Related papers: A Unified Perspective of Complex Band Structure: I…
Band structure analysis is central to understanding wave propagation in periodic media; however, it becomes challenging in open systems owing to energy leakage. Photonic crystal (PhC) slabs exemplify such systems, featuring periodicity in…
Band theory provides the foundation for understanding electronic structure in crystalline materials, but its reliance on exact translational symmetry limits its applicability to systems with defects, disorder, incommensurate modulations, or…
We present the mathematical and numerical theory for evanescent waves in subwavelength band gap materials. We begin in the one-dimensional case, whereby fully explicit formulas for the complex band structure, in terms of the capacitance…
When the electronic dispersion in a material is independent of momentum, it gives rise to strongly correlated flat bands, with the single particle energy, quenched. Though the notion of flat bands had been known since long, their…
The study of band connectivity is a fundamental problem in condensed matter physics. Here, we develop a new method for analyzing band connectivity, which completely solves the outstanding questions of the reducibility and decomposition of…
The last decade has seen a large increase in the number of electronic-structure calculations that involve adding a Hubbard term to the local density approximation band-structure Hamiltonian. The Hubbard term is then solved either at the…
The Hubbard model, which augments independent-electron band theory with a single parameter to describe electron-electron correlations, is widely regarded to be the `standard model' of condensed matter physics. The model has been remarkably…
A remarkable feature of the band structure of bilayer graphene at small twist angle is the appearance of isolated bands near neutrality, whose bandwidth can be reduced at certain magic angles (eg. $\theta\sim 1.05^\circ$). In this regime,…
Topological materials are quantum materials with nontrivial ground-state entanglement that are irremovable so long as certain rules, like invariance under symmetries and the existence of an energy gap, are respected. They showcase…
This work theoretically and experimentally reports the evanescent connections between propagating bands in periodic acoustic materials. The complex band structures obtained by solving for the $k(\omega)$ problem reveal a complete…
A general method is presented to unfold band structures of first-principles super-cell calculations with proper spectral weight, allowing easier visualization of the electronic structure and the degree of broken translational symmetry. The…
We find that the frequency spectra of layered phononic and photonic composites admit a universal struc- ture, independent of the geometry of the periodic-cell and the specific physical properties. We show that this representation extends to…
We highlight recent progress in the study of artificial flat band systems with a threefold focus. First, we discuss single-particle flat band physics, which has advanced through the design of various flat band generators. These generators…
We continue our study of the quantum optics of a single photon interacting with a system of two level atoms. In this work we investigate the case of a periodic arrangement of atoms. We provide a general structure theorem characterizing the…
We introduce the stochastic band structure, a method giving the dispersion relation for waves propagating in periodic media or along waveguides, and subject to material loss or radiation damping. Instead of considering an explicit or…
Twisted multilayer systems, encompassing materials like twisted bilayer graphene (TBG), twisted trilayer graphene, and twisted bilayer transition metal dichalcogenides, have garnered significant attention in condensed matter physics.…
We develop the topological band theory for systems described by non-Hermitian Hamiltonians, whose energy spectra are generally complex. After generalizing the notion of gapped band structures to the non-Hermitian case, we classify "gapped"…
Bacteria can form a great variety of spatially heterogeneous cell density patterns, ranging from simple concentric rings to dynamical spiral waves appearing in growing colonies. These pattern formation phenomena are important as they…
Most elemental metals under ambient conditions adopt simple structures such as BCC, FCC and HCP in specific groupings across the Periodic Table, and on compression, many of these elements undergo transitions to surprisingly complex…
We show how arbitrary unit cells of periodic materials can be represented as graphs whose nodes represent atoms and whose weighted edges represent tunneling connections between atoms. Further, we present methods to calculate the band…