Bloch Wave Research Articles

A mechanistic evaluation of the local Bloch wave approximation in graded arrays of vertical barriers

Wave interaction with graded metamaterials exhibits the phenomenon of rainbow reflection, in which broadband wave signals slow down and separate into their frequency components before being reflected. This phenomenon has been qualitatively understood by describing the wave field in the metamaterial using the local Bloch wave approximation (LBWA), which locally represents the wave field as a superposition of propagating wave solutions in the cognate infinite periodic media (so-called Bloch waves). We evaluate the performance of the LBWA quantitatively in the context of two-dimensional linear water-wave scattering by graded arrays of surface-piercing vertical barriers. To do this, we implement the LBWA numerically so that the Bloch waves in one region of the graded array are coupled to Bloch waves in adjacent regions. This coupling is computed by solving the scattering of Bloch waves across the interface between two semi-infinite arrays of vertical barriers, where the barriers in each semi-infinite array can have different submergence depths. Our results suggest that the LBWA accurately predicts the free surface amplitude across a wide range of frequencies, except those just above the cutoff frequencies associated with each of the vertical barriers in the array. This highlights the importance of decaying Bloch modes above the cutoff in rainbow reflection.

Geometric Aspects of Nonlinear and Nonequilibrium Phenomena

We review recent developments in the research of nonlinear and nonequilibrium phenomena in solids focusing on their geometrical aspects. We start with introducing the basic concepts of geometrical phases of Bloch electrons and Floquet theory for periodically driven systems. Then we review recent attempts to engineer topological phases in nonequilibrium matters such as graphene, magnets, and superconductors irradiated with circularly polarized light. We next review a bulk photovoltaic effect of inversion broken materials focusing on the shift current response. The shift current is described with Berry connections and has a close relationship to the modern theory of polarization. We further review recent extensions of the shift current to correlated electron systems. Finally, we explain the geometric diabatic time evolution in the Zener tunneling process and its consequences on nonreciprocal transport.

Study on Bandgap Property of Three‐Dimensional Star‐Like Double‐Arrow Lattice

Herein, a three‐dimensional star‐like double‐arrow lattice is proposed, which is inspired by the double‐arrow structure. Based on Bloch's theorem and finite element method, the calculation program is made up and the band structures are calculated. The calculation results demonstrate that the bandgap property of the double‐arrow lattice is improved compared with that of a cross lattice. The parametric study is carried out and geometric parameters have strong effects on the bandgap property. As the angle between the external edge and symmetric line increases, the total bandgap width increases apparently, and the opening frequency of low‐order bandgap decreases. This phenomenon reflects that the low‐frequency bandgap property is improved. Via the isosurface of phase velocity and group velocity, the anisotropy is investigated. Strong anisotropy and energy focus appear, which can be used to design waveguides.

Band structures analysis of fluid–solid phononic crystals using wavelet‐based boundary element method and frequency‐independent fundamental solutions

AbstractA novel method of combination of wavelet‐based boundary element method (WBEM) with frequency‐independent fundamental solutions is proposed to determine the band structures of fluid–solid phononic crystals (PCs) with square and triangular lattices. Integral equations established are based on the frequency‐independent fundamental solutions, which can avoid nonlinear eigenvalue problems and reduce computing time. Domain integral terms arising from the use of frequency‐independent fundamental solutions are handled with the radial integration method (RIM) and dual reciprocity method (DRM), respectively. The results show the lower precision in high frequency domain of using RIM to handle domain integral terms than that of using DRM, which can be solved by increasing Gauss point. The B‐spline wavelet on the interval and wavelet coefficients are applied to approximate the physical boundary conditions. It is proved that coupling conditions between matrix and scatterers and Bloch theorem are also applicable to wavelet coefficients. Some small matrix entries generated by wavelet vanishing moment characteristics are truncated by the provided matrix compression technique, and the influence of compressed matrices on the results is studied. Furthermore, the final Eigen equations constructed are modified to avoid numerical instability. Some examples are provided to demonstrate the accuracy and efficiency of the proposed method.

Observation of flat band, Dirac nodal lines and topological surface states in Kagome superconductor CsTi3Bi5

Kagome lattices of various transition metals are versatile platforms for achieving anomalous Hall effects, unconventional charge-density wave orders and quantum spin liquid phenomena due to the strong correlations, spin-orbit coupling and/or magnetic interactions involved in such a lattice. Here, we use laser-based angle-resolved photoemission spectroscopy in combination with density functional theory calculations to investigate the electronic structure of the newly discovered kagome superconductor CsTi3Bi5, which is isostructural to the AV3Sb5 (A = K, Rb or Cs) kagome superconductor family and possesses a two-dimensional kagome network of titanium. We directly observe a striking flat band derived from the local destructive interference of Bloch wave functions within the kagome lattice. In agreement with calculations, we identify type-II and type-III Dirac nodal lines and their momentum distribution in CsTi3Bi5 from the measured electronic structures. In addition, around the Brillouin zone centre, {{mathbb{Z}}}_{2} nontrivial topological surface states are also observed due to band inversion mediated by strong spin-orbit coupling.

Pair density wave facilitated by Bloch quantum geometry in nearly flat band multiorbital superconductors

Bloch electrons in multiorbital systems carry quantum geometric information characteristic of their wavevector-dependent interorbital mixing. The geometric nature impacts electromagnetic responses, and this effect carries over to the superconducting state, which receives a geometric contribution to the superfluid weight. In this paper, we show that this contribution could become negative under certain appropriate circumstances. This may facilitate the stabilization of Cooper pairings with real space phase modulation, i.e. the pair density wave order, as we demonstrate through two-orbital model Bogoliubov de-Gennes mean-field calculations. The quantum geometric effect therefore constitutes an intrinsic mechanism for the formation of such a novel phase of matter in the absence of external magnetic field.

Harnessing chiral buckling structure to design tunable local resonance metamaterial for low-frequency vibration isolation

This paper proposes a tunable local resonance metamaterial with chiral buckling structures for low-frequency vibration isolation. The unit cell consists of the inner and outer buckling stiffness structure, basic structure, and local resonator. The bistability of three kinds of unit cells with different initial shapes of beams is investigated and compared via the elliptic integral method and finite element analysis. Then, their axial stiffness in different states is studied. The dynamic responses of the metamaterial with simple unit cells and hybrid supercells are theoretically derived and analyzed by Bloch's theorem and transfer coefficient method. Theoretical, numerical, and experimental results demonstrate that the unit cell with initially convex downward beams has strong bistability and determinate deformation modes. The axial stiffness of the unit cell in two stable states differs by an order of magnitude. Changing some specific parameters broadens the gap in the axial stiffness between the two stable states. The axial negative stiffness characteristics and rotation effect of the unit cell have the potential for energy dissipation and tensile-torsion material. The metamaterial with simple unit cells has tunable and wide band gap and low-frequency vibration isolation via the stable states switching of the inner and outer buckling stiffness structures. The metamaterial with hybrid supercells can further broaden the band gap width and lower the band gap frequency, which has up to 16 different band gap characteristics.

One-dimensional photonic crystal magnetic sensor design based on Bloch surface waves with high sensitivity and high figure of merit (FOM)

A novel Bloch surface wave (BSW)-based one-dimensional photonic crystal magnetic sensor is proposed. Grating is used to realize the coupling of electromagnetic waves and BSW, and magnetic fluid is placed at the bottom of the sensor as the sensing medium. The sensing characteristics of a one-dimensional photonic crystal magnetic sensor were analyzed using the rigorous coupled wave analysis (RCWA) method. Based on the azimuthal interrogation method, the effects of different pole angles, defect layers, and structural parameters on sensitivity and figure of merit (FOM) were investigated. According to the drift of the resonance peak, the azimuthal sensitivity S = 9 °/mT, and the maximum detection sensitivity S = 14 °/mT were obtained (converted to refractive index sensitivity S = 6536 °/RIU and maximum detection sensitivity S = 9333 °/RIU). Excitingly, we found that the introduction of a defective layer can significantly improve the FOM (1925 RIU-1 to 69,444 RIU-1). The results show that the designed magnetic sensor structure has high sensitivity and a high FOM, which is an order of magnitude higher than other magnetic sensors. This work provides a guideline for the future development of one-dimensional photonic crystals in the field of weak magnetic sensing.

Ultra-high sensitivity Bloch surface wave biosensor design and optimization

In this paper, lithium niobate is used as a grating-coupling layer and Bragg reflector defect layer to couple the incident light and break the periodicity of the photonic crystal, which results in localized electric field enhancement and the excitation of Bloch surface waves. By adjusting the incident angle of the light, the structure can achieve two detection modes: surface diffraction detection and guided mode Bloch detection. The average detection sensitivities for the two modes are 452°/RIU and 3170°/RIU, respectively, with maximum detection sensitivities of 480°/RIU and 4380°/RIU. The designed guided mode Bloch detection has the highest sensitivity currently known.

Geometry and topological photonics

Topological photonics provides a powerful framework to describe and understand many nontrivial wave phenomena in complex electromagnetic platforms. The topological index of a physical system is an abstract global property that depends on the family of operators that describes the propagation of Bloch waves. Here, we highlight that there is a profound geometrical connection between topological physics and the topological theory of mathematical surfaces. We show that topological band theory can be understood as a generalization of the topological theory of surfaces and that the genus of a surface can be regarded as a Chern number of a suitable operator defined over the surface. We point out some nontrivial implications of topology in the context of radiation problems and discuss why for physical problems the topological index is often associated with a bulk-edge correspondence.

Rashba-like spin splitting around non-time-reversal-invariant momenta

The ubiquitous Rashba spin splitting occurring around time-reversal-invariant momenta (TRIM) reflects the fundamental interplay between spin-orbit coupling (SOC) and crystalline symmetry. Unexpectedly, recent measurements reveal novel Rashba spin splitting around the momenta lacking time-reversal symmetry (non-TRIM), whose mechanism remains elusive. Here, we theoretically elucidate the microscopic origin of Rashba spin splitting around non-TRIM and identify the design principles for its appearance. Conventionally, a Zeeman-like spin splitting dominates around non-TRIM due to the broken time-reversal symmetry and diminishes the Rashba-like features. Our results show that the Bloch wave function with specific orbital representation at certain non-TRIM could eliminate the first-order SOC effect. As a result, the corresponding little group hosts a type of quasisymmetry that commutes with the dominating SOC Hamiltonian, leading to a tiny SOC gap and helical spin texture. Furthermore, such a quasi-symmetry-induced tiny gap could manifest large Berry curvature, which is desirable for various topological applications. Our work expands the concept of Rashba physics beyond the conventional TRIM scenario, paving an avenue for designing novel spin-splitting materials through the cooperation of symmetry and orbital engineering.

An eigenvalue method based on the integral equation with a Rankine source for the band structure of water surface waves over periodic scatterers

An eigenvalue model is developed to obtain the band structure of water surface waves in the presence of an infinite array of periodically arranged scatterers, which include both underwater terrains and fixed bodies on the free surface or in the water. Combined with Bloch's theorem, the scattering of waves over arbitrary terrain or bodies is described as a boundary value problem of the Laplace equation, from which the boundary integral equation can be derived and transformed into an eigenvalue problem through the boundary element method to obtain the band structure of water surface waves. Comparisons are made with various existing models and reflection coefficients from experiments, which shows the validity and accuracy of the proposed model.As an application of the present model, the stopbands for convex parabolic terrain, concave parabolic terrain, sinusoidal terrain and cylinders with centres on the still water surface are calculated. The dependence of the stopbands on the relative size of scatterers and relative water depth is investigated and analysed.

Bandgap and wave attenuation optimization of tetra-chiral metamaterial using PSO algorithm

The development of vibration suppression systems with desired efficiency and low cost is one of the significant challenges in engineering. In this study, a parametric lattice model is considered to analyze the wave mitigation features in the metamaterial based on a tetra-chiral topology of the periodic cell equipped with internal resonators. Bloch wave theorem and finite element method are employed to explore the bandgap of the structure and its wave mitigation features. Since the unit cell geometry can be designed to open and shift bandgaps, particle swarm optimization algorithm is used to find the largest possible gap in the desired frequency range. The optimization method is programmed using MATLAB combined with an in-house finite element solver, considering the parameters' ranges to ensure geometric compatibility. In all studied cases, the optimized geometry leads to superior vibration suppression and larger complete bandgaps.

Origin of surface and subband states at the InAs(111)A surface

The atomic structure of surfaces and interfaces plays a vital role in the electronic quality and properties of quantum devices. The interplay between the surface and confined bulk subband states in terms of their susceptibility has been investigated in relation to crystal defects on an InAs(111)A-$(2\ifmmode\times\else\texttimes\fi{}2)$ reconstructed surface, using low-temperature scanning tunneling microscopy and spectroscopy. We measure the two-dimensional quantized subband states arising from the confined potential imposed by downward bending of the conduction band edge. Furthermore, we show evidence of the existence of surface Bloch states within the confined bulk band gap projected on the surface spectrum which have originated from the surface reconstruction. As expected, larger confined bulk band gaps at the surface and conduction band offset are measured to be 0.58 and 0.31 eV, respectively. We further show the scattering of these quantum states at different surface defects and demonstrate that surface states are more susceptible to the defect potential when compared with the corresponding subband states. This apparent contrast follows from the length scale at which these defect potentials actively interact on or near the surface. Our observed experimental results are supported by empirical tight-binding simulations for the subband states and first-principles density functional theory simulations for the surface states present on the surface.

Symmetry-conserving maximally projected Wannier functions

Wannier functions are a powerful tool for the determination of topological properties of solids based on band structure calculations. Here, the authors present a simple and efficient scheme to obtain symmetry-conserving Wannier functions especially suitable for local orbital codes. They analyze which approximation of the basis contribution to the Berry connection and curvature matrices preserves symmetry and argue which Bloch function gauge is best suited for model systems, where the basis is not explicitly known.

Active sites of Te-hyperdoped silicon by hard x-ray photoelectron spectroscopy

Multiple dopant configurations of Te impurities in close vicinity in silicon are investigated using photoelectron spectroscopy, photoelectron diffraction, and Bloch wave calculations. The samples are prepared by ion implantation followed by pulsed laser annealing. The dopant concentration is variable and high above the solubility limit of Te in silicon. The configurations in question are distinguished from isolated Te impurities by a strong chemical core level shift. While Te clusters are found to form only in very small concentrations, multi-Te configurations of type dimer or up to four Te ions surrounding a vacancy are clearly identified. For these configurations, a substitutional site location of Te is found to match the data best in all cases. For isolated Te ions, this matches the expectations. For multi-Te configurations, the results contribute to understanding the exceptional activation of free charge carriers in hyperdoping of chalcogens in silicon.

Algebra of hyperbolic band theory under magnetic field

We explore algebras associated with the hyperbolic band theory under a magnetic field for the first time. We define the magnetic Fuchsian group associated with a higher genus Riemann surface. By imposing the magnetic boundary conditions for the hyperbolic Bloch states, we construct the hyperbolic magnetic Bloch states and investigate their energy spectrum. We give a connection between such magnetic Bloch states and automorphic forms. Our theory is a general extension of the conventional algebra associated with the band theory defined on a Euclidean lattice/space into that of the band theory on a general hyperbolic lattice/Riemann surface.

Generation of Bloch surface beams with arbitrarily designed phases.

We proposed a new manipulation method for Bloch surface waves that can almost arbitrarily modulate the lateral phase through in-plane wave-vector matching. The Bloch surface beam is generated by a laser beam from a glass substrate incident on a carefully designed nanoarray structure, which can provide the missing momentum between the two beams and set the required initial phase of the Bloch surface beam. An internal mode was used as a channel between the incident and surface beams to improve the excitation efficiency. Using this method, we successfully realized and demonstrated the properties of various Bloch surface beams, including subwavelength-focused, self-accelerating Airy, and diffraction-free collimated beams. This manipulation method, along with the generated Bloch surface beams, will facilitate the development of two-dimensional optical systems and benefit potential applications of lab-on-chip photonic integrations.

Symmetric Wannier states and tight-binding model for quantum spin Hall bands in AB -stacked MoTe2/WSe2

Motivated by the observation of topological states in AB-stacked MoTe$_2$/WSe$_2$, we construct the symmetry-adapted Wannier states and tight-binding model for the quantum spin Hall bands in this system. Our construction is based on the symmetry analysis of Bloch states obtained from the continuum moir\'e Hamiltonian. For model parameters extracted from first-principles calculations, we find that the quantum spin Hall bands can be described by a tight-binding model defined on a triangular lattice. There are two Wannier states per valley, which have the same Wannier center but different angular momenta under threefold rotation. The tight-binding model not only reproduces the energy spectrum, but also accurately describes the topological phase transition induced by the out-of-plane displacement field. Our study sheds new light on the topological states in moir\'e transition metal dichalcogenides bilayers, and provides a route to addressing the many-body physics in AB-stacked MoTe$_2$/WSe$_2$.

Extracting quantum-geometric effects from Ginzburg-Landau theory in a multiband Hubbard model

We first apply functional-integral approach to a multiband Hubbard model near the critical pairing temperature, and derive a generic effective action that is quartic in the fluctuations of the pairing order parameter. Then we consider time-reversal-symmetric systems with uniform (i.e., at both low-momentum and low-frequency) pairing fluctuations in a unit cell, and derive the corresponding time-dependent Ginzburg-Landau (TDGL) equation. In addition to the conventional intraband contribution that depends on the derivatives of the Bloch bands, we show that the kinetic coefficients of the TDGL equation have a geometric contribution that is controlled by both the quantum-metric tensor of the underlying Bloch states and their band-resolved quantum-metric tensors. Furthermore we show that thermodynamic properties such as London penetration depth, GL coherence length, GL parameter and upper critical magnetic field have an explicit dependence on quantum geometry.