Points In Reciprocal Space Research Articles

(Invited) Computing the Newns-Anderson Chemisorption Function from First Principles

In analysing the interactions of adsorbates with extended surfaces, theory, and to a large degree also experiments, tend to rely on adsorption models such as the famous Newns-Anderson model. There, the interaction of adsorbate and substrate is represented by the interaction of the adsorbate's one-electron frontier orbitals with the delocalised Bloch states of the substrate. Together with its simplified cousin, the d-band model, such adsorption models yielded significant insight into the chemistry of extended surfaces.The Newns-Anderson Model gives rise to a so-called chemisorption function, a density of states weighted by the electronic coupling between adsorbate and substrate states, measuring the line broadening of an adsorbate frontier state upon adsorption. In my contribution, I will describe our efforts to compute the chemisorption function from first principles, employing a diabatization scheme to estimate electronic couplings between states. Recognizing the periodic nature of the substrate and the finite extent of computational supercells, we extend the original chemisorption function by a Brillouin zone integration to account for the (generally localized) adsorbate states' coupling to different substrate states at different points in reciprocal space. Including this integration, the chemisorption function not only converges well with both lateral simulation cell size and slab depth, but also compares well with experiments. We test our approach against highly accurate experimental measurements of ultrafast charge transfer of a probe Ar atom on various metal surfaces and find that the chemisorption function reproduces both absolute transfer rates and rate asymmetries due to spin on magnetic surfaces. Next to its predictiveness, though, the Newns Anderson chemisorption function allows us to investigate the charge transfer mechanism in terms of e.g. contributions of states with different angular momentum character, showing the importance of phase cancellation effects in interpreting charge transfer at surfaces.

2D Helium Atom Diffraction from a Microscopic Spot.

A method for measuring helium atom diffraction with micron-scale spatial resolution is demonstrated in a scanning helium microscope (SHeM) and applied to study a micron-scale spot on the (100) plane of a lithium fluoride (LiF) crystal. The positions of the observed diffraction peaks provide an accurate measurement of the local lattice spacing, while a combination of close-coupled scattering calculations and MonteCarlo ray-tracing simulations reproduce the main variations in diffracted intensity. Subsequently, the diffraction results are used to enhance image contrast by measuring at different points in reciprocal space. The results open up the possibility for using helium microdiffraction to characterize the morphology of delicate or electron-sensitive materials on small scales. These include many fundamentally and technologically important samples which cannot be studied in conventional atom scattering instruments, such as small grain size exfoliated 2D materials, polycrystalline samples, and other surfaces that do not exhibit long-range order.

Loss Difference Induced Localization in a Non-Hermitian Honeycomb Photonic Lattice.

Non-Hermitian systems with complex-valued energy spectra provide an extraordinary platform for manipulating unconventional dynamics of light. Here, we demonstrate the localization of light in an instantaneously reconfigurable non-Hermitian honeycomb photonic lattice that is established in a coherently prepared atomic system. One set of the sublattices is optically modulated to introduce the absorptive difference between neighboring lattice sites, where the Dirac points in reciprocal space are extended into dispersionless local flat bands, with two shared eigenstates: low-loss (high-loss) one with fields confined at sublattice B (A). When these local flat bands are broad enough due to larger loss difference, the incident beam with its tangential wave vector being at the K point in reciprocal space is effectively localized at sublattice B with weaker absorption, namely, the commonly seen power exchange between adjacent channels in photonic lattices is effectively prohibited. The current work unlocks a new capability from non-Hermitian two-dimensional photonic lattices and provides an alternative route for engineering tunable local flat bands in photonic structures.

The Dynamics of Oxygen Ion Exchange in Epitaxial Strontium Cobaltite Bilayers

AbstractThe exchange of ions across interfaces is key to the field of iontronics, where the properties of the device can be altered by the local ion concentration. This study investigates a complex oxide system where structural and electronic phase transitions can be driven by changes in the concentration of oxygen ions. In situ coherent X‐ray studies are conducted on epitaxial bilayers of insulating SrCoO2.5 and metallic SrCoO3 − δ. The diffusion of oxygen ions across the bilayer is studied with X‐ray photon correlation spectroscopy to capture the dynamical behavior of the interface in reducing and oxidizing environments. The behavior is strongly asymmetric, with much slower dynamics appearing in reducing versus oxidizing environments. According to the correlation functions determined from different points in reciprocal space, this study finds that the dynamics near the center of the SrCoO2.5 crystal are generally similar to those near the heterointerfaces. The results suggest that the interface is stable and reversible, making SrCoOx a model system for the study of iontronic behavior.

Investigating the magnetoelastic properties in FeSn and Fe3Sn2 flat band metals

Topological quantum magnets FeSn and Fe$_{3}$Sn$_{2}$ were studied using neutron scattering and first-principles calculations. Both materials are metallic but host dispersionless flat bands with Dirac nodes at the $K$ point in reciprocal space. The local structure determined from the pair density function analysis of the neutron diffraction data provided no evidence for electron localization in both compounds, consistent with their metallic nature. At the same time, in FeSn, an anomalous suppression in the $c$-axis lattice constant coupled with changes in the phonon spectra were observed across T$_{N}$ indicating the presence of magneto-elastic coupling and spin-phonon interactions. In addition, it was observed that spin waves persisted well above T$_{N}$, suggesting that the in-plane ferromagnetic spin correlations survive at high temperatures. In contrast, no lattice anomaly was observed in Fe$_{3}$Sn$_{2}$. The inelastic signal could be mostly accounted for by phonons, determined from density functional theory, showing typical softening on warming.

Long-range order Bragg scattering and its effect on the dynamic response of a Penrose-like phononic crystal plate

In this article, we present scattering and localization phenomena in a thin elastic plate comprising an aperiodic arrangement of scatterers. By analyzing the form factor of the scattering cluster, we sample the reciprocal space which shows strong scattering points in reciprocal space associated with nontrivial dynamic response. Specifically, we identify attenuating frequency regimes and bands where strong localization is predicted and experimentally observed. We show that both localization and attenuation are Bragg scattering phenomena, induced by the long-range aperiodic patterns. Illustrative comparisons are drawn with a periodic counterpart having the same density of scatterers. The novel findings are corroborated by analytical estimates, numerical finite-element predictions, and vibrometric experiments. The results are relevant for the research community interested in extending phononic crystal phenomena to lower frequencies.

Kekulé-induced valley birefringence and skew scattering in graphene

In graphene, a Kekul\'e-Y bond texture modifies the electronic band structure generating two concentric Dirac cones with different Fermi velocities lying in the {\Gamma}-point in reciprocal space. The energy dispersion results in different group velocities for each isospin component at a given energy. This energy spectrum combined with the negative refraction index in p-n junctions, allows the emergence of an electronic analog of optical birefringence in graphene. We characterize the valley birefringence produced by a circularly symmetric Kekul\'e patterned and gated region using the scattering approach. We found caustics with two cusps separated in space by a distance dependent on the Kekul\'e interaction and that provides a measure of its strength. Then, at low carrier concentration we find a non-vanishing skew cross section, showing the asymmetry in the scattering of electrons around the axis of the incoming flux. This effect is associated with the appearance of the valley Hall effect as electrons with opposite valley polarization are deflected towards opposite directions.

Control of Quasibound Waves in Spiral Metasurfaces

Resonant light scattering by a subwavelength dielectric resonator array can show narrow, highly tunable resonant lineshapes from the interaction among multiple resonances. Several approaches have been introduced to control the spectral response of resonant light scattering, including optimization of the aspect ratio of cylindrical resonators, breaking in-plane inverse symmetry of coupled resonators, and operating periodic structures at the Γ point in reciprocal space. In this paper, we report the experimental demonstration of the control of resonant light scattering by subwavelength spiral resonator arrays. The fabricated metasurfaces support two types of resonances: the first one characterized by a Lorentzian peak with a long lifetime and the second type with a short lifetime supported by the lattice. By controlling the coupling strength between these two resonances through tailored broken symmetries, the resonant line shape of the spiral metasurface can be precisely tuned. The measured spectra show an ultrawide frequency tuning (over 16 THz) of the resonant mode by changing the spiral parameter at a fixed lattice constant. A temporal couple-mode theory combined with frequency-domain finite element method simulations was used to describe the measured transmission spectra of the fabricated metasurfaces.

Lasing Action from Quasi-Propagating Modes.

Band edges at the high symmetry points in reciprocal space of periodic structures hold special interest in materials engineering for their high density of states. In optical metamaterials, standing waves found at these points have facilitated lasing, bound-states-in-the-continuum, and Bose-Einstein condensation. However, because high symmetry points by definition are localized, properties associated with them are limited to specific energies and wavevectors. Conversely, quasi-propagating modes along the high symmetry directions are predicted to enable similar phenomena over a continuum of energies and wavevectors. Here, quasi-propagating modes in 2D nanoparticle lattices are shown to support lasing action over a continuous range of wavelengths and symmetry-determined directions from a single device. Using lead halide perovskite nanocrystal films as gain materials, lasing is achieved from waveguide-surface lattice resonance (W-SLR) modes that can be decomposed into propagating waves along high symmetry directions, and standing waves in the orthogonal direction that provide optical feedback. The characteristics of the lasing beams are analyzed using an analytical 3D model that describes diffracted light in 2D lattices. Demonstrations of lasing across different wavelengths and lattice designs highlight how quasi-propagating modes offer possibilities to engineer chromatic multibeam emission important in hyperspectral 3D sensing, high-bandwidth Li-Fi communication, and laser projection displays.

Polariton Bose-Einstein condensate from a bound state in the continuum.

Bound states in the continuum (BICs)1-3 are peculiar topological states that, when realized in a planar photonic crystal lattice, are symmetry-protected from radiating in the far field despite lying within the light cone4. These BICs possess an invariant topological charge given by the winding number of the polarization vectors5, similar to vortices in quantum fluids such as superfluid helium and atomic Bose-Einstein condensates. In spite of several reports of optical BICs in patterned dielectric slabs with evidence of lasing, their potential as topologically protected states with theoretically infinite lifetime has not yet been fully exploited. Here we show non-equilibrium Bose-Einstein condensation of polaritons-hybrid light-matter excitations-occurring in a BIC thanks to its peculiar non-radiative nature, which favours polariton accumulation. The combination of the ultralong BIC lifetime and the tight confinement of the waveguide geometry enables the achievement of an extremely low threshold density for condensation, which is reachednot in the dispersion minimum but at a saddle point in reciprocal space. By bridging bosonic condensation and symmetry-protected radiation eigenmodes, we reveal ways of imparting topological properties onto macroscopic quantum states with unexplored dispersion features. Such an observation may open a route towards energy-efficient polariton condensation in cost-effective integrated devices, ultimately suited for the development of hybrid light-matter optical circuits.

Merging Bound States in the Continuum at Off-High Symmetry Points.

Bound states in the continuum (BICs) confine resonances embedded in a continuous spectrum by eliminating radiation loss. Merging multiple BICs provides a promising approach to further reduce the scattering losses caused by fabrication imperfections. However, to date, BIC merging has been limited to only the Γ point, which constrains potential application scenarios such as beam steering and directional vector beams. Here, we propose a new scheme to construct merging BICs at almost an arbitrary point in reciprocal space. Our approach utilizes the topological features of BICs on photonic crystal slabs, and we merge a Friedrich-Wintgen BIC and an accidental BIC. The Q factors of the resulting merging BIC are enhanced for a broad wave vector range compared with both the original Friedrich-Wintgen BIC and the accidental BIC. Since Friedrich-Wintgen BICs and accidental BICs are quite common in the band structure, our proposal provides a general approach to realize off-Γ merging BICs with superhigh Q factors that can substantially enhance nonlinear and quantum effects and boost the performance of on-chip photonic devices.

Calculation of the Infrared Intensity of Crystalline Systems. A Comparison of Three Strategies Based on Berry Phase, Wannier Function, and Coupled-Perturbed Kohn–Sham Methods

Three alternative strategies for the calculation of the IR intensity of crystalline systems, as determined by Born charges, have been implemented in the Crystal code, using a Gaussian type basis set. One uses the Berry phase (BP) algorithm to compute the dipole moment; another does so, instead, through well localized crystalline orbitals (Wannier functions, WF); and the third is based on a coupled perturbed Hartree–Fock or Kohn–Sham procedure (CP). In WF and BP, the derivative of the dipole moment with respect to the atomic coordinates is evaluated numerically, whereas in CP it is analytical. In the three cases, very different numerical schemes are utilized, so that the equivalence of the obtained IR intensities is not ensured a priori but instead is the result of the high numerical accuracy of the many computational steps involved. The main aspects of the three schemes are briefly recalled, and the dependence of the results on the computational parameters (number of k points in reciprocal space, toleranc...

Three-dimensional quantum anomalous Hall effect in ferromagnetic insulators

The quantum anomalous Hall effect (QAHE) hosts the dissipationless chiral edge states associated with the nonzero Chern number, providing potentially significant applications in future spintronics. The QAHE usually occurs in a two-dimensional (2D) system with time-reversal symmetry breaking. In this work, we propose that the QAHE can exist in three-dimensional (3D) ferromagnetic insulators. By imposing inversion symmetry, we develop the topological constraints dictating the appearance of 3D QAHE based on the parity analysis at the time-reversal invariant points in reciprocal space. Moreover, using first-principles calculations, we identify that 3D QAHE can be realized in a family of intrinsic ferromagnetic insulating oxides, including layered and non-layered compounds that share a centrosymmetric structure with space group $R\bar{3}m$ (No. 166). The Hall conductivity is quantized to be $-\frac{3e^2}{hc}$ with the lattice constant $c$ along $c$-axis. The chiral surface sheet states are clearly visible and uniquely distributed on the surfaces that are parallel to the magnetic moment. Our findings open a promising pathway to realize the QAHE in 3D ferromagnetic insulators.

Polariton condensation in photonic crystals with high molecular orientation

We study Frenkel exciton-polariton Bose–Einstein condensation in a two-dimensional defect-free triangular photonic crystal with an organic semiconductor active medium containing bound excitons with dipole moments oriented perpendicular to the layers. We find photonic Bloch modes of the structure and consider their strong coupling regime with the excitonic component. Using the Gross–Pitaevskii equation for exciton polaritons and the Boltzmann equation for the external exciton reservoir, we demonstrate the formation of condensate at the points in reciprocal space where photon group velocity equals zero. Further, we demonstrate condensation at non-zero momentum states for transverse magnetic-polarized photons in the case of a system with incoherent pumping, and show that the condensation threshold varies for different points in the reciprocal space, controlled by detuning.

Electronic structure of Cr2AlC as observed by angle-resolved photoemission spectroscopy

We investigate the electronic band structure and Fermi surfaces (FSs) of $\mathrm{C}{\mathrm{r}}_{2}\mathrm{AlC}$ single crystals with angle-resolved photoemission spectroscopy. We evidence hole bands centered around the $M$ points and electron bands centered around the $\mathrm{\ensuremath{\Gamma}}$ point in reciprocal space. Electron and hole bands exhibit an open, tubular structure along the $c$ axis, confirming the quasi-two-dimensional character of this highly anisotropic, nanolamellar compound. Dependence of the photoionization cross sections on beam light polarization and orientation allows us to assess the orbital character of each observed band locally. Despite some differences, density functional theory calculations show a good agreement with experiment.

Entropy as a Gene-Like Performance Indicator Promoting Thermoelectric Materials.

High-throughput explorations of novel thermoelectric materials based on the Materials Genome Initiative paradigm only focus on digging into the structure-property space using nonglobal indicators to design materials with tunable electrical and thermal transport properties. As the genomic units, following the biogene tradition, such indicators include localized crystal structural blocks in real space or band degeneracy at certain points in reciprocal space. However, this nonglobal approach does not consider how real materials differentiate from others. Here, this study successfully develops a strategy of using entropy as the global gene-like performance indicator that shows how multicomponent thermoelectric materials with high entropy can be designed via a high-throughput screening method. Optimizing entropy works as an effective guide to greatly improve the thermoelectric performance through either a significantly depressed lattice thermal conductivity down to its theoretical minimum value and/or via enhancing the crystal structure symmetry to yield large Seebeck coefficients. The entropy engineering using multicomponent crystal structures or other possible techniques provides a new avenue for an improvement of the thermoelectric performance beyond the current methods and approaches.

Band warping, band non-parabolicity, and Dirac points in electronic and lattice structures

We illustrate at a fundamental level the physical and mathematical origins of band warping and band non-parabolicity in electronic and vibrational structures. We point out a robust presence of pairs of topologically induced Dirac points in a primitive-rectangular lattice using a p-type tight-binding approximation. We analyze two-dimensional primitive-rectangular and square Bravais lattices with implications that are expected to generalize to more complex structures. Band warping is shown to arise at the onset of a singular transition to a crystal lattice with a larger symmetry group, which allows the possibility of irreducible representations of higher dimensions, hence band degeneracy, at special symmetry points in reciprocal space. Band warping is incompatible with a multi-dimensional Taylor series expansion, whereas band non-parabolicities are associated with multi-dimensional Taylor series expansions to all orders. Still band non-parabolicities may merge into band warping at the onset of a larger symmetry group. Remarkably, while still maintaining a clear connection with that merging, band non-parabolicities may produce pairs of conical intersections at relatively low-symmetry points. Apparently, such conical intersections are robustly maintained by global topology requirements, rather than any local symmetry protection. For two p-type tight-binding bands, we find such pairs of conical intersections drifting along the edges of restricted Brillouin zones of primitive-rectangular Bravais lattices as lattice constants vary relatively to each other, until these conical intersections merge into degenerate warped bands at high-symmetry points at the onset of a square lattice. The conical intersections that we found appear to have similar topological characteristics as Dirac points extensively studied in graphene and other topological insulators, even though our conical intersections have none of the symmetry complexity and protection afforded by the latter more complex structures.

Topological states at the (001) surface of SrTiO3

Defect-free SrTiO3 (STO) is a band insulator but Angle Resolved Photoemission Spectroscopy (ARPES) experiments have demonstrated the existence of a nanometer thin two-dimensional electron liquid (2DEG) at the (001) oriented surface of this compound. The bulk is a trivial insulator, but our theoretical study reveals that the parity of electronic wavefunctions in this 2DEG is inverted in the vicinity of special points in reciprocal space where the low-energy dispersion consists of four gapped Dirac cones with a tilted and anisotropic shape. This gives rise to linearly dispersing topological edge states at the one-dimensional boundary. We propose to probe these modes by measuring the Josephson radiation from gapless bound Andreev states in STO based junctions, as it is predicted that they display distinctive signatures of topology.

Band structure diagram paths based on crystallography

Systematic and automatic calculations of the electronic band structure are a crucial component of computationally-driven high-throughput materials screening. An algorithm, for any crystal, to derive a unique description of the crystal structure together with a recommended band path is indispensable for this task. The electronic band structure is typically sampled along a path within the first Brillouin zone including the surface in reciprocal space. Some points in reciprocal space have higher site symmetries and/or have higher constraints than other points regarding the electronic band structure and therefore are likely to be more important than other points. This work categorizes points in reciprocal space according to their symmetry and provides recommended band paths that cover all special wavevector (k-vector) points and lines necessarily and sufficiently. Points in reciprocal space are labeled such that there is no conflict with the crystallographic convention. The k-vector coefficients of labeled points, which are located at Brillouin zone face and edge centers as well as vertices, are derived based on a primitive cell compatible with the crystallographic convention, including those with axial ratio-dependent coordinates. Furthermore, we provide an open-source implementation of the algorithms within our SeeK-path python code, to allow researchers to obtain k-vector coefficients and recommended band paths in an automated fashion. Finally, we created a free online service to compute and visualize the first Brillouin zone, labeled k-points and suggested band paths for any crystal structure, that we made available at http://www.materialscloud.org/tools/seekpath/.

Electrons, holes, and spin in the IV-VI monolayer four-six-enes

Bandedge states in the indirect-gap group-IV metal monochalcogenide monolayers ('four-six-enes' such as SnS, GeTe, etc.) inherit the properties of nearby reciprocal space points of high symmetry at the Brillouin zone edge. We employ group theory and the method of invariants to capture these essential symmetries in effective Hamiltonians including spin-orbit coupling, and use perturbation theory to shed light on the nature of the bandedge states. In particular, we show how the structure of derived wavefunctions leads to specific dominant momentum and spin scattering mechanisms for both valence holes and conduction electrons, we analyze the direct optical transitions across the bandgap, and expose the interactions responsible for subtle features of the local dispersion relations.