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Topological insulators and superconductors at finite temperature can be characterized by the topological Uhlmann phase. However, a direct experimental measurement of this invariant has remained elusive in condensed matter systems. Here, we…

We present a unified framework to systematically embed complex knotted and linked structures, beyond the torus family, into diverse topological phases, including Hopf insulators, classical spin liquids, topological semimetals, and…

Amorphous solids remain outside of the classification and systematic discovery of new topological materials, partially due to the lack of realistic models that are analytically tractable. Here we introduce the topological Weaire-Thorpe…

Living systems exhibit complex yet organized behavior on multiple spatiotemporal scales. To investigate the nature of multiscale coordination in living systems, one needs a meaningful and systematic way to quantify the complex dynamics, a…

The realization and detection of topological phases with ultracold atomic gases is at the frontier of current theoretical and experimental research. Here, we identify cold atoms in optical ladders subjected to synthetic magnetic fields as…

The study of phase transitions using data-driven approaches is challenging, especially when little prior knowledge of the system is available. Topological data analysis is an emerging framework for characterizing the shape of data and has…

The control of thermal radiation by shaping its spatial and spectral emission characteristics plays a key role in many areas of science and engineering. Conventional approaches to tailor thermal emission using metamaterials are severely…

We use the first Betti number of a complex to characterize the morphological structure of granular samples in mechanical equilibrium. We analyze two-dimensional granular packings after a tapping process by means of both simulations and…

Topology manifesting in many branches of physics deepens our understanding on state of matters. Topological photonics has recently become a rapidly growing field since artificial photonic structures can be well designed and constructed to…

Topological insulating phases are usually found in periodic lattices stemming from collective resonant effects, and it may thus be expected that similar features may be prohibited in thermal diffusion, given its purely dissipative and…

Constructing systems that exhibit time-scales much longer than those of the underlying components, as well as emergent dynamical and collective behavior, is a key goal in fields such as synthetic biology and materials self-assembly.…

Symmetries play a crucial role in the classification of topological phases of matter. Although recent studies have established a powerful framework to search for and classify topological phases based on symmetry indicators, there exists a…

Topological insulators are a new class of materials that have engendered considerable research interest among the condensed matter community owing primarily to their application prospects in quantum computations and spintronics. Many of the…

Topological insulators represent a new quantum state of matter which is characterized by peculiar edge or surface states that show up due to a topological character of the bulk wave functions. This review presents a pedagogical account on…

Concepts such as energy dependence, random deployment, dynamic topological update, self-organization, varying large number of nodes are among many factors that make WSNs a type of complex system. However, when analyzing WSNs properties…

Comparing mathematical models offers a means to evaluate competing scientific theories. However, exact methods of model calibration are not applicable to many probabilistic models which simulate high-dimensional spatio-temporal data.…

Two-dimensional topological insulators possess conducting edge states at their boundary while being insulating in the bulk. The detection of edge states remains an open question in ultracold atom setups. We propose a configuration to…

Topological phases have attracted much interest in recent years. While there are a number of three-dimensional materials exhibiting topological properties, there are relatively few two-dimensional examples aside from the well-known quantum…

Topological photonic systems offer light transport that is robust against defects and disorder, promising a new generation of chip-scale photonic devices and facilitating energy-efficient on-chip information routing and processing. However,…

We present a general analysis of two-dimensional optical lattice models that give rise to topologically non-trivial insulating states. We identify the main ingredients of the lattice models that are responsible for the non-trivial…