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The terms of topological and quantum stabilities of low-dimensional crystalline carbon lattices with multiple non-equivalent sublattices are coined using theoretical analysis, multilevel simulations, and available experimental structural…
Topological flat bands have gained extensive interest as a platform for exploring the interplay between nontrivial band topology and correlation effects. In recent studies, strongly correlated phenomena originating from a topological flat…
Flat bands, in which kinetic energy is quenched and quantum states become macroscopically degenerate, host a rich variety of correlated and topological phases, from unconventional superconductors to fractional Chern insulators. In Hermitian…
Topological media are systems whose properties are protected by topology and thus are robust to deformations of the system. In topological insulators and superconductors the bulk-surface and bulk-vortex correspondence gives rise to the…
A typical f-electron Kondo lattice system Ce exhibits the well-known isostructural transition, the so-called gamma-alpha transition, accompanied by an enormous volume collapse. Most interestingly, we have discovered that a topological-phase…
Topological states of quantum matter exhibit unique disorder-immune surface states protected by underlying nontrivial topological invariants of the bulk. Such immunity from backscattering makes topological surface or edge states ideal…
Carbon, a basic versatile element in our universe, exhibits rich varieties of allotropic phases, most of which possess promising nontrivial topological fermions. In this work, we identify a distinct topological phonon phase in a realistic…
Exploring the synergy between topological physics and nonlinear dynamics unveils profound insights into emergent states of matter. Inspired by recent experimental demonstrations of topological frequency combs in photonics, we theoretically…
Inspired by concepts developed for fermionic systems in the framework of condensed matter physics, topology and topological states are recently being explored also in bosonic systems. The possibility of engineering systems with…
We discuss elastic instabilities of the atomic crystal lattice at zero temperature. Due to long-range shear forces of the solid, at such transitions the phonon velocities vanish, if at all, only along certain crystallographic directions,…
Topological phonons in crystalline materials have been attracting great interest. However, most cases studied so far are direct generalizations of the topological states from electronic systems. Here, we reveal a novel class of topological…
For Y$_2$C$_3$ with a superconducting critical temperature (T$_c$) $\sim$18 K, zone-center imaginary optical phonon modes have been found for the high-symmetry $I$-$43d$ structure due to C dimer wobbling motion and electronic instability…
The superposition of topological phonons and flexoelectronic charge separation in an inhomogeneously strain Si give rise to topological electronic magnetism of phonons. The topological electronic magnetism of phonons is also expected to…
The band theory of solids is arguably the most successful theory of condensed matter physics, providing the description of the electronic energy levels in a variety of materials. Electronic wavefunctions obtained from the band theory allow…
A common feature of topological insulators is that they are characterized by topologically invariant quantity such as the Chern number and the $\mathbb{Z}_2$ index. This quantity distinguishes a nontrivial topological system from a trivial…
The concept of topological energy bands and their manifestations have been demonstrated in condensed matter systems as a fantastic paradigm toward unprecedented physical phenomena and properties that are robust against disorders. Recent…
We investigate the phase diagram of a one-dimensional model of hardcore bosons or spinless fermions with tunable nearest-neighbor interactions. By introducing alternating repulsive and attractive interactions on consecutive bonds, we show…
Quasi-one-dimensional bismuth halides offer an exceptional platform for exploring diverse topological phases, yet the nature of the room-temperature topological phase transition in Bi$_4$I$_4$ remains unresolved. While theory predicts the…
Topological defects, such as domain walls and vortices, have long fascinated physicists. A novel twist is added in quantum systems like the B-phase of superfluid helium He$_3$, where vortices are associated with low energy excitations in…
Solitonic symmetry has been believed to follow the homotopy-group classification of topological solitons. Here, we point out a more sophisticated algebraic structure when solitons of different dimensions coexist in the spectrum. We uncover…