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In-plane anisotropic layered materials (ALMs), such as black phosphorus (BP), exhibit unique angle-resolved polarized Raman (ARPR) spectroscopy characteristics, as attributed to birefringence, linear dichroism and complex Raman tensor. Moreover, the ARPR intensity profiles of BP flakes deposited on multilayer dielectrics are notably sensitive to their thickness, owing to interference effects. The intricate anisotropic effects present challenges in accurately predicting the ARPR intensity of BP flakes. In this study, we propose a comprehensive strategy for predicting the ARPR intensity of BP flakes by explicitly considering optical anisotropy, encompassing birefringence, linear dichroism, and anisotropic cavity interference effects within multilayered structures. Through this approach, we have identified the intrinsic complex Raman tensors for phonon modes, independent of the BP flake thickness. By leveraging this methodology, we have elucidated the flake thickness-dependent effective complex Raman tensor elements, allowing for precise prediction of the observed ARPR intensity profile for the BP flake. This work provides a profound understanding of ARPR behaviors for ALM flakes., Comment: 6 pages, 4 figures

Graphene is an ideal platform to study the coherence of quantum interference pathways by tuning doping or laser excitation energy. The latter produces a Raman excitation profile that provides direct insight into the lifetimes of intermediate electronic excitations and, therefore, on quantum interference, which has so far remained elusive. Here, we control the Raman scattering pathways by tuning the laser excitation energy in graphene doped up to 1.05eV, above what achievable with electrostatic doping. The Raman excitation profile of the G mode indicates its position and full width at half maximum are linearly dependent on doping. Doping-enhanced electron-electron interactions dominate the lifetime of Raman scattering pathways, and reduce Raman interference. This paves the way for engineering quantum pathways in doped graphene, nanotubes and topological insulators., Comment: 18 pages, 4 figures

The atomically thin MnBi2Te4 crystal is a novel magnetic topological insulator, exhibiting exotic quantum physics. Here we report a systematic investigation of ultrafast carrier dynamics and coherent interlayer phonons in few-layer MnBi2Te4 as a function of layer number using time-resolved pump-probe reflectivity spectroscopy. Pronounced coherent phonon oscillations from the interlayer breathing mode are directly observed in the time domain. We find that the coherent oscillation frequency, the photocarrier and coherent phonon decay rates all depend sensitively on the sample thickness. The time-resolved measurements are complemented by ultralow-frequency Raman spectroscopy measurements, which both confirm the interlayer breathing mode and additionally enable observation of the interlayer shear mode. The layer dependence of these modes allows us to extract both the out-of-plane and in-plane interlayer force constants. Our studies not only reveal the interlayer van der Waals coupling strengths, but also shed light on the ultrafast optical properties of this novel two-dimensional material.

We present a Petrov-Gelerkin (PG) method for a class of nonlocal convection-dominated diffusion problems. There are two main ingredients in our approach. First, we define the norm on the test space as induced by the trial space norm, i.e., the optimal test norm, so that the inf-sup condition can be satisfied uniformly independent of the problem. We show the well-posedness of a class of nonlocal convection-dominated diffusion problems under the optimal test norm with general assumptions on the nonlocal diffusion and convection kernels. Second, following the framework of Cohen et al.~(2012), we embed the original nonlocal convection-dominated diffusion problem into a larger mixed problem so as to choose an enriched test space as a stabilization of the numerical algorithm. In the numerical experiments, we use an approximate optimal test norm which can be efficiently implemented in 1d, and study its performance against the energy norm on the test space. We conduct convergence studies for the nonlocal problem using uniform $h$- and $p$-refinements, and adaptive $h$-refinements on both smooth manufactured solutions and solutions with sharp gradient in a transition layer. In addition, we confirm that the PG method is asymptotically compatible.

The selection rule for angle-resolved polarized Raman (ARPR) intensity of phonons from standard group-theoretical method in isotropic materials would break down in anisotropic layered materials (ALMs) due to birefringence and linear dichroism effects. The two effects result in depth-dependent polarization and intensity of incident laser and scattered signal inside ALMs and thus make a challenge to predict ARPR intensity at any laser incidence direction. Herein, taking in-plane anisotropic black phosphorus as a prototype, we developed a so-called birefringence-linear-dichroism (BLD) model to quantitatively understand its ARPR intensity at both normal and oblique laser incidences by the same set of real Raman tensors for certain laser excitation. No fitting parameter is needed, once the birefringence and linear dichroism effects are considered with the complex refractive indexes. An approach was proposed to experimentally determine real Raman tensor and complex refractive indexes, respectively, from the relative Raman intensity along its principle axes and incident-angle resolved reflectivity by Fresnel$'$s law. The results suggest that the previously reported ARPR intensity of ultrathin ALM flakes deposited on a multilayered substrate at normal laser incidence can be also understood based on the BLD model by considering the depth-dependent polarization and intensity of incident laser and scattered Raman signal induced by both birefringence and linear dichroism effects within ALM flakes and the interference effects in the multilayered structures, which are dependent on the excitation wavelength, thickness of ALM flakes and dielectric layers of the substrate. This work can be generally applicable to any opaque anisotropic crystals, offering a promising route to predict and manipulate the polarized behaviors of related phonons., Comment: Accepted by Science Bulletin

Information technology demands high-speed optoelectronic devices, but going beyond the one terahertz (THz) barrier is challenging due to the difficulties associated with generating, detecting, and processing high-frequency signals. Here, we show that femtosecond-laser-driven phonons can be utilized to coherently manipulate the excitonic properties of semiconductors at THz frequencies. The precise control of the pump and subsequent time-delayed broadband probe pulses enables the simultaneous generation and detection processes of both periodic lattice vibrations and their couplings with electronic states. Combining ultralow frequency Raman spectroscopy with first-principles calculations, we identify the unique phonon mode-selective and probe-energy dependent features of electron-phonon interactions in layered PdSe2. Two distinctive types of coherent phonon excitations could couple preferentially to different types of electronic excitations: the intralayer (4.3 THz) mode to carriers and the interlayer (0.35 THz) mode to excitons. This work provides new insights to understand the excited-state phonon interactions of 2D materials, and to achieve future applications of optoelectronic devices operating at THz frequencies.

The vibrational modes in organic/inorganic layered perovskites are of fundamental importance for their optoelectronic properties. The hierarchical architecture of the Ruddlesden-Popper phase of these materials allows for distinct directionality of the vibrational modes withrespect to the main axes of the pseudocubic lattice in the octahedral plane. Here, we study the directionality of the fundamental phonon modes in single exfoliated Ruddlesden-Popper perovskite flakes with polarized Raman spectroscopy at ultralow-frequencies. A wealth of Raman bands is distinguished in the range from 15-150 cm-1 (2-15 meV), whose features depend on the organic cation species, on temperature, and on the direction of the linear polarization of the incident light. By controlling the angle of the linear polarization of the excitation laser with respect to the in-plane axes of the octahedral layer, we gain detailed information on the symmetry of the vibrational modes. The choice of two different organic moieties, phenethylammonium (PEA) and butylammonium (BA) allows to discern the influence of the linker molecules, evidencing strong anisotropy of the vibrations for the (PEA)2PbBr4 samples. Temperature dependent Raman measurements reveal that the broad phonon bands observed at room temperature consist of a series of sharp modes, and that such mode splitting strongly differs for the different organic moieties and vibrational bands., Comment: 25 pages, 4 figures

In this work, we study the reproducing kernel (RK) collocation method for the peridynamic Navier equation. We first apply a linear RK approximation on both displacements and dilatation, then back-substitute dilatation, and solve the peridynamic Navier equation in a pure displacement form. The RK collocation scheme converges to the nonlocal limit and also to the local limit as nonlocal interactions vanish. The stability is shown by comparing the collocation scheme with the standard Galerkin scheme using Fourier analysis. We then apply the RK collocation to the quasi-discrete peridynamic Navier equation and show its convergence to the correct local limit when the ratio between the nonlocal length scale and the discretization parameter is fixed. The analysis is carried out on a special family of rectilinear Cartesian grids for the RK collocation method with a designated kernel with finite support. We assume the Lam\'{e} parameters satisfy $\lambda \geq \mu$ to avoid adding extra constraints on the nonlocal kernel. Finally, numerical experiments are conducted to validate the theoretical results.

Reproducing kernel (RK) approximations are meshfree methods that construct shape functions from sets of scattered data. We present an asymptotically compatible (AC) RK collocation method for nonlocal diffusion models with Dirichlet boundary condition. The scheme is shown to be convergent to both nonlocal diffusion and its corresponding local limit as nonlocal interaction vanishes. The analysis is carried out on a special family of rectilinear Cartesian grids for linear RK method with designed kernel support. The key idea for the stability of the RK collocation scheme is to compare the collocation scheme with the standard Galerkin scheme which is stable. In addition, there is a large computational cost for assembling the stiffness matrix of the nonlocal problem because high order Gaussian quadrature is usually needed to evaluate the integral. We thus provide a remedy to the problem by introducing a quasi-discrete nonlocal diffusion operator for which no numerical quadrature is further needed after applying the RK collocation scheme. The quasi-discrete nonlocal diffusion operator combined with RK collocation is shown to be convergent to the correct local diffusion problem by taking the limits of nonlocal interaction and spatial resolution simultaneously. The theoretical results are then validated with numerical experiments. We additionally illustrate a connection between the proposed technique and an existing optimization based approach based on generalized moving least squares (GMLS).