arXiv subjects

Zhilin Li

Publications and source records attributed to Zhilin Li.

54 records · Page 3Linked to original sources

arXiv2022

Phase-resolved ocean wave forecast with simultaneous current estimation through data assimilation

In Wang & Pan (J. Fluid Mech., vol. 918, A19, 2021), the authors developed the first ensemble-based data assimilation (DA) capability for the reconstruction and forecast of ocean surface waves, namely the EnKF-HOS method coupling an ensemble Kalman filter (EnKF) and the high-order spectral (HOS) method. In this work, we continue to enrich the method by allowing it to simultaneously estimate the ocean current field, which is in general not known a priori and can (slowly) vary in both space and time. To achieve this goal, we incorporate the effect of ocean current (as unknown parameters) on waves to build the HOS-C method as the forward prediction model, and obtain a simultaneous estimation of (current) parameters and (wave) states via an iterative EnKF (IEnKF) method that is necessary to handle the complexity in this DA problem. The new algorithm, named IEnKF-HOS-C method, is first tested in synthetic problems with various forms (steady/unsteady, uniform/non-uniform) of current. It is shown that the IEnKF-HOS-C method is able to not only estimate the current field accurately, but also boost the prediction accuracy of the wave field (even) relative to the state-of-the-art EnKF-HOS method. Finally, using real data from a shipborne radar, we show that the IEnKF-HOS-C method successfully recovers the current speed that matches the in situ measurement by a floating buoy.

physics.flu-dyn↗

arXiv2022

A new parameter free partially penalized immersed finite element and the optimal convergence analysis

This paper presents a new parameter free partially penalized immersed finite element method and convergence analysis for solving second order elliptic interface problems. A lifting operator is introduced on interface edges to ensure the coercivity of the method without requiring an ad-hoc stabilization parameter. The optimal approximation capabilities of the immersed finite element space is proved via a novel new approach that is much simpler than that in the literature. A new trace inequality which is necessary to prove the optimal convergence of immersed finite element methods is established on interface elements. Optimal error estimates are derived rigorously with the constant independent of the interface location relative to the mesh. The new method and analysis have also been extended to variable coefficients and three-dimensional problems. Numerical examples are also provided to confirm the theoretical analysis and efficiency of the new method.

math.NA↗

arXiv2021

Probing the magnetic polaron state in the ferromagnetic semiconductor HgCr$_2$Se$_4$ with resistance fluctuation and muon-spin spectroscopy measurements

Combined resistance noise and muon-spin relaxation ($μ$SR) measurements of the ferromagnetic semiconductor HgCr$_2$Se$_4$ suggest a degree of magnetoelectric coupling and provide evidence for the existence of isolated magnetic polarons. These form at elevated temperatures and undergo a percolation transition with a drastic enhancement of the low-frequency 1/$f$-type charge fluctuations at the insulator-to-metal transition at $\sim 95 - 98$ K in the vicinity of the magnetic ordering temperature $T_C \sim 105 - 107$ K. Upon approaching the percolation threshold from above, the strikingly unusual dynamics of a distinct two-level fluctuator superimposed on the $1/f$ noise can be described by a slowing down of the dynamics of a nanoscale magnetic cluster, a magnetic polaron, when taking into account an effective radius of the polaron depending on the spin correlation length. Coinciding temperature scales found in $μ$SR and noise measurements suggest changes in the magnetic dynamics over a wide range of frequencies and are consistent with the existence of large polarized and domain-wall-like regions at low temperatures, that result from the freezing of spin dynamics at the magnetic polaron percolation transition.

cond-mat.str-el↗

arXiv2021

A simple third order compact finite element method for 1D BVP

A simple third order compact finite element method is proposed for one-dimensional Sturm-Liouville boundary value problems. The key idea is based on the interpolation error estimate, which can be related to the source term. Thus, a simple posterior error analysis or a modified basis functions based on original piecewise linear basis function will lead to a third order accurate solution in the $L^2$ norm, and second order in the $H^1$ or the energy norm. Numerical examples have confirmed our analysis.

math.NA↗

arXiv2019

On jump relations of anisotropic elliptic interface problems

Almost all materials are anisotropic. In this paper, interface relations of anisotropic elliptic partial differential equations involving discontinuities across interfaces are derived in two and three dimensions. Compared with isotropic cases, the invariance of partial differential equations and the jump conditions under orthogonal coordinates transformation is not valid anymore. A systematic approach to derive the interface relations is established in this paper for anisotropic elliptic interface problems, which can be important for deriving high order accurate numerical methods.

math.NA↗

arXiv2019

Unconventional temperature dependence of the anomalous Hall effect in HgCr2Se4

At sufficiently low temperatures, many quantum effects, such as weak localization, electron-electron interaction (EEI), and Kondo screening, can lead to pronounced corrections to the semiclassical electron transport. Although low temperature corrections to longitudinal resistivity, ordinary Hall resistivity, or anomalous Hall resistivity are often observed, the corrections to three of them have never been simultaneously detected in a single sample. Here, we report on the observation of $\sqrt T$-type temperature dependences of the longitudinal, ordinary Hall and AH resistivities at temperatures down to at least 20 mK in $n$-type HgCr$_2$Se$_4$, a half-metallic ferromagnetic semiconductor that can reach extremely low carrier densities. For the samples with moderate disorder, the longitudinal and ordinary Hall conductivities can be satisfactorily described by the EEI theory developed by Altshuler \textit{et al.}, whereas the large corrections to AH conductivity are inconsistent with the existing theory, which predicts vanishing and finite corrections to AH conductivity for EEI and weak localization, respectively.

cond-mat.mes-hall↗

arXiv2018

Tunable surface plasmons in Weyl semimetals TaAs and NbAs

By means of high-resolution electron energy loss spectroscopy, we investigate the low-energy excitation spectrum of transition-metal monopnictides hosting Weyl fermions. We observe gapped plasmonic modes in (001)-oriented surfaces of single crystals of NbAs and TaAs at 66 and 68 meV, respectively. Our findings are consistent with theory and we estimate an effective Coulomb interaction strength $α_{\rm eff}\approx0.41$ for both samples. We also demonstrate that the modification of the surface of transition-metal monopnictides by the adsorption of chemical species (in our case, oxygen and hydrocarbon fragments) changes the frequency of the plasmonic excitations, with a subsequent modification of the effective interaction strength in the 0.30-0.48 range. The remarkable dependence of plasmonic features on the presence of adsorbates paves the way for plasmonic sensors based on Weyl semimetals operating in the mid-infrared.

cond-mat.mes-hall↗

arXiv2018

V$_5$S$_8$: a Kondo lattice based on intercalation of van der Waals layered transition metal dichalcogenide

Since the discovery of graphene, a tremendous amount of two dimensional (2D) materials have surfaced. Their electronic properties can usually be well understood without considering correlations between electrons. On the other hand, strong electronic correlations are known to give rise to a variety of exotic properties and new quantum phases, for instance, high temperature superconductivity, heavy fermions and quantum spin liquids. The study of these phenomena has been one of the main focuses of condensed matter physics. There is a strong incentive to introduce electronic correlations into 2D materials. Via intercalating a van der Waals layered compound VS$_2$, we show an emergence of a Kondo lattice, an extensively studied strongly correlated system, by magnetic, specific heat, electrical and thermoelectric transport studies. In particular, an exceptionally large Sommerfeld coefficient, 440 mJ$\cdot$K$^{-2}\cdot$mol$^{-1}$, indicates a strong electron correlation. The obtained Kadowaki-Woods ratio, $2.7\times 10^{-6}$ $μΩ\cdot$cm$\cdot$mol$^2\cdot$K$^2\cdot$mJ$^{-2}$, also supports the strong electron-electron interaction. The temperature dependence of the resistivity and thermopower corroborate the Kondo lattice picture. The intercalated compound is one of a few rare examples of $d$-electron Kondo lattices. We further show that the Kondo physics persists in ultra-thin films. This work thus demonstrates a route to generate strong correlations in 2D materials.

cond-mat.mtrl-sci↗

arXiv2018

Chiral Landau levels in Weyl semimetal NbAs with multiple topological carriers

Recently, Weyl semimetals have been experimentally discovered in both inversion-symmetry-breaking and time-reversal-symmetry-breaking crystals. The non-trivial topology in Weyl semimetals can manifest itself with exotic phenomena which have been extensively investigated by photoemission and transport measurements. Despite the numerous experimental efforts on Fermi arcs and chiral anomaly, the existence of unconventional zeroth Landau levels, as a unique hallmark of Weyl fermions which is highly related to chiral anomaly, remains elusive owing to the stringent experimental requirements. Here, we report the magneto-optical study of Landau quantization in Weyl semimetal NbAs. High magnetic fields drive the system towards the quantum limit which leads to the observation of zeroth chiral Landau levels in two inequivalent Weyl nodes. As compared to other Landau levels, the zeroth chiral Landau level exhibits a distinct linear dispersion in z momentum direction and allows the optical transitions without the limitation of zero z momentum or square root of magnetic field evolution. The magnetic field dependence of the zeroth Landau levels further verifies the predicted particle-hole asymmetry of the Weyl cones. Meanwhile, the optical transitions from the normal Landau levels exhibit the coexistence of multiple carriers including an unexpected massive Dirac fermion, pointing to a more complex topological nature in inversion-symmetry-breaking Weyl semimetals. Our results provide insights into the Landau quantization of Weyl fermions and demonstrate an effective tool for studying complex topological systems.

cond-mat.mes-hall↗

arXiv2017

Towards diluted magnetism in TaAs

Magnetism in Weyl semimetals is desired to investigate the interaction between the magnetic moments and Weyl fermions, e.g. to explore anomalous quantum Hall phenomena. Here we demonstrate that proton irradiation is an effective tool to induce ferromagnetism in the Weyl semimetal TaAs. The intrinsic magnetism is observed with a transition temperature above room temperature. The magnetic moments from d states are found to be localized around Ta atoms. Further, the first-principles calculations indicate that the d states localized on the nearest-neighbor Ta atoms of As vacancy sites are responsible for the observed magnetic moments and the long-ranged magnetic order. The results show the feasibility of inducing ferromagnetism in Weyl semimetals so that they may facilitate the applications of this material in spintronics.

cond-mat.mtrl-sci↗

arXiv2017

Quantum linear magnetoresistance in NbTe2

NbTe2 crystal is quasi-2D layered semimetal with charge density wave ground state showing a distorted-1T structure at room temperature. Here we report the anisotropic magneto-transport properties of NbTe2. An anomalous linear magnetoresistance up to 30% at 3 K in 9 T was observed, which can be well explained by quantum linear magnetoresistance model. Our results reveal that a large quasi-2D Fermi surface and small Fermi pockets with linearly dispersive bands coexist in NbTe2. The comparison with the isostructural material TaTe2 provides more information about the electronic structure evolution with charge density wave transitions in NbTe2 and TaTe2.

cond-mat.mtrl-sci↗

arXiv2017

Ultra-broadband photodetection of Weyl semimetal TaAs up to infrared 10 μm range at room temperature

Photodetectors with broadband optical response have promising applications in many advanced optoelectronic and photonic devices. Especially, those with the detection range up to mid-infrared at room temperature are very challenging and highly desired. Recently, Weyl semimetal has been discovered and proposed to be favorable for photodetection since in general it breaks Lorentz invariance to have tilted chiral Weyl cones around Fermi level, which leads to chirality dependent photocurrents at arbitrarily long wavelength. Furthermore, the linear dispersion bands in Weyl cones result in very high carrier mobility and much reduced thermal carrier compared with the parabolic ones in narrow-gap semiconductors. Here, we report that the Weyl semimetal TaAs based photodetector can operate at room temperature with spectral range from blue (438.5 nm) to mid-infrared (10.29 μm) light wavelengths and the responsibility and detectivity is more than 78 uA W-1 and 1.88*107 Jones, respectively. This is the first photodetector made by a Weyl semimetal and shows its promising in room-temperature mid-infrared photodetection.

cond-mat.mtrl-sci↗

arXiv2017

Accurate gradient computations at interfaces using finite element methods

New finite element methods are proposed for elliptic interface problems in one and two dimensions. The main motivation is not only to get an accurate solution but also an accurate first order derivative at the interface (from each side). The key in 1D is to use the idea from \cite{wheeler1974galerkin}. For 2D interface problems, the idea is to introduce a small tube near the interface and introduce the gradient as part of unknowns, which is similar to a mixed finite element method, except only at the interface. Thus the computational cost is just slightly higher than the standard finite element method. We present rigorous one dimensional analysis, which show second order convergence order for both of the solution and the gradient in 1D. For two dimensional problems, we present numerical results and observe second order convergence for the solution, and super-convergence for the gradient at the interface.

math.NA↗

arXiv2017

Impurity screening and stability of Fermi arcs against Coulomband magnetic scattering in a Weyl monopnictide

We present a quasiparticle interference study of clean and Mn surface-doped TaAs, a prototypical Weyl semimetal, to test the screening properties as well as the stability of Fermi arcs against Coulomb and magnetic scattering. Contrary to topological insulators, the impurities are effectively screened in Weyl semimetals. The adatoms significantly enhance the strength of the signal such that theoretical predictions on the potential impact of Fermi arcs can be unambiguously scrutinized. Our analysis reveals the existence of three extremely short, previously unknown scattering vectors. Comparison with theory traces them back to scattering events between large parallel segments of spin-split trivial states, strongly limiting their coherence. In sharp contrast to previous work [R. Batabyal et al., Sci. Adv. 2, e1600709 (2016)], where similar but weaker subtle modulations were interpreted as evidence of quasiparticle interference originating from Femi arcs, we can safely exclude this being the case. Overall, our results indicate that intra- as well as inter-Fermi arc scattering are strongly suppressed and may explain why-in spite of their complex multiband structure-transport measurements show signatures of topological states in Weyl monopnictides.

cond-mat.mes-hall↗

arXiv2016

Anisotropic magneto-transport and magnetic properties of low temperature phase of TaTe2

TaTe2 is a quasi-2D charge density wave (CDW) compound with distorted-1T type structure exhibiting double-zigzag chains. Here we report the Fermi surface topology of low temperature phase of TaTe2 (LT-TaTe2) by anisotropic magneto-transport and magnetic measurements on high-quality single crystals. An anomalous large linear magnetoresistance up to 140% at 3 K in 9 T was observed, suggesting the existence of a small Fermi pocket in Dirac cone state in quantum transport models. Meanwhile, strong magnetic anisotropy was observed for B (001) and B//(001). Angle-dependent magnetoresistance and de Hass-van Alphen oscillations suggest the anisotropy of the normal Fermi surface and the small Fermi pocket in Dirac cone state.

cond-mat.str-el↗

arXiv2016

Symmetrical broken and nonlinear response of Weyl semimetal TaAs influenced by the topological surface states and Weyl nodes

A Weyl semimetal (WSM) features Weyl fermions in its bulk and topological surface states on surfaces, and is novel material hosting Weyl fermions, a kind of fundamental particles. The WSM was regarded as a three-dimensional version of "graphene" under the illusion. In order to explore its promising photoelectric properties and applications in photonics and photoelectronics, here, we study the anisotropic linear and nonlinear optical responses of a WSM TaAs, which are determined by the relationship and balance between its topological surface states and Weyl nodes. We demonstrate that topological surface states which break the bulk symmetry are responsible for the anisotropy of the mobility, and the anisotropic nonlinear response shows saturable characteristic with extremely large saturable intensity. We also find that the mobility is anisotropic with the magnitude of 104 cm2V-1s-1 at room temperature and can be accelerated by the optical field. By analyzing the symmetry, the nonlinear response is mainly contributed by the fermions close to the Weyl nodes, and is related to the Pauli's blocking of fermions, electron-electron interaction. This work experimentally discovers the anisotropic ultrahigh mobility of WSMs in the optical field and may start the field for the applications of WSMs in photonics and photoelectronics.

cond-mat.mtrl-sci↗

arXiv2016

Intrinsic diamagnetism in the Weyl semimetal TaAs

We investigate the magnetic properties of TaAs, a prototype Weyl semimetal. TaAs crystals show weak diamagnetism with magnetic susceptibility of about -7 * 10^{-7} emu/(g*Oe) at 5 K. A general feature is the appearance of a minimum at around 185 K in magnetization measurements as a function of temperature. No phase transition is observed in the temperature range between 5 K and 400 K. The magnetic properties indicate that the intrinsic Fermi level in TaAs is not located at the Weyl nodes, in agreement with the theory prediction.

cond-mat.mtrl-sci↗

arXiv2015

Fine numerical analysis of the crack-tip position for a Mumford-Shah minimizer

A new algorithm to determine the position of the crack (discontinuity set) of certain minimizers of Mumford-Shah functional in situations when a crack-tip occurs is introduced. The conformal mapping $w=\sqrt{z}$ in the complex plane is used to transform the free discontinuity problem to a new type of free boundary problem, where the symmetry of the free boundary is an additional constraint of a non-local nature. Instead of traditional Jacobi or Newton iterative methods, we propose a simple iteration method which does not need the Jacobian but is way fast than the Jacobi iteration. In each iteration, a Laplace equation needs to be solved on an irregular domain with a Dirichlet boundary condition on the fixed part of the boundary; and a Neumann type boundary condition along the free boundary. The augmented immersed interface method is employed to solve the potential problem. The numerical results agree with the analytic analysis and provide insight into some open questions in free discontinuity problems.

math.NA↗