Related papers: Topological inverse band theory in waveguide quant…
Coherent control has enabled various novel phenomena in wave scattering. We introduce an effect called coherent orthogonal scattering, where the output wave becomes orthogonal to the reference output state without scatterers. This effect…
We address the problem of analytically extracting a countable infinity of flat, non-dispersive bands in a periodic array of cells that comprise branching Vicsek geometries of higher and higher generations. Through a geometric construction,…
Topology in quantum matter is typically associated with gapped phases. For example, in symmetry protected topological (SPT) phases, the bulk energy gap localizes edge modes near the boundary. In this work we identify a new mechanism that…
The application of topology, a branch of mathematics, to the study of electronic states in crystalline materials has had a revolutionary impact on the field of condensed matter physics. For example, the development of topological band…
Symmetry plays an important role in the topological band theory to remedy the eigenstates' gauge obstruction at the cost of a symmetry anomaly and zero-energy boundary modes. One can also make use of the symmetry to enumerate the…
We consider quantum scattering of particles in media exhibiting strong dispersion degeneracy. In particular, we study flat-banded lattices and linearly dispersed energy bands. The former constitute a prime example of single-particle…
Time-reversal invariant superconductors having nodes of vanishing excitation gap support zero-energy boundary states with topological protection. Existing expressions for the topological invariant are given in terms of the Hamiltonian of an…
The interplay between symmetry and topology leads to a rich variety of electronic topological phases, protecting states such as the topological insulators and Dirac semimetals. Previous results, like the Fu-Kane parity criterion for…
The link between chemical orbitals described by local degrees of freedom and band theory, which is defined in momentum space, was proposed by Zak several decades ago for spinless systems with and without time-reversal in his theory of…
The energy levels and optical transitions of tetrahedral core/shell InP/ZnSe quantum dots (QDs) are investigated by means of multi-band k$\cdot$p theory. Despite the $\overline{T}_d$ symmetry relaxing spherical selection rules, the…
Topological edge states in systems of two (or more) dimensions offer scattering-free transport, exhibiting robustness to inhomogeneities and disorder. In a different domain, time-modulated systems, such as photonic time crystals (PTCs),…
A band gap for electronic states in crystals governs various properties of solids, such as transport, optical and magnetic properties. Its estimation and control have been an important issue in solid state physics. The band gap can be…
The discovery of topological materials has challenged our understanding of condensed matter physics and led to novel and unusual phenomena. This has motivated recent developments to export topological concepts into photonics to make light…
2D topological insulators promise novel approaches towards electronic, spintronic, and quantum device applications. This is owing to unique features of their electronic band structure, in which bulk-boundary correspondences enforces the…
Band structures of electrons in a periodic potential are well-known to host topologies that impact their behaviors at edges and interfaces. The concept however is more general than the single-electron setting. In this work, we consider…
The past decade's apparent success in predicting and experimentally discovering distinct classes of topological insulators (TIs) and semimetals masks a fundamental shortcoming: out of 200,000 stoichiometric compounds extant in material…
We elucidate the general rule governing the response of dislocation lines in three-dimensional topological band insulators. According to this ${\bf K}\text{-}{\bf b}\text{-}{\bf t}$ rule, the lattice topology, represented by dislocation…
We show that topology can protect exponentially localized, zero energy edge modes at critical points between one-dimensional symmetry protected topological phases. This is possible even without gapped degrees of freedom in the bulk ---in…
We study the topological band theory of time reversal invariant topological insulators and interpret the topological $\mathbb{Z}_2$ invariant as an obstruction in terms of Stiefel--Whitney classes. The band structure of a topological…
We investigate the topological properties of a two-chain quantum ladder with uneven legs, i.e. the two chains differ in their periods by a factor of two. Such an uneven ladder presents rich band structures classified by the closure of…