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Topology is key in describing unconventional quantum phases of matter and devising robust quantum technology. Exactly how topology mixes with quantum mechanics remains largely unclear, as testified by the lack of a unifying microscopic…
Magnetic topological materials represent a class of compounds whose properties are strongly influenced by the topology of the electronic wavefunctions coupled with the magnetic spin configuration. Such materials can support chiral…
The long fascination antiferromagnetic materials have exerted on the scientific community over about a century has been entirely renewed recently with the discovery of several unexpected phenomena including various classes of anomalous spin…
The discovery of the quantum spin Hall effect and topological insulators more than a decade ago has revolutionized modern condensed matter physics. Today, the field of topological states of matter is one of the most active and fruitful…
Motivated by recent experiments on the observation of room temperature skyrmions in a layered heterostructure and subsequent demonstration of topological Hall effect in the same system, we have studied a minimal model of itinerant electrons…
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 mutual interplay between electron transport and magnetism has attracted considerable attention in recent years, primarily motivated by strategies to manipulate magnetic degrees of freedom electrically, such as spin-orbit torques and…
Topology establishes a unifying framework for a diverse range of scientific areas including particle physics, cosmology, and condensed matter physics. One of the most fascinating manifestations of topology in the context of condensed matter…
The discovery of the quantum Hall effect founded the field of topological condensed matter physics. Its amazingly accurate quantisation of the Hall conductance, now enshrined in quantum metrology, is topologically protected: it is stable…
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,…
Here, we reveal our recent progress on a geometrical approach of quantum physics and topological crystals linking with Dirac magnetic monopoles and gauge fields through classical electrodynamics. The Bloch sphere of a quantum spin-1/2…
The topology of an object describes global properties that are insensitive to local perturbations. Classic examples include string knots and the genus (number of handles) of a surface: no manipulation of a closed string short of cutting it…
Topological magnetoelectric effect in a three-dimensional topological insulator is a novel phenomenon, where an electric field induces a magnetic field in the same direction, with a universal coefficient of proportionality quantized in…
The topological states of matter and topological materials have been attracting extensive interests as one of the frontier topics in condensed matter physics and materials science since the discovery of quantum Hall effect in 1980s. So far…
The introduction of topological invariants, ranging from insulators to metals, has provided new insights into the traditional classification of electronic states in condensed matter physics. A sudden change in the topological invariant at…
Magnetic skyrmions offer promising prospects for constructing future energy-efficient and high-density information technology, leading to extensive explorations of new skyrmionic materials recently. The topological Hall effect has been…
Electric field control of magnetism in solids, i.e. the converse magnetoelectricity, is highly desired for applications of scalable energy-efficient logic devices. However, it is not only a technical challenge but also a scientific paradox,…
Topological transport phenomena in magnetic materials are a major topic of current condensed matter research. One of the most widely studied phenomena is the ``topological Hall effect'' (THE), which is generated via spin-orbit interactions…
The methods of quantum field theory are widely used in condensed matter physics. In particular, the concept of an effective action was proven useful when studying low temperature and long distance behavior of condensed matter systems. Often…
Realizing effective manipulation and explicit identification of topological spin textures are two crucial ingredients to make them as information carrier in spintronic devices with high storage density, high data handling speed and low…