Multiple Brillouin Zones Research Articles

Ultrafast Suppression of the Ferroelectric Instability in KTaO_{3}.

We use an x-ray free-electron laser to study the lattice dynamics following photoexcitation with ultrafast near-UV light (wavelength 266nm, 50fs pulse duration) of the incipient ferroelectric potassium tantalate, KTaO_{3}. By probing the lattice dynamics corresponding to multiple Brillouin zones through the x-ray diffuse scattering with pulses from the Linac Coherent Light Source (LCLS) (wavelength 1.3Å and <10 fs pulse duration), we observe changes in the diffuse intensity associated with a hardening of the transverse acoustic phonon branches along Γ to X and Γ to M. Using force constants from density functional theory, we fit the quasiequilibrium intensity and obtain the instantaneous lattice temperature and density of photoexcited charge carriers. The density functional theory calculations demonstrate that photoexcitation transfers charge from oxygen 2p derived π-bonding orbitals to Ta 5d derived antibonding orbitals, further suppressing the ferroelectric instability and increasing the stability of the cubic, paraelectric structure.

Topological gap labeling with third Chern numbers in three-dimensional quasicrystals

We study the topological gap labeling of general 3D quasicrystals and we find that every gap in the spectrum is characterized by a set of the third Chern numbers. We show that a quasi-periodic structure has multiple Brillouin zones defined by redundant wavevectors, and the number of states below a gap is quantized as an integer linear combination of volumes of these Brillouin zones. The associated quantum numbers to characterize energy gaps can be expressed as third Chern numbers by considering a formal relationship between an adiabatic charge pumping under cyclic deformation of the quasi-periodic potential and a topological nonlinear electromagnetic response in 6D insulators.

Topological invariants in two-dimensional quasicrystals

We provide a topological concept to characterize energy gaps in general two-dimensional quasiperiodic systems. We show that every single gap is uniquely characterized by a set of integers, which quantize the area of the momentum space in units of multiple Brillouin zones. These integers are found to be equivalent to the second Chern numbers by considering a formal relationship between an adiabatic charge pumping under a potential sliding and the four-dimensional quantum Hall effect. The integers are independent of commensurability, and invariant under an arbitrary continuous deformation, such as a relative rotation of a twisted bilayer system.

Multiphonon diffuse scattering in solids from first principles: Application to layered crystals and two-dimensional materials

Time-resolved diffuse scattering experiments have gained increasing attention due to their potential to reveal non-equilibrium dynamics of crystal lattice vibrations with full momentum resolution. Although progress has been made in interpreting experimental data on the basis of one-phonon scattering, understanding the role of individual phonons can be sometimes hindered by multi-phonon excitations. In Ref. [{\it arXiv:2103.10108}] we have introduced a rigorous approach for the calculation of the all-phonon inelastic scattering intensity of solids from first-principles. In the present work, we describe our implementation in detail and show that multi-phonon interactions are captured efficiently by exploiting translational and time-reversal symmetries of the crystal. We demonstrate its predictive power by calculating the scattering patterns of monolayer molybdenum disulfide (MoS$_2$), bulk MoS$_2$, and black phosphorus (bP), and we obtain excellent agreement with our measurements of thermal electron diffuse scattering. Remarkably, our results show that multi-phonon excitations dominate in bP across multiple Brillouin zones, while in MoS$_2$ they play a less pronounced role. We expand our analysis for each system and examine the effect of individual atomic and interatomic vibrational motion on the diffuse scattering signals. We further demonstrate the high-throughput capability of our approach by reporting all-phonon scattering maps of 2D MoSe2, WSe2, WS2, graphene, and CdI2, rationalizing in each case the effect of multi-phonon processes. As a side point, we show that the special displacement method reproduces the thermally distorted configuration that generates precisely the all-phonon diffuse pattern.

Automating Analysis of Neutron Scattering Time-of-Flight Single Crystal Phonon Data

This article introduces software called Phonon Explorer that implements a data mining workflow for large datasets of the neutron scattering function, S(Q, ω), measured on time-of-flight neutron spectrometers. This systematic approach takes advantage of all useful data contained in the dataset. It includes finding Brillouin zones where specific phonons have the highest scattering intensity, background subtraction, combining statistics in multiple Brillouin zones, and separating closely spaced phonon peaks. Using the software reduces the time needed to determine phonon dispersions, linewidths, and eigenvectors by more than an order of magnitude.

Low-energy magnons in the chiral ferrimagnet Cu2OSeO3 : A coarse-grained approach

We report a comprehensive neutron scattering study of low energy magnetic excitations in the breathing pyrochlore helimagnetic Cu2OSeO3. Fully documenting the four lowest energy magnetic modes that leave the ferrimagnetic configuration of the "strong tetrahedra" intact ( meV), we find gapless quadratic dispersion at the point for energies above 0.2 meV, two doublets separated by 1.6(2) meV at the R point, and a bounded continuum at the X point. Our constrained rigid spin cluster model relates these features to Dzyaloshinskii-Moriya (DM) interactions and the incommensurate helical ground state. Combining conventional spin wave theory with a spin cluster form factor accurately reproduces the measured equal time structure factor through multiple Brillouin zones. An effective spin Hamiltonian describing complex anisotropic intercluster interactions is obtained.

Magnetic clustering, half-moons, and shadow pinch points as signals of a proximate Coulomb phase in frustrated Heisenberg magnets

We study the formation of magnetic clusters in frustrated magnets in their cooperative paramagnetic regime. For this purpose, we consider the $J_1$-$J_2$-$J_3$ classical Heisenberg model on kagome and pyrochlore lattices with $J_2 = J_3=J$. In the absence of farther-neighbor couplings, $J=0$, the system is in the Coulomb phase with magnetic correlations well characterized by pinch-point singularities. Farther-neighbor couplings lead to the formation of magnetic clusters, which can be interpreted as a counterpart of topological-charge clusters in Ising frustrated magnets [T. Mizoguchi, L. D. C. Jaubert and M. Udagawa, Phys. Rev. Lett. {\bf 119}, 077207 (2017)]. The concomitant static and dynamical magnetic structure factors, respectively $\mathcal{S}({\bm{q}})$ and $\mathcal{S}({\bm{q}},\omega)$, develop half-moon patterns. As $J$ increases, the continuous nature of the Heisenberg spins enables the half-moons to coalesce into connected `star' structures spreading across multiple Brillouin zones. These characteristic patterns are a dispersive complement of the pinch point singularities, and signal the proximity to a Coulomb phase. Shadows of the pinch points remain visible at finite energy, $\omega$. This opens the way to observe these clusters through (in)elastic neutron scattering experiments. The origin of these features are clarified by complementary methods: large-$N$ calculations, semi-classical dynamics of the Landau-Lifshitz equation, and Monte Carlo simulations. As promising candidates to observe the clustering states, we revisit the origin of "spin molecules" observed in a family of spinel oxides $AB_2$O$_4$ ($A=$ Zn, Hg, Mg, $B=$ Cr, Fe).

ARPES study of the epitaxially grown topological crystalline insulator SnTe(111)

SnTe is a prototypical topological crystalline insulator, in which the gapless surface state is protected by a crystal symmetry. The hallmark of the topological properties in SnTe is the Dirac cones projected to the surfaces with mirror symmetry, stemming from the band inversion near the L points of its bulk Brillouin zone, which can be measured by angle-resolved photoemission. We have obtained the (111) surface of SnTe film by molecular beam epitaxy on BaF2(111) substrate. Photon-energy-dependence of in situ angle-resolved photoemission, covering multiple Brillouin zones in the direction perpendicular to the (111) surface, demonstrate the projected Dirac cones at the Γ¯ and M¯ points of the surface Brillouin zone. In addition, we observe a Dirac-cone-like band structure at the Γ point of the bulk Brillouin zone, whose Dirac energy is largely different from those at the Γ¯ and M¯ points.

On achieving pure electromagnetic left-handedness through magnetodielectric field compression

The relationship between electromagnetic phase and power flow in metamaterials composed of periodic magnetodielectric inclusions is investigated. The distribution of Poynting vectors in $k$ space across multiple Brillouin zones suggests that backward phase is a result of field compression within the inclusions, and that left-handedness can be achieved without negative electric or magnetic susceptibility (i.e., without out-of-phase dipole moments). This hypothesis is verified by showing that a one-dimensional periodic array of magnetodielectric slabs can be designed to mimic the properties of an ideal (homogeneous) left-handed medium. Furthermore, using exact fields and without any field averaging, it is shown that the structure can be designed such that practically all power is carried in the fundamental left-handed spectral component. In the limit where the fundamental contains all the power, this periodic structure has the same spectral power signature as that of a homogeneous left-handed medium. It is shown that this congruence does not manifest when the inclusions are purely dielectric, nor does it manifest for magnetodielectric inclusions in two or three dimensions.

Spin excitations used to probe the nature of exchange coupling in the magnetically ordered ground state ofPr0.5Ca0.5MnO3

We have used time-of-flight inelastic neutron scattering to measure the spin wave spectrum of the canonical half-doped manganite Pr$_{0.5}$Ca$_{0.5}$MnO$_{3}$, in its magnetic and orbitally ordered phase. The data, which cover multiple Brillouin zones and the entire energy range of the excitations, are compared with several different models that are all consistent with the CE-type magnetic order, but arise through different exchange coupling schemes. The Goodenough model, i.e. an ordered state comprising strong nearest neighbor ferromagnetic interactions along zig-zag chains with antiferromagnetic inter-chain coupling, provides the best description of the data, provided that further neighbor interactions along the chains are included. We are able to rule out a coupling scheme involving formation of strongly bound ferromagnetic dimers, i.e. Zener polarons, on the basis of gross features of the observed spin wave spectrum. A model with weaker dimerization reproduces the observed dispersion but can be ruled out on the basis of discrepancies between the calculated and observed structure factors at certain positions in reciprocal space. Adding further neighbor interactions results in almost no dimerization, i.e. recovery of the Goodenough model. These results are consistent with theoretical analysis of the degenerate double exchange model for half-doping, and provide a recipe for how to interpret future measurements away from half-doping, where degenerate double exchange models predict more complex ground states.

Method to map one-dimensional electronic wave function by using multiple Brillouin zone angle resolved photoemission

Angle resolved photoemission spectroscopy (ARPES) is a powerful tool to investigate electronic structures of solids and has been widely used in studying various materials. Electronic structure information by ARPES is obtained in the momentum space. However, in the case of one-dimensional systems, we show that real space information can be extracted from ARPES data taken over multiple Brillouin zones (BZs). Intensities in multiple BZs are proportional to the photoemission matrix element which contains information on the coefficient of Bloch wave functions. It is shown that the Bloch wave function coefficients can be indeed extracted from ARPES data, which allows us to construct the real space wave function. As a test, we use ARPES data from proto-typical onedimensional system SrCuO2 and construct the real space wave function.

Far-Field Focus and Dispersionless Anticrossing Bands in Two-Dimensional Photonic Crystals

We review the simulation work for the far-field focus and dispersionless anticrossing bands in two-dimensional (2D) photonic crystals. In a two-dimensional photonic-crystal-based concave lens, the far-field focus of a plane wave is given by the distance between the focusing point and the lens. Strong and good-quality far-field focusing of a transmitted wave, explicitly following the well-known wave-beam negative refraction law, can be achieved. The spatial frequency information of the Bloch mode in multiple Brillouin zones (BZs) is investigated in order to indicate the wave propagation in two different regions. When considering the photonic transmission in a 2D photonic crystal composed of a negative phase-velocity medium (NPVM), it is shown that the dispersionless anticrossing bands are generated by the couplings among the localized surface polaritons of the NPVM rods. The photonic band structures of the NPVM photonic crystals are characterized by a topographical continuous dispersion relationship accompanied by many anticrossing bands.

Strong focusing properties and far-field focus in the two-dimensional photonic-crystal-based concave lens

We have demonstrated that the strong and far-field focusing of a point source and a plane wave in a two-dimensional photonic-crystal-based concave lens by the use of the standard finite-difference time-domain simulations. The effect of the distance between the point source and the lens on the focusing is discussed. The far-field focus of a plane wave is shown. In addition, a plane wave is formed with placing the source at the focus point. According to the calculation, the strong and good quality far-field focusing of the transmitted wave, explicitly following the well-known wave beam negative refraction law, can be realized. Moreover, the spatial frequencies information of the Bloch mode in multiple Brillouin zones is investigated in order to indicate the wave propagation in two different regions.

Negative refractive behavior of a two-dimensional negative-index photonic crystals using a wave vector diagram method

We have theoretically studied the negative refractive behavior and the focusing effect in a two-dimensional square-lattice photonic crystal made of air rods in a dielectric background. Detailed explanations are given for the effect of the negative refraction, and the imaging of the plano-concave lens is shown by the use of a wave vector diagram formalism. The typical negative refractive behavior is demonstrated by considering the Bloch mode with the wave vector inside the first Brillouin zone, because only those wave vectors inside the first Brillouin zone of multiple Brillouin zones have a definite meaning. The single propagating beam is analyzed by the use of the wave vector diagram formalism following the folding of the wave vectors. Good-quality focusing of a plane wave can be realized by using a photonic crystal plano-concave lens, while a plane wave is formed by a point source placed at the focal point. Our results are in good agreement with the experimental ones shown for a negative-index plano-concave lens by Vodo et al. [Appl. Phys. Lett. 86 (2005) 201108]. Finally, we also have shown the focusing behavior of a plane wave and a Gaussian pulse by a plano-concave lens structure with high-index modulation instead of air in the concave region.

Direct Observation of Bloch Harmonics and Negative Phase Velocity in Photonic Crystal Waveguides

The eigenfield distribution and the band structure of a photonic crystal waveguide have been measured with a phase-sensitive near-field scanning optical microscope. Bloch modes, which consist of more than one spatial frequency, are visualized in the waveguide. In the band structure, multiple Brillouin zones due to zone folding are observed, in which positive and negative dispersion is seen. The negative slopes are shown to correspond to a negative phase velocity but a positive group velocity. The lateral mode profile for modes separated by one reciprocal lattice vector is found to be different.

High-energy angle-resolved photoemission of NaMo6O17

Abstract Angle-resolved photoelectron spectroscopy of quasi-two-dimensional NaMo6O17 has been investigated with photon energies greater than 70 eV. The underlying quasi-one-dimensional band structure is visualized in multiple Brillouin zones by the constant binding-energy intensity mapping technique. Brillouin zone intensity modulation effects are observed in Fermi-edge intensity maps both as a function of k|| (angle) and of kz (photon energy). Experimental challenges arising from small sample sizes, detection geometry and susceptibility to beam-induced surface damage are also discussed.

Observation of band dispersion in YNi 2B 2C

We report the first angle resolved photoemission spectroscopy (ARPES) study of single crystals of a borocarbide superconductor. In the normal state, there is clear evidence of dispersion within the manifold of Ni 3d features between ~ 1 and 3 eV binding energy. Dispersive features were also observed within ~ 1 eV of the Fermi level ( E F ) near the Γ and Z points of the bulk Brillouin zone. Resonant photoemission indicates partial Ni character for these states. An E F crossing occurs at a k-space position that is consistent with a predicted hole pocket centered on the G 1 point of the reciprocal lattice. In the photon energy range used (17–200 eV), symmetry points in multiple Brillouin zones were consistently located assuming a free electron final state.