Related papers: Hierarchical Topological States without Dimension …
Fathoming interplay between symmetry and topology of many-electron wave-functions has deepened understanding of quantum many body systems, especially after the discovery of topological insulators. Topology of electron wave-functions…
Bound states in the continuum (BICs), with the ability of trapping and manipulating waves within the radiation continuum, have gained significant attention for their potential applications in optics and acoustics. However, challenges arise…
Macroscopic two-dimensional sonic crystals with inversion symmetry are studied to reveal higher-order topological physics in classical wave systems. By tuning a single geometry parameter, the band topology of the bulk and the edges can be…
The canonical Su-Schrieffer-Heeger (SSH) model is one of the basic geometries that have spurred significant interest in topologically nontrivial bandgap modes with robust properties. Here, we show that the inclusion of suitable third-order…
The study of topological band insulators has revealed fascinating phases characterized by band topology indices and anomalous boundary modes protected by global symmetries. In strongly correlated systems, where the traditional notion of…
Strongly correlated analogues of topological insulators have been explored in systems with purely on-site symmetries, such as time-reversal or charge conservation. Here, we use recently developed tensor network tools to study a quantum…
Exploration of topology protected by a certain symmetry is central in condensed matter physics. A recent idea of sub-symmetry-protected (SSP) topology--remains of a broken symmetry can still protect specific topological boundary states--has…
Topological insulators are well-known for their topological edge states, which are protected by the non-trivial bulk topology and characterized by gapless Wannier bands, a phenomenon known as the bulk-boundary correspondence. However,…
The surface of a 3+1d topological insulator hosts an odd number of gapless Dirac fermions when charge conjugation and time-reversal symmetries are preserved. Viewed as a purely 2+1d system, this surface theory would necessarily explicitly…
By breaking the time-reversal-symmetry in three-dimensional topological insulators with introduction of spontaneous magnetization or application of magnetic field, the surface states become gapped, leading to quantum anomalous Hall effect…
One of the most striking features of quantum mechanics is the appearance of phases of matter with topological origins. These phases result in remarkably robust macroscopic phenomena such as the edge modes in integer quantum Hall systems,…
Topological insulators are noninteracting, gapped fermionic systems which have gapless boundary excitations. They are characterized by topological invariants, which can be written in many different ways, including in terms of Green's…
Topology in quantum systems is typically considered in infinite crystals in one, two, or higher integer dimensions. Here, we show that one can continuously transform a system between a topological phase associated with one dimension and a…
The discovery of two-dimensional topological photonic systems has transformed our views on electromagnetic propagation and scattering of classical waves, and a quest for similar states in three dimensions, known to exist in condensed matter…
We numerically verify and analytically prove a winding number invariant that correctly predicts the number of edge states in one-dimensional, nearest-neighbor (between unit cells), two-band models with any complex couplings and open…
The topological insulator is an electronic phase stabilized by spin-orbit coupling that supports propagating edge states and is not adiabatically connected to the ordinary insulator. In several ways it is a spin-orbit-induced analogue in…
The properties of topological systems are inherently tied to their dimensionality. Higher-dimensional physical systems exhibit topological properties not shared by their lower dimensional counterparts and, in general, offer richer physics.…
In this work, we present a collection of three-dimensional higher-order symmetry protected topological phases (HOSPTs) with gapless hinge modes that exist only in strongly interacting systems subject to subsystem symmetry constraints. We…
According to the mathematical classification of topological band structures, there exist a number of fascinating topological states in dimensions larger than three with exotic boundary phenomena and interesting topological responses. While…
Bound states in the continuum, originally proposed within the framework of quantum mechanics, have since been observed in a variety of physical contexts, including electromagnetism, acoustics, and optics. Of particular interest are those…