-axis in real…

Mesoscale and Nanoscale Physics · Physics 2026-03-27 Rui-Heng Liu , Jiangping Hu , Chen Fang

In recent years, manifold methods have moved into focus as tools for dimension reduction. Assuming that the high-dimensional data actually lie on or close to a low-dimensional nonlinear manifold, these methods have shown convincing results…

Machine Learning · Statistics 2020-12-23 Moritz Herrmann , Fabian Scheipl

Motivated by new capabilities to realise artificial gauge fields in ultracold atomic systems, and by their potential to access correlated topological phases in lattice systems, we present a new strategy for designing topologically…

Quantum Gases · Physics 2012-11-22 N. R. Cooper , R. Moessner

Topological neural networks (TNNs) are information processing architectures that model representations from data lying over topological spaces (e.g., simplicial or cell complexes) and allow for decentralized implementation through localized…

Information Theory · Computer Science 2025-02-17 Simone Fiorellino , Claudio Battiloro , Paolo Di Lorenzo

Photonic structures with Weyl points (WPs), including type-I and type-II, promise nontrivial surface modes and intriguing light manipulations for their three-dimensional topological bands. While previous studies mainly focus on exploring…

We provide a mathematically proven, simple and efficient algorithm to build localised Wannier functions, with the only requirement that the system has vanishing Chern numbers. Our algorithm is able to build localised Wannier for topological…

Mathematical Physics · Physics 2019-03-27 David Gontier , Antoine Levitt , Sami Siraj-Dine

Recent discoveries have spurred the theoretical prediction and experimental realization of novel materials that have topological properties arising from band inversion. Such topological insulators are insulating in the bulk but have…

Mesoscale and Nanoscale Physics · Physics 2017-07-26 M. Kotulla , U. Zülicke

Complex network topology might get pretty complicated challenging many network analysis objectives, such as community detection for example. This however makes common emergent network phenomena such as scale-free topology or small-world…

Social and Information Networks · Computer Science 2018-06-12 Stanislav Sobolevsky

The maximally localized Wannier functions play a very important role in the study of chemical bonding, ballistic transport and strongly-correlated system, etc. A significant development in this branch was made in 1997 and conjectured that…

Materials Science · Physics 2014-07-28 Sangryol Ri , Suil Ri

Topological materials are often characterized by unique edge states which are in turn used to detect different topological phases in experiments. Recently, with the discovery of various higher-order topological insulators, such spectral…

Mesoscale and Nanoscale Physics · Physics 2022-07-13 Ze-Lin Kong , Zhi-Kang Lin , Jian-Hua Jiang

The band-unfolding method is widely used to calculate the effective band structures of a disordered system from its supercell model. The unfolded band structures show the crystallographic symmetry of the underlying structure, where the…

Materials Science · Physics 2017-01-18 Yuji Ikeda , Abel Carreras , Atsuto Seko , Atsushi Togo , Isao Tanaka

A model for two-dimensional electronic, photonic, and mechanical metamaterial systems is presented, which has flat one-dimensional zero-mode energy bands and stable localized states of a topological origin confined within twin boundaries,…

Mesoscale and Nanoscale Physics · Physics 2019-02-06 Linghua Zhu , Emil Prodan , Keun Hyuk Ahn

In this work, we construct a Wannier tight-binding model for TaS$_2$ under a superlattice potential modulation, based on the Joint Automated Repository for Various Integrated Simulations database established by the U.S. National Institute…

Materials Science · Physics 2024-12-17 Thi-Nga Do , Godfrey Gumbs

In this paper we analyze the notion of morphisms of rings of superfunctions which is the basic concept underlying the definition of supermanifolds as ringed spaces (i.e. following Berezin, Leites, Manin, etc.). We establish a representation…

Mathematical Physics · Physics 2016-08-16 Frédéric Hélein

We elaborate that for topological insulators and topological superconductors described by Dirac models in any dimension and symmetry class, the topological order can be mapped to lattice sites by a universal topological marker. Deriving…

Mesoscale and Nanoscale Physics · Physics 2023-01-25 Wei Chen

Maximally localized Wannier functions use the gauge freedom of Bloch wavefunctions to define the optimally smooth subspace with matrix elements that depend smoothly on crystal momentum. The associated Wannier functions are real-space…

Materials Science · Physics 2024-10-24 Giulio Volpato , Stefano Mocatti , Giovanni Marini , Matteo Calandra