Related papers: The bulk-edge correspondence for continuous honeyc…
Electron hopping models on the honeycomb lattice are studied. The lattice consists of two triangular sublattices, and it is non-Bravais. The dual space has non-trivial topology. The gauge fields of Bloch electrons have the U(1) symmetry and…
We analytically study boundary conditions of the Dirac fermion models on a lattice, which describe the first and second order topological insulators. We obtain the dispersion relations of the edge and hinge states by solving these boundary…
Topological edge solitons that bifurcate and inherit topological protection from linear edge states and, therefore, demonstrate immunity to disorder and defects upon propagation, attract considerable attention in a rapidly growing field of…
We study edge states of a random Schroedinger operator for an electron submitted to a magnetic field in a finite macroscopic two dimensional system of linear dimensions equal to L. The y direction is L-periodic and in the x direction the…
In this article, we investigate the combinatorial and algebraic properties of the lcm-lattice associated with the edge ideal of a hypergraph. Let $\H$ be a hypergraph, $I(\H)$ its corresponding edge ideal in a polynomial ring in $n$…
The bulk-boundary correspondence relates topologically-protected edge modes to bulk topological invariants, and is well-understood for short-range free-fermion chains. Although case studies have considered long-range Hamiltonians whose…
The classical lattice dynamics of honeycomb lattices is studied in the harmonic approximation. Interactions between nearest neighbors are represented by springs connecting them. A short and necessary introduction of the lattice structure is…
We describe a method for exactly diagonalizing clean $D$-dimensional lattice systems of independent fermions subject to arbitrary boundary conditions in one direction, as well as systems composed of two bulks meeting at a planar interface.…
Anomalous topological phases, where edge states coexist with topologically trivial Chern bands, can only appear in periodically driven lattices. When the driving is smooth and continuous, the bulk-edge correspondence is guaranteed by the…
In the context of topological insulators, the shallow-water model was recently shown to exhibit an anomalous bulk-edge correspondence. For the model with a boundary, the parameter space involves both longitudinal momentum and boundary…
The magneto-optical longitudinal, transverse Hall and circularly-polarized response of silicene and other materials described by a Kane-Mele Hamiltonian are calculated. Particular attention is paid to the effects of an external electric…
By extending the gauge covariant magnetic perturbation theory to operators defined on half-planes, we prove that for $2d$ random ergodic magnetic Schr\"odinger operators, the zero-temperature bulk-edge correspondence can be obtained from a…
The interplay of topology and correlations defines a new playground to study boundary criticality in quantum systems. We employ large scale auxiliary field quantum Monte Carlo simulations to study a two-dimensional Kane-Mele-Hubbard model…
We derive the boundary conditions for MoS$_2$ and similar transition-metal dichalcogenide honeycomb (2H polytype) monolayers with the same type of $\mathbf{k}\!\cdot\!\mathbf{p}$ Hamiltonian within the continuum model around the K points.…
The bulk-edge correspondence for topological quantum liquids states that the spectrum of the reduced density matrix of a large subregion reproduces the thermal spectrum of a physical edge. This correspondence suggests an intricate…
The unambiguous detection of the band topology for topological nodal systems remains an urgent problem in this field. Usually in experiments this relies on the detection for the topological edge modes, which may requires the high demands…
The correspondence between the edge theory and the entanglement spectrum is firmly established for the chiral topological phases. We study gapped, topologically ordered, non-chiral states with a conserved $U(1)$ charge and show that the…
We illustrate possible topological phases in honeycomb lattice with textures in electron hopping energy between nearest-neighboring sites and show that they are characterized by the mirror winding number intimately related to the chiral (or…
The emergent concept of magnetic charge quasi-particle provides a new realm to study the evolution of magnetic properties in two-dimensional artificially frustrated magnets. We report on the exploration of magnetic phases due to various…
A weak topological insulator in dimension $3$ is known to have a topologically protected gapless mode along the screw dislocation. In this paper we formulate and prove this fact with the language of C*-algebra K-theory. The proof is based…