Anomalous Nernst effect in type-II Weyl semimetals

Topological Weyl semimetals (WSM), a new state of quantum matter with gapless nodal bulk spectrum and open Fermi arc surface states, have recently sparked enormous interest in condensed matter physics. Based on the symmetry and fermiology, it has been proposed that WSMs can be broadly classified into two types, type-I and type-II Weyl semimetals. While the undoped, conventional, type-I WSMs have point like Fermi surface and vanishing density of states (DOS) at the Fermi energy, the type-II Weyl semimetals break Lorentz symmetry explicitly and have tilted conical spectra with electron and hole pockets producing finite DOS at the Fermi level. The tilted conical spectrum and finite DOS at Fermi level in type-II WSMs have recently been shown to produce interesting effects such as a chiral anomaly induced longitudinal magnetoresistance that is strongly anisotropic in direction and a novel anomalous Hall effect. In this work, we consider the anomalous Nernst effect in type-II WSMs in the absence of an external magnetic field using the framework of semi-classical Boltzmann theory. Based on both a linearized model of time-reversal breaking WSM with a higher energy cut-off and a more realistic lattice model, we show that the anomalous Nernst response in these systems is strongly anisotropic in space, and can serve as a reliable signature of type-II Weyl semimetals in a host of magnetic systems with spontaneously broken time reversal symmetry.     

Tunable enhanced spatial shifts of reflective beam on the surface of a twisted bilayer of hBN

We investigated Goos-Hänchen (GH) and Imbert-Fedorov (IF) shifts of a reflective beam on a twisted bilayer of hexagonal boron nitride (hBN), where a left circularly polarized beam was incident on the surface. Our results demonstrate that the twist angle between the two optical axes plays an important role in obtaining large shifts with a high reflectivity. The GH shift with 10λ₀ is achieved, while the reflectivity is near 100% by tuning the twist angle. The maximum of the IF shift is found in the certain condition satisfied by the reflective coefficients, and the shift strongly depends on the twist angle between the optical axes of the two slabs. The spatial shifts obtained directly from the GH and IF shift definitions were provided, which indicate that the theoretical results from the stationary phase method are believable. These results may open up a new way for developing the nano-optical devices.     

Intrinsic anomalous Hall effect in type-II Weyl semimetals

Recently, a new type of Weyl semimetal called type-II Weyl semimetal has been proposed. Unlike the usual (type-I) Weyl semimetal, which has a point-like Fermi surface, this new type of Weyl semimetal has a tilted conical spectrum around the Weyl point. Here we calculate the anomalous Hall conductivity of a Weyl semimetal with a tilted conical spectrum for a pair of Weyl points, using the Kubo formula. We find that the Hall conductivity is not universal and can change sign as a function of the parameters quantifying the tilts. Our results suggest that even for the case where the separation between the Weyl points vanishes, tilting of the conical spectrum could give rise to a finite anomalous Hall effect, if the tilts of the two cones are not identical.     

Anisotropic and valley-resolved beam-splitter based on a tilted Dirac system

We investigate theoretically valley-resolved lateral shift of electrons traversing an n–p–n junction bulit on a typical tilted Dirac system (8-Pmmn borophene). A gauge-invariant formula on Goos–Hänchen (GH) shift of transmitted beams is derived, which holds for any anisotropic isoenergy surface. The tilt term brings valley dependence of relative position between the isoenergy surface in n region and that in the p region. Consequently, valley double refraction can occur at the n–p interface. The exiting positions of two valley-polarized beams depend on the incident angle and energy of incident beam and barrier parameters. Their spatial distance D can be enhanced to be ten to a hundred times larger than the barrier width. Due to tilting-induced high anisotropy of the isoenergy surface, D depends strongly on the barrier orientation. It is always zero when the junction is along the tilt direction of Dirac cones. Thus GH effect of transmitted beams in tilted Dirac systems can be utilized to design anisotropic and valley-resolved beam-splitter.     

High-order harmonic generations in tilted Weyl semimetals

We investigate high-order harmonic generations (HHGs) under comparison of Weyl cones in two types. Due to the hyperboloidal electron pocket structure, strong noncentrosymmetrical generations in high orders are observed around a single type-II Weyl point, especially at zero frequency. Such a remarkable DC signal is proved to have attributions from the intraband transition after spectral decomposition. Under weak pulse electric field, the linear optical response of a non-tilted Weyl cone is consistent with the Kubo theory. With extensive numerical simulations, we conclude that the non-zero chemical potential can enhance the even-order generations, from the slightly tilted system to the over-tilted systems. In consideration of dynamical symmetries, type-I and type-II Weyl cones also show different selective responses under the circularly polarized light. Finally, using a more realistic model containing two pairs of Weyl points, we demonstrate that paired Weyl points with opposite chirality can suppress the overall even-order generations.     

Coherent Control of the Goos-Hänchen Shifts in a Four-Level N Type Atomic Medium

The behavior of the Goos-Hänchen (GH) shifts of the reflected and transmitted probe light beams is theoretically investigated. In a fixed geometrical configuration, the effect of quantum interference induced by spontaneous emission on the phase control of the GH shifts is analyzed in this paper. It is found that in a four-level N-type atomic system as an intracavity medium, the GH shifts of the reflected and transmitted probe light beam are completely phase dependent.     

Goos-Hänchen and Imbert-Fedorov shifts of a nondiffracting Bessel beam

Goos-H?nchen (GH) and Imbert-Fedorov (IF) shifts are diffractive corrections to geometric optics that have been extensively studied for a Gaussian beam that is reflected or transmitted by a dielectric interface. Propagating in free space before and after reflection or transmission, such a Gaussian beam spreads due to diffraction. We address here the question of how the GH and IF shifts behave for a "nondiffracting" Bessel beam.     

Role of spatial coherence in Goos-Hänchen and Imbert-Fedorov shifts

We present a theory for Goos-H?nchen (GH) and Imbert-Fedorov (IF) shifts for beams of light with arbitrary spatial coherence. By applying the well-known theory of partial spatial coherence, we can calculate explicitly spatial and angular GH and IF shifts for completely polarized beams of any shape and spatial coherence. For the specific case of a Gauss-Schell source, we find that only the angular part of GH and IF shifts is affected by the spatial coherence of the beam. A physical explanation of our results is given.     

Collective modes of type-ⅡWeyl fermions with repulsive S-wave interaction

Three-dimensional type-ⅡWeyl fermions possess overtilted cone-like low-energy band dispersion.Unlike the closed ellipsoidal Fermi surface for type-ⅠWeyl fermions,the Fermi surface is an open hyperboloid for type-ⅡWeyl fermions.We evaluate the spin and density susceptibility of type-ⅡWeyl fermions with repulsive S-wave interaction by means of Green’s functions.We obtain the particle–hole continuum along the tilted momentum direction and perpendicular to the tilted momentum direction respectively.We find the zero sound mode in some repulsive interaction strengths by numerically solving the pole equations of the susceptibility within the random-phase approximation.     

Pressure-induced Lifshitz transition in the type Ⅱ Dirac semimetal PtTe_2

Numerous exotic properties have been discovered in Dirac Semimetals(DSMs) and Weyl Semimetals(WSMs). In a given DSM/WSM, the Dirac/Weyl nodes usually coexist with other bulk states, making their respective contribution elusive. In this work, we distinguish the role of bulk states from the tilted Dirac nodes on the transport properties in DSMs. Specifically, we applied pressure to a type-II DSM material, PtTe2, and studied its pressure modified electronic and lattice structure systematically by using in situ transport measurements and X-ray diffraction(XRD). A pressure-induced transition at about 20 GPa is revealed in the transport properties, while the layered lattice structure is robust against pressure as illustrated in XRD measurement results.Density functional theory(DFT) calculations suggest that this is originated from the Lifshitz transition in the bulk states. Our findings provide evidence to identify the bulk states' influence on transport from the topologically-protected DSM states in the DSM material.     

Type-III and IV interacting Weyl points

3+1-dimensional Weyl fermions in interacting systems are described by effective quasi-relativistic Green’s functions parametrized by a 16-element matrix e _α ^μ in an expansion around the Weyl point. The matrix e _α ^μ can be naturally identified as an effective tetrad field for the fermions. The correspondence between the tetrad field and an effective quasi-relativistic metric g_μν governing the Weyl fermions allows for the possibility to simulate different classes of metric fields emerging in general relativity in interacting Weyl semimetals. According to this correspondence, there can be four types of Weyl fermions, depending on the signs of the components g ⁰⁰ and g ₀₀ of the effective metric. In addition to the conventional type-I fermions with a tilted Weyl cone and type-II fermions with an overtilted Weyl cone for g ⁰⁰ > 0 and, respectively, g ₀₀ > 0 or g ₀₀ < 0, we find additional “type-III” and “type-IV” Weyl fermions with instabilities (complex frequencies) for g ⁰⁰ < 0 and g ₀₀ > 0 or g ₀₀ < 0, respectively. While the type-I and type-II Weyl points allow us to simulate the black hole event horizon at an interface where g ⁰⁰ changes sign, the type-III Weyl point leads to effective spacetimes with closed timelike curves.     

Hybrid Weyl semimetal under crossed electric and magnetic fields: Field tuning of spectrum type

There are two types (WSM-I and WSM-II) of the WSMs. The WSMs of different types have various topological and transport properties. Besides pure WSM-I and WSM-II, there exists a novel type, dubbed “hybrid Weyl semimetal”, which contains the Weyl points of both types. In this Letter we consider the hybrid WSM under crossed magnetic and electric fields. The electromagnetic field induces transition between different types of spectrum in Weyl point (WP). Thus, hybrid phase of the WSM can be tunable using the electromagnetic field. Finally, we proposed a new field-induced type of hybrid WSM in which two different regimes of spectrum coexist. In this case, the spectrum near the first WP corresponds to electric regime (no Landau levels) and the spectrum in the second WP with opposite chirality corresponds to magnetic regime (there are Landau levels).     

Electric control of spin-dependent Goos–Hänchen shift in a magnetically modulated semiconductor nanostructure

We theoretically investigate how to manipulate spin-dependent Goos–Hänchen (GH) shifts by an applied bias in a realistic magnetic-barrier nanostructure, which is experimentally created by depositing a ferromagnetic stripe with perpendicular magnetization on the top of heterostructure. GH shifts of transmitted electron beams are calculated numerically with the help of the stationary phase method. It is shown that both magnitude and sign of spin polarization in GH shifts are closely relative to the applied bias, which can give rise to a bias-controllable spin beam splitter.     

BBOⅠ类相位匹配光参量放大中群速失配的补偿

描述了在BBOⅠ类相位匹配的飞秒光参量放大（OPA）中，利用非共线结构和倾斜抽运光的脉 冲波面来完全补偿三波群速失配的方法.理论计算了三波群速匹配时，非共线角、相位匹配 角、抽运光的脉冲波面倾斜角随信号光波长的变化，并分析了对抽运光光斑尺寸的要求和对 空间走离长度的影响.结果表明，利用该方法不仅能够实现最大的参量带宽，而且能够完全 补偿飞秒OPA中三波的群速失配.此外，选取合适的抽运光光斑尺寸和非线性晶体的长度对提 高参量增益也至关重要. 关键词： 群速匹配 非共线相位匹配 脉冲波面倾斜 飞秒光参量放大     

高斯反射镜及其倾斜对平凹腔激光场分布的影响

 从菲涅尔-基尔霍夫衍射积分公式出发，运用边界元法数值计算了平凹腔平面镜均匀反射率时倾斜和未倾斜情况下基模的场强分布、相位分布和本征值，同时与高斯反射率平面镜在腔镜倾斜时的情况做了比较。研究表明，腔镜倾斜使激光场模式分布沿发生倾斜的方向向镜边缘偏移，而且在腔镜倾斜较严重时模式分布发生畸变，不再是对称的高斯分布，基模本征值随倾斜角增大而变小，光束远场分布变差。同等条件下，高斯反射率平凹腔腔镜倾斜对谐振腔引起的模畸变小于均匀反射率平凹腔，且基模光场及本征值随镜倾斜的变化关系稍不同于均匀反射率平凹腔。     

Investigation of the limit of lateral beam shifts on a symmetrical metal-cladding waveguide

This paper reports that Goos--H\"anchen (GH) shifts occurring on a symmetrical metal-cladding waveguide are experimentally identified. It was found that there exists a critical thickness of the upper metal layer, h_cr, above which negative shift is observed and, reversely, positive shift occurs. Both positive and negative GH shifts near the critical thickness do not vary dramatically and can achieve a maximum on the submillimeter scale, which is different from simulated results using the stationary-phase method. It also shows that this critical thickness, h_cr, can be obtained at the position for zero reflectivity by setting the intrinsic damping to be the same as the radiative damping. The GH effects observed near the critical thickness are produced by extreme distortion of the reflected beam profiles, which limits the amplitude of the GH shift and, further, the sensitivity of the GH optical sensor based on the symmetrical metal-cladding waveguide.     

圆形高斯镜平凹腔腔镜倾斜时光场模式分析

运用边界元素法把圆形高斯镜平凹腔的自再现模的衍射积分方程转化为有限阶矩阵方程。计算了谐振腔在理想情况和高斯反射率平面输出镜倾斜情况下基模的场强分布、相位分布和本征值。研究表明,腔镜倾斜使激光场模式分布沿发生倾斜的方向向镜边缘偏移,而且在腔镜倾斜较严重时模式分布发生畸变,不再是对称的拉盖尔-高斯基模分布。基模本征值随倾斜角增大而变小,光束远场分布变差。减小高斯分布反射率的膜斑半径,则能减弱因倾斜引起的模式畸变。     

RKKY interaction in three-dimensional tilted Dirac and Weyl semimetals

We theoretically investigate the Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction between two magnetic impurities of the tilted Dirac and Weyl semimetals in three dimensions. In accordance with the untilted scenario, the RKKY interaction contains three terms, namely the Heisenberg term, the Ising term, and the Dzyaloshinsky-Moriya term. The main influence of tilt on the RKKY Hamiltonian is a modulation to the oscillation frequencies of range functions. Our results enrich the knowledge of the magnetic properties of materials with tilted Dirac cones and may see an important application in spintronics.     

圆锥透镜对倾斜球面波光束的衍射模式

由于球面波入射圆锥透镜所产生的出射光束具有焦深长和中心光斑直径较小的特点,适合激光通信以及长距离测量.在实际使用中,入射球面波很可能与圆锥透镜的光轴发生倾斜.研究了圆锥透镜对倾斜球面波光束的衍射特性,通过基尔霍夫衍射理论以及稳相法分析,分析了其径向衍射光场分布形式,并用计算机进行了仿真.使用了半径为15 mm、底角为1°的圆锥透镜进行实验,并对仿真结果进行了验证.仿真和实验证明,减小入射球面波曲率半径、出射光束传输距离和入射光束倾斜角都可以减弱入射光束倾斜对衍射图的影响.     

倍频激光器中KTP晶体失调研究

针对目前常用的KTP晶体,研究其倾斜失调和旋转失调对倍频激光器转换效率的影响。基于主轴坐标系变换,建立KTP晶体倾斜失调理论模型,对倾斜失调和旋转失调时激光非线性频率变换过程进行理论分析并设计实验验证。结果表明,倾斜失调时,转换效率会随着倾斜失调方向的变化出现2个大小不同的窄峰值,且倾斜角度越大,两峰值所在方向夹角越小,其余方向转换效率为零,与理论计算一致;对于旋转失调,Ⅰ和Ⅱ类相位匹配转换效率随失调角度分别呈和/2周期变化。该结果可用于倍频激光器设计。