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The discovery of topological phases has recently led to a paradigm shift in condensed matter physics, and facilitated breakthroughs in engineered photonics and acoustic metamaterials. Topological insulators (TIs) enable the generation of…
Three dimensional (3D) third-order topological insulators (TIs) have zero-dimensional (0D) corner states, which are three dimensions lower than bulk. Here we investigate the third-order TIs on breathing pyrochlore lattices with p-orbital…
Inspired by recent experimental observations of hybrid topological states [Hossain et al. Nature 628, 527 (2024)], we predict hybrid-order topological insulators in 1H transition metal compounds (TMCs), where both second-order and…
We propose a framework to realize helical edge states in phononic systems using two identical lattices with interlayer couplings between them. A methodology is presented to systematically transform a quantum mechanical lattice which…
It is shown that superfluids in two and three dimensions which have time reversal invariant ground states have phases which are distinguished by a topological invariant. Further, it is shown that the B-phase of $^3$ He is a superfluid in…
The bulk-boundary correspondence is a generic feature of topological states of matter, reflecting the intrinsic relation between topological bulk and boundary states. For example, robust edge states propagate along the edges and corner…
Topological photonics provides a novel platform to explore topological physics beyond traditional electronic materials and stimulates promising applications in topologically protected light transport and lasers. Classical degrees of freedom…
We propose a minimal interacting lattice model for two-dimensional class-$D$ higher-order topological superconductors with no free-fermion counterpart. A Lieb-Schultz-Mattis-type constraint is proposed and applied to guide our lattice model…
We present a class of time-reversal-symmetric fractional topological liquid states in two dimensions that support fractionalized excitations. These are incompressible liquids made of electrons, for which the charge Hall conductance vanishes…
The discovery of higher-order topological insulator (HOTI) has established a new paradigm for understanding symmetry-constrained boundary electronic states. Here, based on first-principles calculations, we demonstrate the emergence of HOTI…
Higher-order topological insulators are established as topological crystalline insulators protected by crystalline symmetries. One celebrated example is the second-order topological insulator in three dimensions that hosts chiral hinge…
As the novel topological states, the higher-order topological insulators have attracted great attentions in the past years. However, their realizations in realistic materials, in particular in two dimensional systems, remains the big…
Hyperbolic topological transitions refer to the transformation of is isofrequency contours in hyperbolic materials from one topology (e.g., hyperbolic) to another (e.g., elliptical or a different hyperbolic topology). However, current…
The possibility of topological phase transition with or without a magnetic flux trapped in the cells of a class of decorated lattices is explored in details.Using a tight binding Hamiltonian and a real space decimation scheme we…
Non-Euclidean geometry, discovered by negating Euclid's parallel postulate, has been of considerable interest in mathematics and related fields for the description of geographical coordinates, Internet infrastructures, and the general…
Second-order topological insulator, which has (d-2)-dimensional topological hinge or corner states, has been observed in three-dimensional materials, but has yet not been observed in two-dimensional system. In this Letter, we theoretically…
We show that topological phases with fractional excitations can occur in two-dimensional ultracold dipolar gases on a particular class of optical lattices. Due to the dipolar interaction and lattice confinement, a quantum dimer model…
Photonic topological states have revolutionized our understanding on the propagation and scattering of light. Recent discovery of higher-order photonic topological insulators opens an emergent horizon for zero-dimensional topological corner…
We describe the possibility for topologically robust edge states existing on interfaces of triangular lattices which are supported by rotational symmetries that are sensitive to boundary conditions. Such states are trivial from the…
We study $s$-wave superconductivity in hyperbolic spaces using the Bogoliubov-de Gennes theory for discrete hyperbolic lattices and the Ginzburg-Landau theory for the continuous hyperbolic plane. Hyperbolic lattices maintain a finite…