相关论文: Topological phases of amorphous matter

The discovery of topological phases in condensed matter systems has changed the modern conception of phases of matter. The global nature of topological ordering makes these phases robust and hence promising for applications. However, the…

We construct in the K matrix formalism concrete examples of symmetry enriched topological phases, namely intrinsically topological phases with global symmetries. We focus on the Abelian and non-chiral topological phases and demonstrate by…

Symmetry-breaking phase transitions are ubiquitous in condensed matter systems and in quantum field theories. There is also good reason to believe that they feature in the very early history of the Universe. At many such transitions…

It is shown theoretically that a one-dimensional crystal with time reversal symmetry is characterized by a Z_{2} topological invariant that predicts the existence or otherwise of edge states. This is confirmed experimentally through the…

The study of continuous phase transitions triggered by spontaneous symmetry breaking has brought new concepts that revolutionized the way we understand many-body systems. Recently, through the discovery of symmetry protected topological…

Topological states of matter in disordered systems without translation symmetry have attracted great interest in recent years. These states with topological characters are not only robust against certain disorders, but also can be…

There are two prominent applications of the mathematical concept of topology to the physics of materials: band topology, which classifies different topological insulators and semimetals, and topological defects that represent immutable…

We examine the interplay of symmetry and topological order in $2+1$ dimensional topological phases of matter. We present a definition of the \it topological symmetry \rm group, which characterizes the symmetry of the emergent topological…

The succession of suggested mechanisms of solid-state phase transitions - Second-order, Lambda, Martensitic, Displacive, Topological, Order-Disorder, Soft-mode, Incommensurate, Scaling and Quantum - are analyzed and explained why they…

We consider the possibility for phases of matter in which a continuous symmetry is spontaneously broken in a \emph{topologically non-trivial} way, which, roughly, means that the action for the Goldstone modes contains a quantized…

For the classification of topological phases of matter, an important consideration is whether a system is spinless or spinful, as these two classes have distinct symmetry algebra that gives rise to fundamentally different topological…

The first-principles band theory paradigm has been a key player not only in the process of discovering new classes of topologically interesting materials, but also for identifying salient characteristics of topological states, enabling…

Topological phases of matter give rise to exotic physics that can be leveraged for next generation quantum computation and spintronic devices. Thus, the search for topological phases and the quantum states that they exhibit have become the…

The question of the local stability of the (replica-symmetric) amorphous solid state is addressed for a class of systems undergoing a continuous liquid to amorphous-solid phase transition driven by the effect of random constraints. The…

Topological phases are generally characterized by topological invariants denoted by integer numbers. However, different topological systems often require different topological invariants to measure, such as geometric phases, topological…

We construct algorithms and topological invariants that allow us to distinguish the topological type of a surface, as well as functions and vector fields for their topological equivalence. In the first part we discus the main structures…

Topology, a well-established concept in mathematics, has nowadays become essential to describe condensed matter. At its core are chiral electron states on the bulk, surfaces and edges of the condensed matter systems, in which spin and…

The concept of topological phases has been generalized to higher-order topological insulators and superconductors with novel boundary states on corners or hinges. Meanwhile, recent experimental advances in controlling dissipation (such as…

Time crystals are unexpected states of matter that spontaneously break time translation symmetry either in a discrete or continuous manner. However, spatially-mesoscale space-time crystals that break both the space and time symmetries have…

Disorder inevitably exists in realistic samples, manifesting itself in various exotic properties for the topological states. In this paper, we summarize and briefly review work completed over the last few years, including our own, regarding…