Strain Tunable Berry Curvature Dipole, Orbital Magnetization and Nonlinear Hall Effect in WSe_(2) Monolayer

The electronic topology is generally related to the Berry curvature,which can induce the anomalous Hall effect in time-reversal symmetry breaking systems.Intrinsic monolayer transition metal dichalcogenides possesses two nonequivalent K and K’ valleys,having Berry curvatures with opposite signs,and thus vanishing anomalous Hall effect in this system.Here we report the experimental realization of asymmetrical distribution of Berry curvature in a single valley in monolayer WSe_(2) via applying uniaxial strain to break C_(3v) symmetry.As a result,although the Berry curvature itself is still opposite in K and K’ valleys,the two valleys would contribute equally to nonzero Berry curvature dipole.Upon applying electric field E,the emergent Berry curvature dipole D would lead to an out-of-plane orbital magnetization M ∝ D·E,which further induces an anomalous Hall effect with a linear response to E^(2),known as nonlinear Hall effect.We show the strain modulated transport properties of nonlinear Hall effect in monolayer WSe_(2) with moderate hole-doping by gating.The second-harmonic Hall signals show quadratic dependence on electric field,and the corresponding orbital magnetization per current density M/J can reach as large as 60.In contrast to the conventional Rashba-Edelstein effect with in-plane spin polarization,such current-induced orbital magnetization is along the out-of-plane direction,thus promising for high-efficient electrical switching of perpendicular magnetization.

Janus VXY monolayers with tunable large Berry curvature

The Rashba effect and valley polarization provide a novel paradigm in quantum information technology. However,practical materials are scarce. Here, we found a new class of Janus monolayers VXY(X = Cl, Br, I;Y = Se, Te) with excellent valley polarization effect. In particular, Janus VBrSe shows Zeeman type spin splitting of 14 meV, large Berry curvature of 182.73 bohr2,and, at the same time, a large Rashba parameter of 176.89 meV·?. We use the k·p theory to analyze the relationship between the lattice constant and the curvature of the Berry. The Berry curvature can be adjusted by changing the lattice parameter,which will greatly improve the transverse velocities of carriers and promote the efficiency of the valley Hall device. By applying biaxial strain onto VBrSe, we can see that there is a correlation between Berry curvature and lattice constant, which further validates the above theory. All these results provide tantalizing opportunities for efficient spintronics and valleytronics.

Gate-tunable Berry curvature in van der Waals itinerant ferromagnetic Cr_(7)Te_(8)

The anomalous Hall effect(AHE)that associated with the Berry curvature of occupied electronic states in momentum-space is one of the intriguing aspects in condensed matter physics,and provides an alternative for potential applications in topological electronics.Previous experiments reported the tunable Berry curvature and the resulting magnetization switching process in the AHE based on strain engineering or chemical doping.However,the AHE modulation by these strategies are usually irreversible,making it difficult to realize switchable control of the AHE and the resultant spintronic applications.Here,we demonstrated the switchable control of the Berry-curvature-related AHE by electrical gating in itinerant ferromagnetic Cr_(7)Te_(8)with excellent ambient stability.The gate-tunable sign reversal of the AHE can be attributed to the redistribution of the Berry curvature in the band structure of Cr_(7)Te_(8)due to the intercalation-induced change in the Fermi level.Our work facilitates the applications of magnetic switchable devices based on gate-tunable Berry curvature.

基于不同物理机制的固体高次谐波产生对激光参数依赖特性的理论研究

高次谐波产生(high-order harmonic generation,HHG)机制的研究,主要集中在带间极化和带内电流,以及由Berry曲率引起的反常电流机制上.将强激光诱导完整电流分解为不同机制的贡献,得到长期以来被忽视的混合项电流.通过数值求解半导体Bloch方程(semiconductor Bloch equation,SBE),研究了不同机制产生高次谐波的峰值振幅和激光波长相关性,探索了各电流机制之间的相干性.研究发现,无论是随着波长变化还是随着峰值振幅的变化,混合项电流与带间极化电流诱导的高次谐波谱有着十分相似的变化规律,以及极其接近的谐波强度;同时发现Berry曲率诱导的反常谐波只能产生垂直于激光场偏振方向的偶次谐波,且在波长和峰值强度变化过程中出现的极小值是反常谐波独有的特征.通过分析不同机制之间的干涉作用,发现带间极化谐波与带内谐波(包括反常谐波)在垂直偏振方向上发生了明显的相互干涉,而混合项谐波与带内谐波的相干则微乎其微.

固体物理学中的贝里曲率

固体中周期性势场和布洛赫定理赋予贝里曲率新的内涵,对于布里渊区k点处第n个能带,其布洛赫函数的调幅因子为u_(nk)(r),则相应贝里曲率Ω_(nk)=▽×A_(nk),其中贝里联络A_(nk)=〈u_(nk)|i▽_(k)|u_(nk)〉.如果晶体同时存在中心反演和时间反演对称性,贝里曲率在倒空间处处为零.若上述对称性被打破,或者存在自旋轨道耦合,或者存在能带交叉,则存在非零的贝里曲率.贝里曲率的存在使布洛赫电子产生与外电场垂直方向的反常速度,由此产生本征反常霍尔效应和自旋霍尔效应以及非线性霍尔效应.本文有助于加深对布洛赫波函数以及玻尔兹曼输运方程的理解.

Quantum geometric tensor and the topological characterization of the extended Su-Schrieffer-Heeger model

We investigate the quantum metric and topological Euler number in a cyclically modulated Su-Schrieffer-Heeger(SSH)model with long-range hopping terms.By computing the quantum geometry tensor,we derive exact expressions for the quantum metric and Berry curvature of the energy band electrons,and we obtain the phase diagram of the model marked by the first Chern number.Furthermore,we also obtain the topological Euler number of the energy band based on the Gauss-Bonnet theorem on the topological characterization of the closed Bloch states manifold in the first Brillouin zone.However,some regions where the Berry curvature is identically zero in the first Brillouin zone result in the degeneracy of the quantum metric,which leads to ill-defined non-integer topological Euler numbers.Nevertheless,the non-integer"Euler number"provides valuable insights and an upper bound for the absolute values of the Chern numbers.

参数空间上的量子几何张量

量子几何张量的实部和虚部均有重要意义,研究二者可以清楚地认识量子系统中的几何与拓扑性质.本文从规范变换作用在实空间上的情况引入,继而延伸到规范变换作用在抽象参数空间上的情况,从而详细地介绍了量子几何张量及一系列概念,加深了对量子几何的进一步理解和认知.

粒子与集体行为

布洛赫电子的运动受到贝里曲率的影响,已是人们熟知的量子几何效应。凝聚态系统中的各种集体行为,以及它们与电子系统的耦合,为量子几何现象的探索提供了更加广阔的舞台。针对几种典型的对称破缺状态,文章就下列方向中的有关研究和应用作出简略回顾和展望,包括晶格振动与声子、磁化动力学与自旋波、玻色凝聚体与量子涡旋、超导序参量与准粒子以及晶格形变与人工引力。

布洛赫电子的拓扑与几何

文章回顾了电子的拓扑几何理论发展的初期,大约二十多年的历史。首先介绍拓扑陈数在凝聚态物理中的两个重要应用。其一关于量子霍尔效应,绝缘条件下霍尔电导可以写成一个陈数拓扑不变量,从而解释实验结果的精确量子化。其二关于绝热泵浦,它描述布洛赫能带的绝热电流响应,与电子极化有密切联系。拓扑陈数是布里渊区上贝里曲率的积分,后者本身也有独立的物理意义。接着介绍贝里曲率对电子动力学的影响,包括反常速度和轨道磁化等概念。作者还将这个理论推广到多带情况,使其可以应用到自旋输运等现象。最后,文中展示了再量子化方法,从半经典模型来获得布洛赫电子的有效量子理论。在非相对论极限下,泡利—薛定谔方程可以看作是狄拉克电子在正能谱上的等效量子理论,其中的自旋轨道耦合即是一种几何物理效应。

半经典响应理论

对电子响应性质的研究,如平衡态下的磁化率和非平衡态下的输运系数等,是早期固体理论发展的原初动力之一。当朴素的经典粒子观经由量子力学原理和多体作用的锤炼升华至半经典粒子观后,进一步辅以对几何相位和拓扑性的深刻认识,人们终获得理解响应性质的完善、准确、颇具物理直观性的半经典理论框架。文章将介绍基于现代的电子粒子观和几何相位的半经典响应理论这一基本框架,并摘选热电响应、自旋输运、非线性响应、外禀机制这四个重要研究方向中的一些代表性问题,来解释半经典响应理论的内涵并展示其在固体物理研究中的价值。

Berry Approach to Intrinsic Anomalous Hall Conductivity in Dilute Magnetic Semiconductors (Ga_1-xMn_xAs)

We develop a model Hamiltonian to treat intrinsic anomalous Hall conductivity in dilute magnetic semiconductor (DMS) of type (III, Mn, V) and obtain the Berry potential and Berry curvature which are responsible for intrinsic anomalous Hall conductivity in Ga1-x MnxAs DMS. Based on Kubo formalism, we establish the relation between Berry curvature and intrinsic anomalous Hall conductivity. We find that for strong spin-orbit interaction intrinsic anomalous Hall conductivity is quantized which is in agreement with recent experimental observation. In addition, we show that the intrinsic anomalous Hall conductivity (AHC) can be controlled by changing concentration of magnetic impurities as well as exchange field. Since Berry curvature related contribution of anomalous Hall conductivity is believed to be dissipationless, our result is a significant step toward achieving dissipationless electron transport in technologically relevant conditions in emerging of spintronics.

磁性拓扑材料中贝利曲率驱动的非常规电输运行为

近年来,磁性拓扑材料特别是磁性Weyl半金属越来越多地被发现,为研究拓扑输运行为提供了重要载体.磁性拓扑半金属材料具有动量空间的强贝利曲率,显著增强了电子的常规横向输运行为,也使得曾经被忽略或无法观测的输运效应逐渐浮现出来,导致当前广泛采用的经典输运方程不能准确地描述磁性拓扑电子的输运行为.本文从半经典输运方程出发,介绍磁性拓扑材料中新近出现的非常规电输运行为,内容涉及化学掺杂、磁场调制拓扑电子态、贝利曲率相关的线性正磁电阻及磁场线性依赖的输运行为.这些行为为磁性与拓扑相互作用下的电输运行为提供新的理解和思考.最后,对非常规电输运的发展进行总结和展望.

二维莫尔超晶格中的非线性霍尔效应

1879年发现的霍尔效应是凝聚态物理学中最古老也是最重要的领域之一.最近发现的非线性霍尔效应是霍尔效应家族的新成员.与大部分需要打破时间反演对称的霍尔效应不同,非线性霍尔效应存在于少数空间反演破缺但仍具有时间反演对称的系统中,并且因其高频特性和不需额外施加磁场而在诸多领域具有令人期待的应用前景.然而,除空间反演破缺以外,非线性霍尔效应对材料对称性的要求十分苛刻,只在极少数材料中观测到了由贝里曲率偶极矩产生的非线性霍尔效应.近年来快速发展的范德瓦耳斯堆叠技术为剪裁和调控晶体的对称性,制备具有特殊物理性质的人工二维莫尔晶体提供了一个崭新的途径.本文主要围绕二维莫尔超晶格结构在实现非线性霍尔效应方面的特性,介绍了近年来理论和实验上石墨烯超晶格以及过渡金属硫族化合物超晶格中非线性霍尔效应的研究进展,并展望了未来基于二维莫尔超晶格材料的非线性霍尔效应的研究方向和应用前景.

Nonmonotonic anomalous Hall effect and anisotropic magnetoresistance in SrRuO_(3)/PbZr_(0.52)Ti_(0.48)O_(3)heterostructures

We fabricate SrRuO_(3)/PbZr_(0.52)Ti_(0.48)O_(3)heterostructures each with an in-plane tensile-strained SrRuO_(3)layer and investigate the effect of an applied electric field on anomalous Hall effect.The four-fold symmetry of anisotropic magnetoresistance and the nonmonotonic variation of anomalous Hall resistivity are observed.By applying positive electric field or negative electric field,the intersecting hump-like feature is suppressed or enhanced,respectively.The sign and magnitude of the anomalous Hall conductivity can be effectively controlled with an electric field under a high magnetic field.The electric-field-modulated anomalous Hall effect is associated with the magnetization rotation in SrRuO_(3).The experimental results are helpful in modulating the magnetization rotation in spintronic devices based on SrRuO_(3)heterostructures.

Evolution of Berry curvature and reentrant quantum anomalous Hall effect in an intrinsic magnetic topological insulator

Recently, the magnetic topological insulator(TI) MnBi2Te4 emerged as a competitive platform to realize quantum anomalous Hall(QAH) states. We report a Berry curvature splitting mechanism to realize the QAH effect in the disordered magnetic TI multilayers when switching from an antiferromagnetic order to a ferromagnetic order. We reveal that the splitting of spin-resolved Berry curvature, originating from the separation of the critical points during the magnetic switching, can give rise to a QAH insulator. We present a global phase diagram, and also provide a phenomenological picture to elucidate the Berry curvature splitting mechanism by the evolution of topological charges. At last, we predict that the Berry curvature splitting mechanism will lead to a reentrant QAH effect, which can be detected by tuning the gate voltage. Our theory will be instructive for the studies of the QAH effect in MnBi2Te4 in future experiments.

圆偏振光伏效应

自旋电子学和谷电子学作为半导体物理的新方向,旨在利用电子的自旋和谷自由度来实现新型的逻辑运算和信息处理.圆偏振光伏效应是近年来研究自旋电子学和谷电子学的重要实验手段,也是实现新型的自旋与谷存储器件的一个可能的方式,为下一代的器件信息的处理方法提出了一种新的可能.圆偏振光伏效应是一种二阶非线性光电响应,是指材料在圆偏振光的激发下产生随偏振角度变化的光电流.光电流的产生依赖于自旋、谷极化、对称性以及Berry曲率等诸多因素,可以揭示出材料深层次的物理性质.本篇综述主要讨论了在不同材料体系产生圆偏振光伏效应的主要机制,包括在半导体异质结由对称性破缺导致的Rashba自旋轨道耦合引起的圆偏振光电流,以及拓扑Weyl半金属由Berry曲率以及泡利阻塞造成的电子动量选择,以及二维层状过渡金属硫化物中圆偏振光产生的谷极化电流等.在此基础上,本文还简略介绍了一些新型二维材料中的圆偏振光伏效应的可能实现的方式,以及一些潜在的应用.

拓扑声子与声子霍尔效应

拓扑学与物理的结合是近几十年物理学蓬勃发展的一个新领域,它不仅活跃在量子场理论以及高能物理中,更广泛地存在于凝聚态物理体系中,包括量子(反常、自旋)霍尔效应和拓扑绝缘体(超导体)等.声子是凝聚态体系中热输运的主要载体;最近由于各种声子器件的发现,声子学得到了广泛的关注.本文介绍了声子的拓扑性质以及声子的霍尔效应现象,分别评述了在破坏时间反演对称、破坏空间反演对称、以及同时破坏时间和空间反演对称三种情况下所产生的声子霍尔效应、声子谷霍尔效应等相关物理研究进展.最后对拓扑学在其他声学体系中的应用做了简单介绍,并进一步讨论了其未来的发展方向.

二维材料中贝里曲率诱导的磁性响应

二维材料中由贝里曲率诱导的新型磁学响应是近年来的新兴领域.这些二维材料所表现出的磁学特性及量子输运与贝里曲率直接相关,而贝里曲率又与晶体的对称性、电子的轨道磁性、自旋轨道耦合以及磁电效应等息息相关.研究这些新型磁性响应一方面有益于研究不同量子效应间的耦合作用,另一方面可探索量子效应在电子与信息器件领域的应用.本文介绍了近几年来二维材料中新型磁响应的实验研究进展,特别介绍了二硫化钼和石墨烯等材料中的谷霍尔和磁电效应、低对称性的二碲化钨等材料中的量子非线性霍尔以及转角石墨烯中的反常霍尔和量子反常霍尔效应.本文结合二维材料的晶体结构以及电子结构,介绍了这些新奇现象的现有物理解释、回顾了相关研究的最新发展、讨论了其中尚未理解的现象,并作出展望.

Strain-dependent resistance and giant gauge factor in monolayer WSe_(2)

We report the strong dependence of resistance on uniaxial strain in monolayer WSe_(2)at various temperatures,where the gauge factor can reach as large as 2400.The observation of strain-dependent resistance and giant gauge factor is attributed to the emergence of nonzero Berry curvature dipole.Upon increasing strain,Berry curvature dipole can generate net orbital magnetization,which would introduce additional magnetic scattering,decreasing the mobility and thus conductivity.Our work demonstrates the strain engineering of Berry curvature and thus the transport properties,making monolayer WSe_(2)potential for application in the highly sensitive strain sensors and high-performance flexible electronics.

Inheritance of the exciton geometric structure from Bloch electrons in two-dimensional layered semiconductors

We theoretically studied the exciton geometric structure in layered semiconducting transition metal dichalcogenides.Based on a three-orbital tight-binding model for Bloch electrons which incorporates their geometric structures,an effective exciton Hamiltonian is constructed and solved perturbatively to reveal the relation between the exciton and its electron/hole constituent.We show that the electron−hole Coulomb interaction gives rise to a non-trivial inheritance of the exciton geometric structure from Bloch electrons,which manifests as a valley-dependent center-of-mass anomalous Hall velocity of the exciton when two external fields are applied on the electron and hole constituents,respectively.The obtained center-of-mass anomalous velocity is found to exhibit a non-trivial dependence on the fields,as well as the wave function and valley index of the exciton.These findings can serve as a general guide for the field-control of the valley-dependent exciton transport,enabling the design of novel quantum optoelectronic and valleytronic devices.