Hyperbolic band theory.
Ontology highlight
ABSTRACT:
SUBMITTER: Maciejko J
PROVIDER: S-EPMC8442860 | biostudies-literature |
REPOSITORIES: biostudies-literature
Similar Datasets
Project description:Electromagnetic responses in superconductors provide valuable information on the pairing symmetry as well as physical quantities such as the superfluid density. However, at the superconducting gap energy scale, optical excitations of the Bogoliugov quasiparticles are forbidden in conventional Bardeen-Cooper-Schrieffer superconductors when momentum is conserved. Accordingly, far-infrared optical responses have been understood in the framework of a dirty-limit theory by Mattis and Bardeen for over 60 years. Here we show, by investigating the selection rules imposed by particle-hole symmetry and unitary symmetries, that intrinsic momentum-conserving optical excitations can occur in clean multi-band superconductors when one of the following three conditions is satisfied: (i) inversion symmetry breaking, (ii) symmetry protection of the Bogoliubov Fermi surfaces, or (iii) simply finite spin-orbit coupling with unbroken time reversal and inversion symmetries. This result indicates that clean-limit optical responses are common beyond the straightforward case of broken inversion symmetry. We apply our theory to optical responses in FeSe, a clean multi-band superconductor with inversion symmetry and significant spin-orbit coupling. This result paves the way for studying clean-limit superconductors through optical measurements.
| S-EPMC7954819 | biostudies-literature
Project description:We develop a unified view of topological phase transitions (TPTs) in solids by revising the classical band theory with the inclusion of topology. Reevaluating the band evolution from an "atomic crystal" (a normal insulator (NI)) to a solid crystal, such as a semiconductor, we demonstrate that there exists ubiquitously an intermediate phase of topological insulator (TI), whose critical transition point displays a linear scaling between electron hopping potential and average bond length, underlined by deformation-potential theory. The validity of the scaling relation is verified in various two-dimensional (2D) lattices regardless of lattice symmetry, periodicity, and form of electron hoppings, based on a generic tight-binding model. Significantly, this linear scaling is shown to set an upper bound for the degree of structural disorder to destroy the topological order in a crystalline solid, as exemplified by formation of vacancies and thermal disorder. Our work formulates a simple framework for understanding the physical nature of TPTs with significant implications in practical applications of topological materials.
| S-EPMC7262673 | biostudies-literature
Project description:Enforcing a straight-line condition of the total energy upon removal/addition of fractional electrons on eigen states has been successfully applied to atoms and molecules for calculating ionization potentials and electron affinities, but fails for solids due to the extended nature of the eigen orbitals. Here we have extended the straight-line condition to the removal/addition of fractional electrons on Wannier functions constructed within the occupied/unoccupied subspaces. It removes the self-interaction energies of those Wannier functions, and yields accurate band gaps for solids compared to experiments. It does not have any adjustable parameters and the computational cost is at the DFT level. This method can also work for molecules, providing eigen energies in good agreement with experimental ionization potentials and electron affinities. Our approach can be viewed as an alternative approach of the standard LDA+U procedure.
| S-EPMC4845067 | biostudies-literature
Project description:When engineered on scales much smaller than the operating wavelength, metal-semiconductor nanostructures exhibit properties unobtainable in nature. Namely, a uniaxial optical metamaterial described by a hyperbolic dispersion relation can simultaneously behave as a reflective metal and an absorptive or emissive semiconductor for electromagnetic waves with orthogonal linear polarization states. Using an unconventional multilayer architecture, we demonstrate luminescent hyperbolic metasurfaces, wherein distributed semiconducting quantum wells display extreme absorption and emission polarization anisotropy. Through normally incident micro-photoluminescence measurements, we observe absorption anisotropies greater than a factor of 10 and degree-of-linear polarization of emission >0.9. We observe the modification of emission spectra and, by incorporating wavelength-scale gratings, show a controlled reduction of polarization anisotropy. We verify hyperbolic dispersion with numerical simulations that model the metasurface as a composite nanoscale structure and according to the effective medium approximation. Finally, we experimentally demonstrate >350% emission intensity enhancement relative to the bare semiconducting quantum wells.
| S-EPMC5473634 | biostudies-literature
Project description:Band gaps and electron affinities of binary and ternary, wurtzite (wz-) and zincblende (zb-) III-nitrides are investigated using a unified hybrid density functional theory, and band offsets between wz- and zb- alloys are calculated using Anderson's electron affinity model. A conduction (and valence) band offset of 1.85 (0.89) eV has been calculated for zb-GaN/InN heterojunctions, which is 0.25 eV larger (and 0.26 eV smaller) than that of the wz- counterpart. Such polarization-free zb-GaN/InGaN/GaN quantum well structures with large conduction band offsets have the potential to suppress electron leakage current and quantum-confined Stark effects (QCSEs). Contrarily, the conduction (and valence) band offset of zb-AlN/GaN heterojunctions is calculated to be 1.32 (0.43) eV, which is 1.15 eV smaller (and 0.13 eV larger) than that of the wz- case. The significant reduction in zb-AlN/GaN band offsets is ascribed to the smaller and indirect band gap of zb-AlN-the direct-to-indirect crossover point in zb-Al X Ga1-X N is when X ∼ 65%. The small band gap of the zb-AlN barrier and the small conduction band offsets imply that electrons can be injected into zb-AlN/GaN/AlN quantum well heterostructures with small bias and less energy loss when captured by the quantum wells, respectively, i.e., loss as heat is reduced. The band gap of ternary III-nitrides does not linearly depend on alloy compositions, implying a nonlinear dependence of band offsets on compositions. As a result, the large bowing of the conduction band offset is identified and ascribed to the cation-like behavior of the conduction band minimum, while the linear dependence of the valence band offset on compositions is attributed to the anion-like character of the valence band maximum.
| S-EPMC7057329 | biostudies-literature
Project description:We analyse the fine convergence properties of one parameter families of hyperbolic metrics that move always in a horizontal direction, i.e. orthogonal to the action of diffeomorphisms. Such families arise naturally in the study of general curves of metrics on surfaces, and in one of the gradients flows for the harmonic map energy.
| S-EPMC6432971 | biostudies-literature
Project description:Patterns of gene expressions play a key role in determining cell state. Although correlations in gene expressions have been well documented, most of the current methods treat them as independent variables. One way to take into account gene correlations is to find a low-dimensional curved geometry that describes variation in the data. Here we develop such a method and find that gene expression across multiple cell types exhibits a low-dimensional hyperbolic structure. When more genes are taken into account, hyperbolic effects become stronger but representation remains low dimensional. The size of the hyperbolic map, which indicates the hierarchical depth of the data, was the largest for human cells, the smallest for mouse embryonic cells, and intermediate in differentiated cells from different mouse organs. We also describe how hyperbolic metric can be incorporated into the t-SNE method to improve visualizations compared with leading methods.
| S-EPMC7970362 | biostudies-literature
Project description:Recently, exchange-correlation potentials in density functional theory were developed with the goal of providing improved band gaps in solids. Among them, the semilocal potentials are particularly interesting for large systems since they lead to calculations that are much faster than with hybrid functionals or methods like GW. We present an exhaustive comparison of semilocal exchange-correlation potentials for band gap calculations on a large test set of solids, and particular attention is paid to the potential HLE16 proposed by Verma and Truhlar. It is shown that the most accurate potential is the modified Becke-Johnson potential, which, most noticeably, is much more accurate than all other semilocal potentials for strongly correlated systems. This can be attributed to its additional dependence on the kinetic energy density. It is also shown that the modified Becke-Johnson potential is at least as accurate as the hybrid functionals and more reliable for solids with large band gaps.
| S-EPMC5423078 | biostudies-literature
Project description:The two-way insertion loss of a 1 m length of waveguide was reduced by nearly 5 dB over a 4% bandwidth at W-band (94 GHz) for an electron paramagnetic resonance (EPR) spectrometer relative to WR10 waveguide. The waveguide has an oversize section of commercially available rectangular WR28 and a novel pair of tapers that vary in cross section with axial position according to a hyperbolic-cosine (HC) function. The tapers connect conventional rectangular WR10 waveguide to the WR28. For minimum loss, the main mode electric field is parallel to the long side of the WR28. Using mode coupling theory, the position of maximum flare (inflection point) in the taper was optimized with respect to the coupling to higher order modes and the reflection of the main mode. The optimum inflection point position is about one-tenth of the taper length from the small end of the taper. Reflection and coupling were reduced by about 20 dB relative to a pyramidal (linear) taper of the same length. Comb-like dips in the transmission coefficient produced by resonances of the higher order modes in the oversize section were about 0.03 dB. Specially designed high-precision, adjustable WR28 flanges with alignment to about 5 μm were required to keep higher order mode amplitudes arising from the flanges comparable to those from the HC tapers. Minimum return loss was about 30 dB. This paper provides a foundation for further optimization, if needed. Methods are not specific to EPR or the microwave frequency band.
| S-EPMC3155584 | biostudies-other
Project description:We derive more than 80 embeddings of 2D hyperbolic honeycombs in Euclidean 3 space, forming 3-periodic infinite polyhedra with cubic symmetry. All embeddings are "minimally frustrated," formed by removing just enough isometries of the (regular, but unphysical) 2D hyperbolic honeycombs [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], and [Formula: see text] to allow embeddings in Euclidean 3 space. Nearly all of these triangulated "simplicial polyhedra" have symmetrically identical vertices, and most are chiral. The most symmetric examples include 10 infinite "deltahedra," with equilateral triangular faces, 6 of which were previously unknown and some of which can be described as packings of Platonic deltahedra. We describe also related cubic crystalline packings of equal hyperbolic discs in 3 space that are frustrated analogues of optimally dense hyperbolic disc packings. The 10-coordinated packings are the least "loosened" Euclidean embeddings, although frustration swells all of the hyperbolic disc packings to give less dense arrays than the flat penny-packing even though their unfrustrated analogues in [Formula: see text] are denser.
| S-EPMC6142264 | biostudies-literature