Related papers: A One-Particle Density Matrix Framework for Mode-S…
We rigorously yet concisely prove the bulk-edge correspondence for general $d$-dimensional ($d$D) topological insulators in complex Altland-Zirnbauer classes, which states that the bulk topological number equals to the edge-mode index.…
We develop a chiral anomalous fermion hamiltonian proposal to study the higher order topological (HOT) phase with chiral symmetry $\mathcal{C}$ fractionalized like $\mathcal{C}_{x}\mathcal{C}_{y}\mathcal{C}_{z}$. First, we solve the…
Topology plays an increasing role in physics beyond the realm of topological insulators in condensed mater. From geophysical fluids to active matter, acoustics or photonics, a growing family of systems presents topologically protected…
In the research of the topological band phases, the conventional wisdom is to start from the crystalline translational symmetry systems. Nevertheless, the translational symmetry is not always a necessary condition for the energy bands. Here…
This paper proposes a quantitative description of the low energy edge states at the interface between two-dimensional topological insulators. They are modeled by continuous Hamiltonians as systems of Dirac equations that are amenable to a…
Topological magnon insulators exhibit robust edge modes with chiral properties similar to quantum Hall edge states. However, due to their strong localization at the edges, interactions between these chiral edge magnons can be significant,…
We construct a topological invariant that classifies density matrices of symmetry-protected topological orders in two-dimensional fermionic systems. As it is constructed out of the previously introduced Uhlmann phase, we refer to it as the…
The realization of interacting topological states of matter such as fractional Chern insulators (FCIs) in cold atom systems has recently come within experimental reach due to the engineering of optical lattices with synthetic gauge fields…
Higher-order topological insulators (HOTI) are a novel topological phase beyond the framework of the conventional bulk-boundary correspondence. In these peculiar systems, the topologically nontrivial boundary modes are characterized by a…
Higher-order topological phases (HOTPs) host exotic topological states that go beyond the traditional bulk-boundary correspondence. Up to now, there is still a lack of experimentally measurable momentum-space topological characterization…
In the present work, we consider multi-scale computation and convergence for nonlinear time-dependent thermo-mechanical equations of inhomogeneous shells possessing temperature-dependent material properties and orthogonal periodic…
This paper reviews recent results on the classification of partial differential operators modeling bulk and interface topological insulators in Euclidean spaces. Our main objective is the mathematical analysis of the unusual,…
Mechanical systems can display topological characteristics similar to that of topological insulators. Here we report a large class of topological mechanical systems related to the BDI symmetry class. These are self-assembled chains of rigid…
In this work, we supply an engineering solution that paves the way to the implementation of the full classification table of topological insulators with passive acoustic crystals. As an example, we design an acoustic crystal displaying the…
We extend the theory of dipole moments in crystalline insulators to higher multipole moments. In this paper, we expand in great detail the theory presented in Ref. 1, and extend it to cover associated topological pumping phenomena, and a…
Bulk boundary correspondence in topological materials allows to study their bulk topology through the investigation of their topological boundary modes. However, for classes that share similar boundary phenomenology, the growing diversity…
We discuss the proximate phases of a three-dimensional system with Dirac-like dispersion. Using the cubic lattice with plaquette $\pi$-flux as a model, we find, among others phases, a chiral topological insulator and singlet topological…
The standard boundary state of a topological insulator in 3+1 dimensions has gapless charged fermions. We present model systems that reproduce this standard gapless boundary state in one phase, but also have gapped phases with topological…
We show that higher-order topological insulators can be created from usual square structure by twisting waveguides in each unit cell around the axis passing through the center of the unit cell, even without changing intracell distance…
While tremendous research has revealed that symmetry enriches topological phases of matter, more general principles that protect topological phases have yet to be explored. In this Letter, we elucidate the roles of subspaces in…