We present an analytic prescription for computing the edge dispersion E (k) of a tight-
binding Dirac Hamiltonian terminated at an abrupt crystalline edge. Specifically, we consider …

We construct a generalized transfer matrix corresponding to noninteracting tight-binding
lattice models, which can subsequently be used to compute the bulk bands as well as the …

We present a generalization of Bloch's theorem to finite-range lattice systems of
independent fermions, in which translation symmetry is broken solely due to arbitrary …

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 …

Finite topologically nontrivial systems are characterized, among many other unique
properties, by the presence of bound states at their physical edges. These topological edge …

The hallmark of topological phases is their robust boundary signature whose intriguing
properties—such as the one-way transport on the chiral edge of a Chern insulator and the …

Topological edge modes, which are robust against disorders, have been used to enhance
the spatial stability of lasers. Recently, it was revealed that topological lasers can be further …

We present a generic and systematic approach for constructing D-dimensional lattice
models with exactly solvable d-dimensional boundary states localized to corners, edges …

Floquet engineering provides a toolbox for the realization of novel quantum phases without
static counterparts, while conventionally the realization may rely on the manipulation of …

While the deviation of the edge on-site potential from the bulk values in a magnonic
topological honeycomb lattice leads to the formation of edge states in a bearded boundary …