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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…

This article reviews recent theoretical and experimental work on a new class of topological material - topological Kondo insulators, which develop through the interplay of strong correlations and spin-orbit interactions. The history of…

The discovery of the quantised Hall effect, and its subsequent topological explanation, demonstrated the important role topology can play in determining the properties of quantum systems. This realisation led to the development of…

Experimental realizations of topological quantum systems and detections of topological invariants in ultracold atomic systems have been a greatly attractive topic. In this work, we propose a scheme to realize topologically different phases…

Motivated by the growing interest in the novel quantum phases in materials with strong electron correlations and spin-orbit coupling, we study the interplay between the spin-orbit coupling, Kondo interaction, and magnetic frustration of a…

Thouless pumping provides one of the simplest manifestations of topology in quantum systems, and has attracted a lot of recent interest, both theoretically and experimentally. Since the seminal works by Thouless and Niu in 1983 and 1984, it…

Zero bias anomalies in topological nanowires have recently captured significant attention, as they are possible signatures of Majorana modes. Yet there are many other possible origins of zero bias peaks in nanowires, for example, weak…

Possible topological nature of Kondo and mixed valence insulators has been a recent topic of interest in condensed matter physics. Attention has focused on SmB6, which has long been known to exhibit low temperature transport anomaly, whose…

Despite of many efforts, we still lack a clear picture on how heavy electrons emerge and develop on the Kondo lattice. Here we introduce a key concept named the hybridization bond phase and propose a scenario based on phase correlation to…

Many-body interactions in topological quantum systems can give rise to new phases of matter, which simultaneously exhibit both rich spatial features and topological properties. In this work, we consider spinless fermions on a checkerboard…

Topological Kondo insulators are a rare example of an interaction-enabled topological phase of matter in three-dimensional crystals - making them an intriguing but also hard case for theoretical studies. Here, we aim to advance their…

The discovery of superconductivity and correlated electronic phases in twisted bilayer WSe$_2$ (Xia et al., Nature 2024; Guo et al., Nature 2025) has generated considerable excitement. Accompanying the superconductivity and a correlated…

The Kondo lattice is one of the classic examples of strongly correlated electronic systems. We conduct a controlled study of the Kondo lattice in one dimension, highlighting the role of excitations created by the composite fermion operator.…

Electric circuits are known to realize topological quadrupole insulators. We explore electric circuits made of capacitors and inductors forming the breathing Kagome and pyrochlore lattices. They are known to possess three phases (trivial…

Topological insulators are new phases of matter whose properties are derived from a number of qualitative yet robust topological invariants rather than specific geometric features or constitutive parameters. Here, Kagome lattices are…

We present universal characteristics of quantum entanglement and topology through virtual entanglement modes that fluctuate into existence in subsystem measurements. For generic interacting systems and extensive conserved quantities, these…

We study the stability of topological order against local perturbations by considering the effect of a magnetic field on a spin model -- the toric code -- which is in a topological phase. The model can be mapped onto a quantum loop gas…

Utilizing synthetic dimensions generated by spatial or temporal modulation, topological pumping enables the exploration of higher-dimensional topological phenomena through lower-dimensional physical systems. In this letter, we propose a…

Local quantum phase transitions driven by Kondo correlations have been theoretically proposed in several magnetic nanosystems; however, clear experimental signatures are scant. Modeling a nickelocene molecule on a Cu(100) substrate as a…

Curved spaces play a fundamental role in many areas of modern physics, from cosmological length scales to subatomic structures related to quantum information and quantum gravity. In tabletop experiments, negatively curved spaces can be…