Entire Brillouin Zone Research Articles

The bain and orthorhombic paths of the bcc–fcc transformation in a bcc metal

The energy of the Bain and orthorhombic paths in niobium and the instability of phonons during uniaxial deformation along <001> are studied with the application of the ab initio method. The orthorhombic transformation path is refined with regard to its symmetry. The calculation of the phonon spectrum in the entire irreducible Brillouin zone depending on deformation makes it possible to find the softest branches of the phonon spectrum responsible for the loss of stability of the structure. The nature of the loss of stability is revealed, and the strain at which stability is lost both in tension and compression is evaluated. Possible mechanisms determining the stability of the structure and theoretical strength of niobium are discussed. The results obtained can relate to experimental situations when small defect-free regions are deformed, for example, in nanostructured materials, when surface layers are modified by modern methods of plastic deformation, and during nanoindentation.

Distinct spin and orbital dynamics in Sr2RuO4

The unconventional superconductor Sr2RuO4 has long served as a benchmark for theories of correlated-electron materials. The determination of the superconducting pairing mechanism requires detailed experimental information on collective bosonic excitations as potential mediators of Cooper pairing. We have used Ru L3-edge resonant inelastic x-ray scattering to obtain comprehensive maps of the electronic excitations of Sr2RuO4 over the entire Brillouin zone. We observe multiple branches of dispersive spin and orbital excitations associated with distinctly different energy scales. The spin and orbital dynamical response functions calculated within the dynamical mean-field theory are in excellent agreement with the experimental data. Our results highlight the Hund metal nature of Sr2RuO4 and provide key information for the understanding of its unconventional superconductivity.

Direct Observation of Topological Phonons in Graphene.

Phonons, as the most fundamental emergent bosons in condensed matter systems, play an essential role in the thermal, mechanical, and electronic properties of crystalline materials. Recently, the concept of topology has been introduced to phonon systems, and the nontrivial topological states also exist in phonons due to the constraint by the crystal symmetry of the space group. Although the classification of various topological phonons has been enriched theoretically, experimental studies were limited to several three-dimensional (3D) single crystals with inelastic x-ray or neutron scatterings. The experimental evidence of topological phonons in two-dimensional (2D) materials is absent. Here, using high-resolution electron energy loss spectroscopy following our theoretical predictions, we directly map out the phonon spectra of the atomically thin graphene in the entire 2D Brillouin zone, and observe two nodal-ring phonons and four Dirac phonons. The closed loops of nodal-ring phonons and the conical structure of Dirac phonons in 2D momentum space are clearly revealed by our measurements, in nice agreement with our theoretical calculations. The ability of 3D mapping (2D momentum space and energy space) of phonon spectra opens up a new avenue to the systematic identification of the topological phononic states. Our work lays a solid foundation for potential applications of topological phonons in superconductivity, dynamic instability, and phonon diode.

(Invited) Unraveling Electron-Phonon Coupling in 2D Materials in Momentum and Time with Ultrafast Electron Diffuse Scattering (UEDS)

The nature of the couplings within and between lattice and charge degrees of freedom is central to an understanding of electrical and heat transport in materials. These interactions are essential to phenomena as diverse as superconductivity, charge density waves and carrier mobility in semiconductors and metals. Despite their fundamental role, detailed momentum-dependent information on the strength of electron-phonon coupling (EPC) and phonon-phonon coupling (PPC) across the entire Brillouin zone has proved to be very difficult to obtain.I will describe an emerging pump-probe technique, ultrafast electron diffuse scattering (UEDS), that provides such information from the perspective of the phonon system directly. Recent examples of the application of UEDS to layered (2D) materials will be the focus. First, in the thermoelectric material SnSe – a strongly polar semiconductor – we directly observe the phonon dressing processes that yield carrier localization and polaron formation with UEDS. In SnSe these phonon dressing dynamics are profoundly bimodal, with the fast (300 fs) process associated with the formation of a quasi-1D lattice distortion and a relatively large polaron and the slower (4 ps, an order of magnitude slower timescale) process associated with small polaron formation. The observations in SnSe are consistent with electron and hole polarons being different sizes, or the process of polaron formation being instrincially bimodal for both carriers in a manner reminiscent of Lars Onsager’s inverse snowball effect. Second, the extension of UEDS to a MoS2 monolayer heterostructure will be demonstrated. These results reveal substrate dielectric screening of the electron-phonon interaction within the monolayer as well as the monomentum-dependent carrier-phonon equilibration. These results are compared directly against ab-initio simulations of these processes Figure 1

Time-, spin-, and angle-resolved photoemission spectroscopy with a 1-MHz 10.7-eV pulse laser.

We describe a setup of time-, spin-, and angle-resolved photoemission spectroscopy (tr-SARPES) employing a 10.7 eV (λ = 115.6nm) pulse laser at a 1MHz repetition rate as a probe photon source. This equipment effectively combines the technologies of a high-power Yb:fiber laser, ultraviolet-driven harmonic generation in Xe gas, and a SARPES apparatus equipped with very-low-energy-electron-diffraction spin detectors. A high repetition rate (1MHz) of the probe laser allows experiments with the photoemission space-charge effects significantly reduced, despite a high flux of 1013 photons/s on the sample. The relatively high photon energy (10.7eV) also brings the capability of observing a wide momentum range that covers the entire Brillouin zone of many materials while ensuring high momentum resolution. The experimental setup overcomes the low efficiency of spin-resolved measurements, which gets even more severe for the pump-probed unoccupied states, and affords the opportunity to investigate ultrafast electron and spin dynamics of modern quantum materials with energy and time resolutions of 25meV and 360fs, respectively.

Straight and twisted Weyl nodal line phonons in Ho2CF2 material

Based on first-principles calculations, symmetry analysis and model construction, we predict that Ho2CF2 hosts both straight and twisted Weyl nodal lines in its bulk phonon spectrum. We identify that the top two phonon bands entangle with each other, forming two straight Weyl nodal lines on the K–H and K′–H′ paths at the Brillouin zone (BZ) boundary, and six twisted Weyl nodal lines within the BZ. All the Weyl nodal lines along the kz direction and across the entire BZ. The symmetry analysis indicates that these Weyl nodal lines are protected by the symmetry and crystal symmetry. The Berry phase and drumhead-like nontrivial surface states are calculated. We also construct a tight-binding model to describe these nodal lines. Our work provides an excellent material platform for exploring the fascinating physics associated with straight and twisted Weyl nodal line phonons.

Multi-dimensional band structure spectroscopy in the synthetic frequency dimension

The concept of synthetic dimensions in photonics provides a versatile platform in exploring multi-dimensional physics. Many of these physics are characterized by band structures in more than one dimensions. Existing efforts on band structure measurements in the photonic synthetic frequency dimension however are limited to either one-dimensional Brillouin zones or one-dimensional subsets of multi-dimensional Brillouin zones. Here we theoretically propose and experimentally demonstrate a method to fully measure multi-dimensional band structures in the synthetic frequency dimension. We use a single photonic resonator under dynamical modulation to create a multi-dimensional synthetic frequency lattice. We show that the band structure of such a lattice over the entire multi-dimensional Brillouin zone can be measured by introducing a gauge potential into the lattice Hamiltonian. Using this method, we perform experimental measurements of two-dimensional band structures of a Hermitian and a non-Hermitian Hamiltonian. The measurements reveal some of the general properties of point-gap topology of the non-Hermitian Hamiltonian in more than one dimensions. Our results demonstrate experimental capabilities to fully characterize high-dimensional physical phenomena in the photonic synthetic frequency dimension.

Assessment of tight-binding models for high-harmonic generation in zinc blende materials.

Using a simulator for semiconductor Bloch equations (SBEs) accounting for the entire Brillouin zone, we examine the tight-binding (TB) description for zinc blende structure as a model for high-harmonic generation (HHG). We demonstrate that TB models of GaAs and ZnSe exhibit second-order nonlinear coefficients that compare favorably with measurements. For the higher-order portion of the spectrum, we use the results published by Xia et al. in Opt. Express26, 29393 (2018)10.1364/OE.26.029393 and show that the HHG spectra measured in reflection can be closely reproduced by our simulations free of adjustable parameters. We conclude that despite their relative simplicity, the TB models of GaAs and ZnSe represent useful tools to study both the low- and higher-order harmonic response in realistic simulations.

Anisotropic Phonon Bands in H-Bonded Molecular Crystals: The Instructive Case of α-Quinacridone

Phonons play a crucial role in the thermodynamic and transport properties of solid materials. Nevertheless, rather little is known about phonons in organic semiconductors. Thus, we employ highly reliable quantum mechanical calculations for studying the phonons in the α-polymorph of quinacridone. This material is particularly interesting, as it has highly anisotropic properties with distinctly different bonding types (H-bonding, π-stacking, and dispersion interactions) in different spatial directions. By calculating the overlaps of modes in molecular quinacridone and the α-polymorph, we associate Γ-point phonons with molecular vibrations to get a first impression of the impact of the crystalline environment. The situation becomes considerably more complex when analyzing phonons in the entire 1st Brillouin zone, where, due to the low symmetry of α-quinacridone, a multitude of avoided band crossings occur. At these, the character of the phonon modes typically switches, as can be inferred from mode participation ratios and mode longitudinalities. Notably, avoided crossings are observed not only as a function of the length but also as a function of the direction of the phonon wave vector. Analyzing these avoided crossings reveals how it is possible that the highest frequency acoustic band is always the one with the largest longitudinality, although longitudinal phonons in different crystalline directions are characterized by fundamentally different molecular displacements. The multiple avoided crossings also give rise to a particularly complex angular dependence of the group velocities, but combining the insights from the various studied quantities still allows drawing general conclusions, e.g., on the relative energetics of longitudinal vs transverse deformations (i.e., compressions and expansions vs slips of neighboring molecules). They also reveal how phonon transport in α-quinacridone is impacted by the reinforcing H-bonds and by π-stacking interactions (resulting from a complex superposition of van der Waals, charge penetration, and exchange repulsion).

Strain tuning of the electronic structure and optical properties of novel Janus MgBrI monolayer: Insights from first-principles calculations

Using first-principles calculations in the framework of density functional theory (DFT), we systematically carry out the dynamic stability, electronic and optical properties of the Janus MgBrI monolayer and its parent MgI2 and MgBr2 monolayers. Our findings show that these systems have no imaginary frequencies in the entire Brillouin zone (BZ), which means they are very stable. At the equilibrium state, the results indicate that the Janus MgBrI monolayer is a direct band gap insulator with an energy gap of 3.475 eV, which is smaller than the bandgap of MgI2 and MgBr2 monolayers. The studied optical properties including the complex dielectric function, refractive index, reflectivity, extinction coefficient and absorption coefficient as a function of the photon energy have been investigated. The absorption coefficient shows a strong absorption of the light in the ultraviolet (UV) region. We studied how biaxial strain effects the electronic and optical properties of the Janus MgBrI monolayer. When the strain ranged from −10% to 10%, the Janus MgBrI monolayer showed an insulator characteristic with a direct band gap, which changed to an indirect band gap when the biaxial compressive strain was −10%. In addition, the Janus MgBrI displays an absorption of around 105 cm−1 in the ultra-violet (UV) region. Our results highlight an intriguing new two-dimensional (2D) material that could be used in optoelectronic devices and UV absorbers.

Formation of the solid-state high-order harmonic generation plateau through destructive interference

In frequently studied two-band models for solid-state high-order harmonic generation, interband harmonics, in principle, can range from the minimum to the maximum band gap. However, it is known that a laser-intensity-dependent cutoff exists that may be well below the maximum band gap unless the laser intensity is so high that the electrons explore the entire Brillouin zone. We show that this laser-intensity-dependent cutoff is formed by destructive interference of the emission of electrons starting at different initial states in the Brillouin zone. The calculations in this work are for Su-Schrieffer-Heeger chains, but our findings apply to other two-band systems as well. The destructive interference is complete and forms the cutoff only when the sampling of the Brillouin zone is fine enough or, equivalently, a finite chain is long enough in position space. For coarser sampling and shorter chains all harmonics between minimum and maximum band gap are emitted. A time-frequency analysis shows how certain trajectories are responsible for the formation of the cutoff.

Tuning the Photoluminescence and Raman Response of Single-Layer WS2 Crystals Using Biaxial Strain

Chemical vapor deposited WS2 monolayers are subjected for the first time to controlled pure biaxial tensile strain up to 0.7%. From photoluminescence (PL) spectroscopy, the trion and neutral exciton deformation potentials are found to be similar, approximately −130 meV/%. It is shown that the excess carrier concentration as well as residual strain in WS2 samples can be determined from the PL spectra. The experimental Grüneisen parameter of the in-plane E′ Raman mode for 1L-WS2 is found to be equal to the corresponding mode (E2g) mode in bulk WS2. The impact of mechanical strain on the electronic and phonon band structures is also calculated in the framework of density functional theory. The theoretically obtained deformation potential for the direct transition is in very good agreement with the experiment. The reduced dimensionality of the monolayer enables the visualization over the entire Brillouin zone of both the calculated phonon dispersions and the Grüneisen parameters, which are compared with the experimentally accessible ones. This work contributes to the experimental implementation of mechanical strain engineering applications in semiconducting two-dimensional transition metal dichalcogenides.

Complex Berry phase and imperfect non-Hermitian phase transitions

In many classical and quantum systems described by an effective non-Hermitian Hamiltonian, spectral phase transitions, from an entirely real-energy spectrum to a complex spectrum, can be observed as a non-Hermitian parameter in the system is increased above a critical value. A paradigmatic example is provided by systems possessing parity-time ($\mathcal{PT}$) symmetry, where the energy spectrum remains entirely real in the unbroken $\mathcal{PT}$ phase while a transition to complex energies is observed in the broken $\mathcal{PT}$ phase. Such spectral phase transitions are universally sharp. However, when the system is slowly and periodically cycled, the phase transition can become smooth, i.e., imperfect, owing to the complex Berry phase associated to the cyclic adiabatic evolution of the system. This remarkable phenomenon is illustrated by considering the spectral phase transition of the Wannier-Stark ladders in a $\mathcal{PT}$-symmetric class of two-band non-Hermitian lattices subjected to an external dc field, revealing that a nonvanishing imaginary part of the Zak phase---the Berry phase picked up by a Bloch eigenstate evolving across the entire Brillouin zone---is responsible for imperfect spectral phase transitions.

Spinful Topological Phases in Acoustic Crystals with Projective PT Symmetry.

For the classification of topological phases of matter, an important consideration is whether a system is spinless or spinful, as these two classes have distinct symmetry algebra that gives rise to fundamentally different topological phases. However, only recently has it been realized theoretically that in the presence of gauge symmetry, the algebraic structure of symmetries can be projectively represented, which possibly enables the switch between spinless and spinful topological phases. Here, we report the experimental demonstration of this idea by realizing spinful topological phases in "spinless" acoustic crystals with projective space-time inversion symmetry. In particular, we realize a one-dimensional topologically gapped phase characterized by a 2Z winding number, which features double-degenerate bands in the entire Brillouin zone and two pairs of degenerate topological boundary modes. Our Letter thus overcomes a fundamental constraint on topological phases by spin classes.

Nonlinear wave propagation analysis in architected materials with consideration of extension, shear and bending effects

The current paper deals with the wave dispersion characteristics of two-dimensional architected materials, considering both the linear and nonlinear regimes. We study the full non-linear coupling between the shear, extension, and bending deformation modes on the inner material deformation of the square, triangular, hexagonal, and re-entrant hexagonal unit cells. The dynamical analysis is done at high and low frequencies and for two different wave amplitudes. Based on the Linstedt–Poincare perturbation method, the non-linear correction to the dispersion diagram is evaluated. The relative contribution of each non-linear energy mode on the nonlinear wave dispersion attributes is quantified. The obtained results show that both the wavenumber and lattice design play an important role in the nonlinear wave corrections of the dispersion characteristics. The shear mode is shown to have the highest effect in the non-linear correction for all considered architected materials, compared to the flexural mode, which has the lowest energy contribution. The eigenwaves vectors are used to compare the deformation of hexagonal and re-entrant hexagonal unit cells at low and high frequencies over the entire Brillouin zone. Overall, the present work provides some guideline as to the proper selection of the inner design of architected materials prone to strong nonlinear dynamical effects.

Full-Brillouin-zone calculation of high-order harmonic generation from solid-state media

Solid-state high-order harmonic generation (HHG) continues to attract a lot of interest. From the theory and simulation standpoint, two issues are still open; The first is the so-called transition-dipole phase problem. It has been recognized that the dipoles must be treated as complex-valued quantities and that their corresponding Berry connections must be included to ensure phase-gauge invariance. However, while this has been successfully implemented for lower-dimensional systems, fully vectorial and three-dimensional simulations remain challenging. The second issue concerns the symmetry of the high-order harmonic response, when simulations sometimes fail to honor the symmetry of the crystalline material. This work addresses both of these problems with the help of a HHG-simulation approach which (a) is manifestly free of the transition-dipole phase problem, (b) does not require calculation of dipole moments, (c) can account for the contributions from the entire Brillouin zone, and (d) faithfully preserves the symmetry of the simulated crystalline material. We use the method to show that high-order harmonic sources are distributed throughout the Brillouin zone with various phase shifts giving rise to significant cancellations. As a consequence, for the simulated response to correctly capture the material symmetry, contributions from the entire Brillouin zone must be included. Our results have important implications for a number of HHG applications, including all-optical band and dipole reconstruction.

Active Metadamping: A phenomenon of damping enhancement in metamaterial via feedback control

Metadamping is defined as the enhancement of dissipation (or the damped response) of an acoustic metamaterial over an equivalent phononic crystal for the same amount of prescribed damping.The emergence of metadamping and decay coefficient in conjunction with active feedback control is the prime novelty of this paper. The wave-number-dependent active metadamping is defined as the difference between the damping ratio of the active-controlled and that of the uncontrolled metamaterial to indicate its improved energy dissipation. The controller design is based on the Linear Quadratic Regulator with output feedback of velocity, and displacement as well as velocity. The damping emergence metric over the entire Brillouin zone is obtained from the dispersion relationship by applying Bloch’s theorem, and a parametric study is performed to get an insight into the metadamping phenomenon. Velocity feedback control (VC) provides the highest value of total damping ratio when compared to the case of displacement- and velocity-based feedback control (DVC) for an identical long wave sound speed; however, at the expense of reduced attenuation bandwidth. The decay coefficient of DVC is higher compared to that of VC up to a threshold of long wave speed of sound. Beyond that threshold, both VC and DVC provide almost equal decay. We identified the possibility of obtaining high damping in a stiff metamaterial via active control, which will be useful for applications in the field of vibrations and acoustics, impact mitigation, shock absorption, and vehicle dynamics.

Numerical package for QFT calculations of defect-induced phenomena in graphene

We introduce a computationally efficient method based on the path integral formalism to describe defect-modified graphene. By taking into account the entire Brillouin zone, our approach respects the lattice symmetry and can be used to investigate both short-range and long-range effects. The proposed method’s key advantage is that the computational complexity does not increase with the system size, scaling, instead, with the number of defects. Our aim is to make the quantum-field calculations in graphene accessible to the experimental community. We demonstrate our method’s capabilities by exploring the well-known graphene-mediated Ruderman–Kittel–Kasuya–Yoshida interaction and by performing a detailed study of the atomic collapse in the presence of defects.

Topological photonics by breaking the degeneracy of line node singularities in semimetal-like photonic crystals.

Degeneracy is an omnipresent phenomenon in various physical systems, which has its roots in the preservation of geometrical symmetry. In electronic and photonic crystal systems, very often this degeneracy can be broken by virtue of strong interactions between photonic modes of the same energy, where the level repulsion and the hybridization between modes causes the emergence of photonic bandgaps. However, most often this phenomenon does not lead to a complete and inverted bandgap formation over the entire Brillouin zone. Here, by systematically breaking the symmetry of a two-dimensional square photonic crystal, we investigate the formation of Dirac points, line node singularities, and inverted bandgaps. The formation of this complete bandgap is due to the level repulsion between degenerate modes along the line nodes of a semimetal-like photonic crystal, over the entire Brillouin zone. Our numerical experiments are performed by a home-build numerical framework based on a multigrid finite element method. The developed numerical toolbox and our observations pave the way towards designing complete bandgap photonic crystals and exploring the role of symmetry on the optical behaviour of even more complicated orders in photonic crystal systems.

Excitations in the Ordered and Paramagnetic States of Honeycomb Magnet Na_{2}Co_{2}TeO_{6}.

Na_{2}Co_{2}TeO_{6} is a proposed approximate Kitaev magnet, yet its actual magnetic interactions are elusive due to a lack of knowledge on the full excitation spectrum. Here, using inelastic neutron scattering and single crystals, we determine the system's temperature-dependent magnetic excitations over the entire Brillouin zone. Without committing to specific models, we unveil a distinct signature of the third-nearest-neighbor coupling in the spin waves, which signifies the associated distance as an emerging effective link in the ordered state. The presence of at least six nonoverlapping spin-wave branches is at odds with all models proposed to date. Above the ordering temperature, persisting dynamic correlations can be described by equal-time magnetic structure factors of a hexagonal cluster, which reveal the leading instabilities. Our result sets definitive constraints on theoretical models for Na_{2}Co_{2}TeO_{6} and provides new insight for the materialization of the Kitaev model.