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Soft interfaces can mediate interactions between particles bound to them. The force transmitted through the surface geometry on a particle may be expressed as a closed line integral of the surface stress tensor around that particle. This…
The interplay between ferroelectricity and band topology can give rise to a wide range of both fundamental and applied research. Here, we map out the emergence of nontrivial corner states in two-dimensional ferroelectrics, and remarkably…
This article is meant as a gentle introduction to the "topological terms" that often play a decisive role in effective theories describing topological quantum effects in condensed matter systems. We first take up several prominent examples,…
We discuss physical properties of `integer' topological phases of bosons in D=3+1 dimensions, protected by internal symmetries like time reversal and/or charge conservation. These phases invoke interactions in a fundamental way but do not…
Topological superconductors have become a subject of intense research due to their potential use for technical applications in device fabrication and quantum information. Besides fully gapped superconductors, unconventional superconductors…
Angle resolved photoemission spectroscopy is used to observe changes in the electronic structure of bulk-doped topological insulator Cu$_x$Bi$_2$Se$_3$ as additional copper atoms are deposited onto the cleaved crystal surface. Carrier…
Two-dimensional higher-order topological insulators can display a number of exotic phenomena such as half-integer charges localized at corners or disclination defects. In this paper, we analyze these phenomena, focusing on the paradigmatic…
Topological insulator is a new state of matter which exhibits exotic surface electronic properties. Determining the spin texture of this class of material is of paramount importance for understanding its topological order and can lead to…
Topological insulators [1-6] is a new quantum phase of matter with exotic properties such as dissipationless transport and protection against Anderson localization [7]. These new states of quantum matter could be one of the missing links…
We survey some results on real rational surfaces focused on their topology and their birational geometry.
Ultracold atom research presents many avenues to study problems at the forefront of physics. Due to their unprecedented controllability, these systems are ideally suited to explore new exotic states of matter, which is one of the key…
Experimental methods allow the shape and chemical composition of solid surfaces to be controlled at a mesoscopic level. Exposing such structured substrates to a gas close to coexistence with its liquid can produce quite distinct adsorption…
Topological insulators (TIs) with robust boundary states against perturbations and disorders provide a unique approach for manipulating waves, whereas curved space can effectively control the wave propagation on curved surfaces by the…
The effect of surface disorder on electronic systems is particularly interesting for topological phases with surface and edge states. Using exact diagonalization, it has been demonstrated that the surface states of a 3D topological…
We develop a coarse notion of bundle and use it to understand the coarse geometry of group extensions and, more generally, groups acting on proper metric spaces. The results are particularly sharp for groups acting on (locally finite) trees…
Topological principles constitute at present an integral component of condensed matter physics, permeating the modern characterization of electronic states while also guiding materials design. In this brief Perspective, I highlight three…
Application of the noncommutative geometry to several physical models is considered.
Theintertwining of electron-hole correlation and nontrivial topology is known to give rise to exotic topological excitonic insulators. Here, we show that the involvement of quantum geometry can characterize more exotic excitonic phases…
A discretisation scheme that preserves topological features of a physical problem is extended so that differential geometric structures can be approximated in a consistent way thus giving access to the study of physical systems which are…
This research highlight (originally published at http://www.ntu.edu.sg/ias/newsletters/Documents/APPN/APPNv5n2May2016-lowres.pdf) introduces recent developments in Topological Insulators and Holography, and provides an overview of how one…