The Berry curvature (BC) - a quantity encoding the geometric properties of the electronic wavefunctions in a solid - is at the heart of different Hall-like transport phenomena, including the anomalous Hall and the non-linear Hall and Nernst effects. In non-magnetic quantum materials with acentric crystalline arrangements, local concentrations of BC are generally linked to single-particle wavefunctions that are a quantum superposition of electron and hole excitations. BC-mediated effects are consequently observed in two-dimensional systems with pairs of massive Dirac cones and three-dimensional bulk crystals with quartets of Weyl cones. Here, we demonstrate that in materials equipped with orbital degrees of freedom local BC concentrations can arise even in the complete absence of hole excitations. In these solids, the crystals fields appearing in very low-symmetric structures trigger BCs characterized by hot-spots and singular pinch points. These characteristics naturally yield giant BC dipoles and large non-linear transport responses in time-reversal symmetric conditions.
Berry curvature dipole plays an important role in various nonlinear quantum phenomena. However, the maximum symmetry allowed for nonzero Berry curvature dipole in the transport plane is a single mirror line, which strongly limits its effects in materials. Here, via probing the nonlinear Hall effect, we demonstrate the generation of Berry curvature dipole by applied dc electric field in WTe2, which is used to break the symmetry constraint. A linear dependence between the dipole moment of Berry curvature and the dc electric field is observed. The polarization direction of the Berry curvature is …
We study the quantum nonlinear Hall effect in two-dimensional materials with time-reversal symmetry. When only one mirror line exists, a transverse charge current occurs in second-order response to an external electric field, as a result of the Berry curvature dipole in momentum space. Candidate 2D materials to observe this effect are two-dimensional transition-metal dichalcogenides~(TMDCs). First we use an ab initio based tight-binding approach to demonstrate that monolayer $T_d$-stricture TMDCs exhibit a finite Berry curvature dipole. In the $1H$ and $1T'$ phase of TMDCs, we show the emergen…
Noncentrosymmetric metals are anticipated to exhibit a $dc$ photocurrent in the nonlinear optical response caused by the Berry curvature dipole in momentum space. Weyl semimetals (WSMs) are expected to be excellent candidates for observing these nonlinear effects because they carry a large Berry curvature concentrated in small regions, i.e., near the Weyl points. We have implemented the semiclassical Berry curvature dipole formalism into an $ab~initio$ scheme and investigated the second-order nonlinear response for two representative groups of materials: the TaAs-family type-I WSMs and MoTe$_2…
Various nonlinear characteristics of solid states, such as the circular photogalvanic effect of time-reversal symmetric insulators, the quantized photogalvanic effect of Weyl semimetals, and the nonlinear Hall effect of time-reversal symmetric metals, have been associated with the Berry curvature dipole (BCD). Here, we explore the question of whether the Berry curvature dipole and multipoles of time-reversal symmetric insulators can be traced in the nonlinear optical responses. We performed real-time time-dependent density functional theory calculations and examined the second harmonic generat…
The electronic topology is generally related to the Berry curvature, which can induce the anomalous Hall effect in time-reversal symmetry breaking systems. Intrinsic monolayer transition metal dichalcogenides possesses two nonequivalent K and K' valleys, having Berry curvatures with opposite signs, and thus vanishing anomalous Hall effect in this system. Here we report the experimental realization of asymmetrical distribution of Berry curvature in a single valley in monolayer WSe2 through applying uniaxial strain to break C3v symmetry. As a result, although the Berry curvature itself is still …
The Berry curvature dipole is a physical quantity that is expected to allow various quantum geometrical phenomena in a range of solid-state systems. Monolayer transition metal dichalcogenides provide an exceptional platform to modulate and investigate the Berry curvature dipole through strain. Here we theoretically demonstrate and experimentally verify for monolayer MoS$_\rm{2}$ the generation of valley orbital magnetization as a response to an in-plane electric field due to the Berry curvature dipole. The measured valley orbital magnetization shows excellent agreement with the calculated Berr…
The physics related to Berry curvature is now a central research topic in condensed matter physics. The Berry curvature dipole (BCD) is a significant and intriguing condensed matter phenomenon that involves inversion symmetry breaking. However, the creation and controllability of BCDs have so far been limited to far below room temperature (RT) and non-volatile (i.e., ferroic) BCDs have not yet been discovered, hindering further progress in topological physics. In this work, we demonstrate a switchable and non-volatile BCD effect at RT in a topological crystalline insulator, Pb1-xSnxTe (PST), w…
Recent experiments have measured local uniaxial strain fields in twisted bilayer graphene (TBG). Our calculations found that the finite Berry curvature generated by breaking the sublattice symmetry and the band proximity between narrow bands in these TBG induces a giant Berry dipole of order 10\,nm or larger. The large Berry dipole leads to transverse topological non-linear charge currents which dominates over the linear bulk valley current at experimentally accessible crossover in-plane electric field of $\sim 0.1 {\rm mV} / μ\rm{m}$. This anomalous Hall effect, due to Berry dipole, is strong…
Surface-bulk hybridization enhances the Berry curvature dipole in GaAs(110)
Institute for Theoretical Solid State Physics, IFW Dresden（德累斯顿亥姆霍兹中心IFW凝聚态物理理论研究所）；Centro Atómico Bariloche, Instituto de Nanociencia y Nanotecnología (CNEA-CONICET)（巴里洛切原子中心，纳米科学与技术研究所（阿根廷核能委员会-国家科学研究委员会））；Instituto Balseiro（巴尔塞罗研究所）；Würzburg-Dresden Cluster of Excellence ctd.qmat（维尔茨堡-德累斯顿卓越集群ctd.qmat）
It has been recently established that optoelectronic and non-linear transport experiments can give direct access to the dipole moment of the Berry curvature in non-magnetic and non-centrosymmetric materials. Thus far, non-vanishing Berry curvature dipoles have been shown to exist in materials with substantial spin-orbit coupling where low-energy Dirac quasiparticles form tilted cones. Here, we prove that this topological effect does emerge in two-dimensional Dirac materials even in the complete absence of spin-orbit coupling. In these systems, it is the warping of the Fermi surface that trigge…
Piezotronics is an emerging field, which exploits strain to control the transport properties in condensed matters. At present, piezotronics research majorly focuses on insulators with tunable electric dipole by strain. Metals are excluded in this type of applications due to the absence of electric dipole. The recently discovered Berry curvature dipole can exist in metals, thus introduces the possibility of the piezotronics phenomena in them. In this paper, we predict that strain can switch the Berry curvature dipole, and lead the nonlinear Hall effect in the two-dimensional (2D) 1$H$-MX$_2$ (M…
We provide a unified semiclassical theory for thermoelectric responses of any observable represented by an operator $\hat{\boldsymbolθ}$ that is well-defined in periodic crystals. The Einstein and Mott relations are established generally, in the presence of Berry-phase effects, for various physical realizations of $\hat{\boldsymbolθ}$ in electronic systems, including the familiar case of the electric current as well as the currently controversial cases of the spin polarization and spin current. The magnetization current, which has been proven indispensable in the thermoelectric response of ele…
New Cornerstone Science Laboratory, Department of Physics, The University of Hong Kong（新Cornerstone科学实验室，香港大学物理系）；State Key Laboratory of Optical Quantum Materials, The University of Hong Kong（香港大学光学量子材料国家重点实验室）；Department of Electrical and Electronic Engineering, The University of Hong Kong（香港大学电子电气工程系）；Quantum Science Center of Guangdong-Hong Kong-Macao Great Bay Area（粤港澳大湾区量子科学中心）；Materials Innovation Institute for Life Sciences and Energy (MILES), HKU-SIRI, Shenzhen（深圳港大西丽研究院生命科学与能源材料创新研究所）
In symmetry-broken crystalline solids, pole structures of Berry curvature (BC) can emerge, and they have been utilized as a versatile tool for controlling transport properties. For example, the monopole component of the BC is induced by the time-reversal symmetry breaking, and the BC dipole arises from a lack of inversion symmetry, leading to the anomalous Hall and nonlinear Hall effects, respectively. Based on first-principles calculations, we show that the ferroelectricity in a tin telluride monolayer produces a unique BC distribution, which offers charge- and spin-controllable photocurrents…
Recent experimental evidence for the quantum spin Hall (QSH) state in monolayer WTe$_2$ has bridged two of the most active fields of condensed matter physics, 2D materials and topological physics. This 2D topological crystal also displays unconventional spin-torque and gate-tunable superconductivity. While the realization of QSH has demonstrated the nontrivial topology of the electron wavefunctions of monolayer WTe$_2$, the geometrical properties of the wavefunction, such as the Berry curvature, remain unstudied. On the other hand, it has been increasingly recognized that the Berry curvature p…
Transitions between topologically distinct electronic states have been predicted in different classes of materials and observed in some. A major goal is the identification of measurable properties that directly expose the topological nature of such transitions. Here we focus on the giant-Rashba material bismuth tellurium iodine (BiTeI) which exhibits a pressure-driven phase transition between topological and trivial insulators in three-dimensions. We demonstrate that this transition, which proceeds through an intermediate Weyl semi-metallic state, is accompanied by a giant enhancement of the B…
Topological aspects of electron wavefunction play a crucial role in determining the physical properties of materials. Berry curvature and Chern number are used to define the topological structure of electronic bands. While Berry curvature and its effects in materials have been studied, detecting changes in the topological invariant, Chern number, is challenging. In this regard, twisted double bilayer graphene (TDBG) has emerged as a promising platform to gain electrical control over the Berry curvature hotspots and the valley Chern numbers of its flat bands. In addition, strain induced breakin…
Light-tunable quantum metric non-linear Hall response in Berry dipole semimetals
Centre for Nanotechnology, Indian Institute of Technology Roorkee（印度理工学院鲁尔基分校纳米技术中心）；Solid State and Structural Chemistry Unit, Indian Institute of Science, Bangalore（印度科学学院固态与结构化学单元）
For a long period of time, we have been seeking how Berry curvature influnces the transport properties in materials breaking time-reversal symmetry. In time-reversal symmetric material, there will be no thermoelectric current induced by Berry curvature in linear regime. However, the nonlinear Hall current can be shown in non-magnetic and non-centrosymmetric materials, where Berry curvature dipole plays an important role. Most studies are developed from semi-classical Boltzmann equation. Here we show the quantum kinetic theory for nonlinear Nernst effect and introduce a new type of Berry curvat…
Second-order dc conductivity in the velocity-gauge Keldysh formalism: gauge-invariant decomposition into nonlinear Drude, Berry-curvature-dipole, and quantum-metric responses
The smooth topology change of Berry's phase from a Dirac monopole-like configuration to a dipole configuration, when one approaches the monopole position in the parameter space, is analyzed in an exactly solvable model. A novel aspect of Berry's connection ${\cal A}_{k}$ is that the geometrical center of the monopole-like configuration and the origin of the Dirac string are displaced in the parameter space. Gauss' theorem $\int_{S}(\nabla\times {\cal A})\cdot d\vec{S}=\int_{V} \nabla\cdot (\nabla\times {\cal A}) dV=0$ for a volume $V$ which is free of singularities shows that a combination of …
Berry curvature (BC) governs topological phases of matter and generates anomalous transport. When a magnetic field is applied, phonons can acquire BC indirectly through spin-lattice coupling, leading to a linear phonon Hall effect. Here, we show that polar lattice distortion directly couples to a phonon BC dipole, which causes a switchable non-linear phonon Hall effect. In a SnS monolayer, the in-plane ferroelectricity induces a phonon BC and leads to the phononic version of the non-volatile BC memory effect. As a new type of ferroelectricity-phonon coupling, the phonon Rashba effect emerges a…
Under broken time reversal symmetry such as in the presence of external magnetic field or internal magnetization, a transverse voltage can be established in materials perpendicular to both longitudinal current and applied magnetic field, known as classical Hall effect. However, this symmetry constraint can be relaxed in the nonlinear regime, thereby enabling nonlinear anomalous Hall current in time-reversal invariant materials - an underexplored realm with exciting new opportunities beyond classical linear Hall effect. Here, using group theory and first-principles theory, we demonstrate a rema…
We report the strong dependence of resistance on uniaxial strain in monolayer WSe2 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 W…
Recently, signatures of nonlinear Hall effects induced by Berry-curvature dipoles have been found in atomically thin 1T'/Td-WTe$_2$. In this work, we show that in strained polar transition-metal dichalcogenides(TMDs) with 2H-structures, Berry-curvature dipoles created by spin degrees of freedom lead to strong nonlinear Hall effects. Under an easily accessible uniaxial strain of order 0.2%, strong nonlinear Hall signals, characterized by a Berry-curvature dipole on the order of 1Å, arise in electron-doped polar TMDs such as MoSSe, and this is easily detectable experimentally. Moreover, the magn…
Linear thermal noise induced by Berry curvature dipole in a four-terminal system
College of Physics and Optoelectronic Engineering, Shenzhen University（深圳大学物理与光电工程学院）；Quantum Science Center of Guangdong-Hongkong-Macao Greater Bay Area (Guangdong)（粤港澳大湾区量子科学中心（广东））；Department of Physics, The University of Hong Kong（香港大学物理系）
本文研究了四端系统中有限 Berry 曲率偶极子引起的线性热噪声，通过非平衡 Green 函数方法与 semiclassical 结果对比，建立了多端系统终端分辨噪声与 bulk 运输方向分辨噪声的一一对应关系，揭示了量子输运中的对称性选择规则。
Electrons moving in a Bloch band are known to acquire an anomalous Hall velocity proportional to the Berry curvature of the band which is responsible for the intrinsic linear Hall effect in materials with broken time-reversal symmetry. Here, we demonstrate that there is also an anomalous correction to the electron acceleration which is proportional to the Berry curvature dipole and is responsible for the Nonlinear Hall effect recently discovered in materials with broken inversion symmetry. This allows us to uncover a deeper meaning of the Berry curvature dipole as a nonlinear version of the Dr…
Topological Weyl semimetals (WSMs) have been predicted to be excellent candidates for detecting Berry curvature dipole (BCD) and the related non-linear effects in electronics and optics due to the large Berry curvature concentrated around the Weyl nodes. And yet, linearized models of isolated tilted Weyl cones only realize a diagonal non-zero BCD tensor which sum to zero in the model of WSM with multiple Weyl nodes in the presence of mirror symmetry. On the other hand, recent \textit{ab initio} work has found that realistic WSMs like TaAs-type or MoTe$_2$-type compounds, which have mirror symm…
Semiconductor transistors are essential elements of electronic circuits as they enable, for example, the isolation or amplification of voltage signals. While conventional transistors are point-type (lumped-element) devices, it may be highly interesting to realize a distributed transistor-type optical response in a bulk material. Here, we show that low-symmetry two-dimensional metallic systems may be the ideal solution to implement such a distributed-transistor response. To this end, using the semiclassical Boltzmann equation approach, we characterize the optical conductivity of a two-dimension…
