Semiconductor Surface Studies

Contains research summary and reports on three research projects.Joint Services Electronics Program (Contract DAAG29-83-K-0003

Semiconductor Surface Studies

Contains research objectives and summary of research on one research project.Joint Services Electronics Program (Contract DAAB07-76-C-1400

Reflection-Free One-Way Edge Modes in a Gyromagnetic Photonic Crystal

We point out that electromagnetic one-way edge modes analogous to quantum Hall edge states, originally predicted by Raghu and Haldane in 2D gyroelectric photonic crystals possessing Dirac point-derived bandgaps, can appear in more general settings. In particular, we show that the TM modes in a gyromagnetic photonic crystal can be formally mapped to electronic wavefunctions in a periodic electromagnetic field, so that the only requirement for the existence of one-way edge modes is that the Chern number for all bands below a gap is non-zero. In a square-lattice gyromagnetic Yttrium-Iron-Garnet photonic crystal operating at microwave frequencies, which lacks Dirac points, time-reversal breaking is strong enough that the effect should be easily observable. For realistic material parameters, the edge modes occupy a 10% band gap. Numerical simulations of a one-way waveguide incorporating this crystal show 100% transmission across strong defects, such as perfect conductors several lattice constants wide, larger than the width of the waveguide.Comment: 4 pages, 3 figures (Figs. 1 and 2 revised.

Weyl points and line nodes in gapless gyroid photonic crystals

Weyl points and line nodes are three-dimensional linear point- and line-degeneracies between two bands. In contrast to Dirac points, which are their two-dimensional analogues, Weyl points are stable in the momentum space and the associated surface states are predicted to be topologically non-trivial. However, Weyl points are yet to be discovered in nature. Here, we report photonic crystals, based on the double-gyroid structures, exhibiting frequency-isolated Weyl points with intricate phase diagrams. The surface states associated with the non-zero Chern numbers are demonstrated. Line nodes are also found in similar geometries; the associated surface states are shown to be flat bands. Our results are readily experimentally realizable at both microwave and optical frequencies.Comment: 6 figures and 8 pages including the supplementary informatio

Non-Abelian Generalizations of the Hofstadter model: Spin-orbit-coupled Butterfly Pairs

The Hofstadter model, well-known for its fractal butterfly spectrum, describes two-dimensional electrons under a perpendicular magnetic field, which gives rise to the integer quantum hall effect. Inspired by the real-space building blocks of non-Abelian gauge fields from a recent experiment [Science, 365, 1021 (2019)], we introduce and theoretically study two non-Abelian generalizations of the Hofstadter model. Each model describes two pairs of Hofstadter butterflies that are spin-orbit coupled. In contrast to the original Hofstadter model that can be equivalently studied in the Landau and symmetric gauges, the corresponding non-Abelian generalizations exhibit distinct spectra due to the non-commutativity of the gauge fields. We derive the genuine (necessary and sufficient) non-Abelian condition for the two models from the commutativity of their arbitrary loop operators. At zero energy, the models are gapless and host Weyl and Dirac points protected by internal and crystalline symmetries. Double (8-fold), triple (12-fold), and quadrupole (16-fold) Dirac points also emerge, especially under equal hopping phases of the non-Abelian potentials. At other fillings, the gapped phases of the models give rise to $\mathbb{Z}_2$ topological insulators. We conclude by discussing possible schemes for the experimental realizations of the models in photonic platforms

Generalized Gilat-Raubenheimer method for density-of-states calculation in photonic crystals

Efficient numeric algorithm is the key for accurate evaluation of density of states (DOS) in band theory. Gilat-Raubenheimer (GR) method proposed in 1966 is an efficient linear extrapolation method which was limited in specific lattices. Here, using an affine transformation, we provide a new generalization of the original GR method to any Bravais lattices and show that it is superior to the tetrahedron method and the adaptive Gaussian broadening method. Finally, we apply our generalized GR (GGR) method to compute DOS of various gyroid photonic crystals of topological degeneracies.Comment: 7 pages, 2 figures; typos added, appendix B added. Programs are available at: https://github.com/boyuanliuoptics/DOS-calculatio