Layered materials exhibit different electronic and phonon properties along in-plane and out-of-plane directions;existing studies focus on their in-plane behaviors,and the influence of such anisotropies on the dynamics...Layered materials exhibit different electronic and phonon properties along in-plane and out-of-plane directions;existing studies focus on their in-plane behaviors,and the influence of such anisotropies on the dynamics of photocarriers and phonons is unknown.Here,we fabricate layered PdSe_(2)crystals with flat edge surfaces and compare the time-resolved ultrafast spectroscopies on their basal and edge surfaces.Pronounced differences in the transient reflection spectroscopies reveal the inconsistent photocarrier and phonon dynamics behaviors on the two surfaces:the slow hot carrier relaxation process is accelerated and the thermoelasticity-induced longitudinal coherent acoustic phonon oscillation completely vanishes on the edge surface,as compared with the basal surface.Theoretical analysis reveals that the inconsistent hot carrier dynamics originate from the anisotropic properties of low-energy phonons in PdSe_(2),and the absence of phonon oscillation on the edge surface results from the wavevector-limited sensitivity of acoustic B_(1u)mode.Moreover,polarization-dependent spectroscopies indicate the diverse optical anisotropies beyond the in-plane of PdSe_(2).This work provides a new method to explore unique physical properties and modulate the optical anisotropy of layered materials.展开更多
We consider an Adaptive Edge Finite Element Method （AEFEM） for the 3D eddy currents equations with variable coefficients using a residual-type a posteriori error estimator. Both the components of the estimator and c...We consider an Adaptive Edge Finite Element Method （AEFEM） for the 3D eddy currents equations with variable coefficients using a residual-type a posteriori error estimator. Both the components of the estimator and certain oscillation terms, due to the occurrence of the variable coefficients, have to be controlled properly within the adaptive loop which is taken care of by appropriate bulk criteria. Convergence of the AEFEM in terms of reductions of the energy norm of the discretization error and of the oscillations is shown. Numerical results are given to illustrate the performance of the AEFEM.展开更多
基金supported by the National Natural Science Foundation of China(Grant Nos.12074202,and 12174207)the Natural Science Foundation of Tianjin City(Grant No.22JCYBJC00390)the Fundamental Research Funds for the Central Universities-Nankai University(Grant No.63231065)。
文摘Layered materials exhibit different electronic and phonon properties along in-plane and out-of-plane directions;existing studies focus on their in-plane behaviors,and the influence of such anisotropies on the dynamics of photocarriers and phonons is unknown.Here,we fabricate layered PdSe_(2)crystals with flat edge surfaces and compare the time-resolved ultrafast spectroscopies on their basal and edge surfaces.Pronounced differences in the transient reflection spectroscopies reveal the inconsistent photocarrier and phonon dynamics behaviors on the two surfaces:the slow hot carrier relaxation process is accelerated and the thermoelasticity-induced longitudinal coherent acoustic phonon oscillation completely vanishes on the edge surface,as compared with the basal surface.Theoretical analysis reveals that the inconsistent hot carrier dynamics originate from the anisotropic properties of low-energy phonons in PdSe_(2),and the absence of phonon oscillation on the edge surface results from the wavevector-limited sensitivity of acoustic B_(1u)mode.Moreover,polarization-dependent spectroscopies indicate the diverse optical anisotropies beyond the in-plane of PdSe_(2).This work provides a new method to explore unique physical properties and modulate the optical anisotropy of layered materials.
基金The work of the first author was supported by the NSF under Grant No.DMS-0411403 and Grant No.DMS-0511611The second author acknowledges the support from the Austrian Science Foundation(FWF)under Grant No.Start Y-192Both authors acknowledge support and the inspiring athmosphere at the Johann Radon Institute for Computational and Applied Mathematics(RICAM),Linz,Austria,during the special semester on computational mechanics
文摘We consider an Adaptive Edge Finite Element Method （AEFEM） for the 3D eddy currents equations with variable coefficients using a residual-type a posteriori error estimator. Both the components of the estimator and certain oscillation terms, due to the occurrence of the variable coefficients, have to be controlled properly within the adaptive loop which is taken care of by appropriate bulk criteria. Convergence of the AEFEM in terms of reductions of the energy norm of the discretization error and of the oscillations is shown. Numerical results are given to illustrate the performance of the AEFEM.
