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Symmetry-protected topological phases of matter have challenged our understanding of condensed matter systems and harbour exotic phenomena promising to address major technological challenges. Considerable understanding of these phases of…

The interplay between band topology and magnetic order plays a key role in quantum states of matter. MnBi2Te4, a van der Waals magnet, has recently emerged as an exciting platform for exploring Chern insulator physics. Its layered…

Modern theory of electric polarization is formulated by the Berry phase, which, when quantized, leads to topological phases of matter. Such a formulation has recently been extended to higher electric multipole moments, through the discovery…

Topology is a fundamental aspect of quantum physics, and it has led to key breakthroughs and results in various fields of quantum materials. In condensed matters, this has culminated in the recent discovery of symmetry-protected topological…

Topological insulators are states of matter distinguished by the presence of symmetry protected metallic boundary states. These edge modes have been characterised in terms of transport and spectroscopic measurements, but a thermodynamic…

We present exactly solvable examples that topological Mott insulators can emerge from topologically trivial states due to strong interactions between atoms for atomic mixtures trapped in one-dimensional optical superlattice systems. The…

In the framework of the tight binding approximation, we study a non-interacting model on the three-component dice lattice with real nearest-neighbor and complex next-nearest-neighbor hopping subjected to $\Lambda$- or V-type sublattice…

The detection of phase transitions is a fundamental challenge in condensed matter physics, traditionally addressed through analytical methods and direct numerical simulations. In recent years, machine learning techniques have emerged as…

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…

We investigate the effect of a high frequency electromagnetic field with both of circularly and linearly polarization, on the emergence of quantum phases on thin topological insulators. Simultaneously, the influence of the system parameters…

The use of topological invariants to describe geometric phases of quantum matter has become an essential tool in modern solid state physics. The first instance of this paradigmatic trend can be traced to the study of the quantum Hall…

Classification and identification of different phases and the transitions between them is a central task in condensed matter physics. Machine learning, which has achieved dramatic success in a wide range of applications, holds the promise…

The modern theory of electric polarization in crystals associates the dipole moment of an insulator with a Berry phase of its electronic ground state [1, 2]. This concept constituted a breakthrough that not only solved the long-standing…

Robustness against disorder and defects is a pivotal advantage of topological systems, manifested by absence of electronic backscattering in the quantum Hall and spin-Hall effects, and unidirectional waveguiding in their classical analogs.…

Presence of entangled states is explicitly shown in Topological insulator (TI) $Bi_2Te_3$. The surface and bulk state are found to have the different structures of entanglement. The surface states live as maximally entangled states in the…

Topological materials are often characterized by unique edge states which are in turn used to detect different topological phases in experiments. Recently, with the discovery of various higher-order topological insulators, such spectral…

Topological phases of electrons such as topological insulators and quantum Hall states typically require strong spin-orbit coupling or magnetic fields. In this study, we consider an electron system coupled to a spin system, where electrons…

One of the most intriguing advantage of Floquet engineering is to generate new phases with large topological invariants. In this work, we experimentally simulate a periodically quenched generalized Haldane model on an NV center in diamond,…

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…

Quantized electric quadrupole insulators have recently been proposed as novel quantum states of matter in two spatial dimensions. Gapped otherwise, they can feature zero-dimensional topological corner mid-gap states protected by the bulk…