Electro-optic Kerr effect induced by nonlinear transport in monolayer WTe 2

The anomalous Hall effect in time-reversal symmetry broken systems is underpinned by the concept of Berry curvature in band theory. However, recent experiments reveal that the nonlinear Hall effect (NHE) can be observed in non-magnetic systems without applying an external magnetic field. The emergence of NHE under time-reversal symmetric conditions can be explained in terms of non-vanishing Berry curvature dipole (BCD) arising from inversion symmetry breaking. In this work, we availed realistic tight-binding models, first-principles calculations, and symmetry analyses to explore the combined effect of transverse electric field and strain, which leads to a giant BCD in the elemental buckled honeycomb lattices—silicene, germanene, and stanene. The external electric field breaks the inversion symmetry of these systems, while strain helps to attain an asymmetrical distribution of Berry curvature of a single valley. Furthermore, the topology of the electronic wavefunction switches from the band inverted quantum spin Hall state to normal insulating one at the gapless point. This band gap closing at the critical electric field strength is accompanied by an enhanced Berry curvature and concomitantly a giant BCD at the Fermi level. Our results predict the occurrence of an electrically switchable nonlinear electrical and thermal Hall effect in a new class of elemental systems that can be experimentally verified.

As known, when a magnetic field is applied at right angles to the direction of an electric current or a thermal gradient, galvano- and thermo-magnetic effects appear in the material. In this paper, we shall show that if we study these effects in non-linear regime, the Thermodynamic Field Theory (TFT) foresees a new interesting effect: the Non Linear Hall effect. This prediction is herein submitted to experimental verification. In this paper, we shall analyse this new effect studying materials with weak thermo-electric power coefficients. We shall show the agreement between the theoretical predictions of the TFT and experiments. Expermental curves related to the non-linear Hall effect allow to determine the order of magnitude of the constant x introduced in the TFT.

The interplay between charge density wave (CDW) formation and electron correlations can lead to the emergence of novel topological phases in materials. In quasi‐2D 1T‐TaS 2 , below approximately 150 K, the system transitions from a nearly commensurate (NC) to a commensurate (C) CDW phase. Here, it is shown that the NC‐CDW to C‐CDW phase transition is marked by the emergence of a finite planar Hall and nonlinear Hall effect, alongside sign changes in the ordinary Hall and thermoelectric signals, indicating the reconstruction of the Fermi surface in the C‐CDW phase. The theoretical calculations suggest that the C‐CDW phase, stabilized by specific layer stacking, breaks both mirror and inversion symmetries. This leads to finite Berry curvature and a substantial Berry curvature dipole, giving rise to the observed planar Hall and nonlinear Hall effect. This study highlights the nontrivial band geometry‐driven physics of 1T‐TaS 2 and opens new possibilities for developing innovative sensors.

Recently, signatures of nonlinear Hall effects induced by Berry-curvature dipoles have been found in atomically thin 1T'/T-d-WTe2. In this paper, 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 1 angstrom, arise in electron-doped polar TMDs such as MoSSe, and this is easily detectable experimentally. Moreover, the magnitude and sign of the nonlinear Hall current can be easily tuned by electric gating and strain. These properties can be used to distinguish nonlinear Hall effects from classical mechanisms such as ratchet effects. Importantly, our system provides a potential scheme for building electrically switchable energy-harvesting rectifiers.

In the study of the anomalous Hall effect, the scaling relations between the anomalous Hall and longitudinal resistivities play the central role. The scaling parameters by definition are fixed as the scaling variable (longitudinal resistivity) changes. Contrary to this paradigm, we unveil that the electron-phonon scattering can result in apparent temperature dependence of scaling parameters when the longitudinal resistivity is tuned through temperature. An experimental approach is proposed to observe this hitherto unexpected temperature dependence. We further show that this phenomenon also exists in the nonlinear Hall effect in nonmagnetic inversion-breaking materials and may help identify experimentally the presence of the side-jump contribution besides the Berry-curvature dipole.

Two-dimensional materials are a fertile ground for exploring quantum geometric phenomena, with Berry curvature and its first moment, the Berry curvature dipole, playing a central role in their electronic response. These geometric properties influence electronic transport and result in the anomalous and nonlinear Hall effects, and are typically controlled using static electric fields or strain. However, the possibility of modulating quantum geometric quantities in real-time remains unexplored. Here, we demonstrate the dynamic modulation of Berry curvature and its moments, as well as the generation of a pseudo-electric field and their coupling. By placing heterostructures on a membrane, we introduce oscillatory strain together with an in-plane AC electric field and measure Hall signals that are modulated at linear combinations of the frequencies of strain and electric field. We also present direct experimental and theoretical evidence for coupling between pseudo-electric field and quantum geometry that results in an unusual dynamic strain-induced Hall response. This approach opens up a new pathway for controlling quantum geometry on demand, moving beyond conventional static perturbations. The coupling of the pseudo-electric field with Berry curvature provides a framework for external electric field-free anomalous Hall response and opens new avenues for probing the topological properties.

Non-centrosymmetric topological material has attracted intense attention due to its superior characteristics as compared with the centrosymmetric one, although probing the local quantum geometry in non-centrosymmetric topological material remains challenging. The non-linear Hall (NLH) effect provides an ideal tool to investigate the local quantum geometry. Here, we report a non-centrosymmetric topological phase in ZrTe5, probed by using the NLH effect. The angle-resolved and temperature-dependent NLH measurement reveals the inversion and ab-plane mirror symmetries breaking at <30 K, consistently with our theoretical calculation. Our findings identify a new non-centrosymmetric phase of ZrTe5 and provide a platform to probe and control local quantum geometry via crystal symmetries.

A new addition to the family of Hall effects is the nonlinear Hall effect. We investigate the role of hexagonal warping of the band structure of surface Dirac fermions in the nonlinear Hall effect in 3D topological insulators. Most relevant to our study is Bi2Te3, where we show that its surface states exhibit pronounced nonlinear Hall effect in the presence of warping. We investigate this nonlinear Hall effect as a function of Fermi energy, bandgap, warping strength, and temperature.

We predict a nonlinear Hall effect in certain Weyl semimetals with broken inversion symmetry. When the energy dispersions about pairs of Weyl nodes are skewed -- the Weyl cones are "tilted" -- the concerted actions of the anomalous velocity and the chiral anomaly give rise to the nonlinear Hall effect. This Hall conductivity is linear in both electric and magnetic fields, and depends critically on the tilting of the Weyl cones. We also show that this effect does not rely on a finite Berry curvature dipole, in contrast to the intrinsic quantum nonlinear Hall effect that was recently observed in type-II Weyl semimetals.

We have measured the influence of the electro-optic (EO) Kerr effect on the response of a spun highbirefringence (hi-bi) fiber current sensor in a simulated Gas Insulated System (GIS) environment. We show that the EO Kerr effect distorts the response of the sensor, and that the second-harmonic signal has a small dependence on the input polarizer angle. We also, have theoretically modeled a polarimetric current sensor using spun hi-bi fiber and compared the models to our experimental results. With the models we predict the response of a fiber current sensor in a 550 kV GIS application.

We report a first-principles study elucidating the valleytronic and nonlinear transport phenomena in buckled hexagonal MX (M = Zn, Cd; X = S, Se, Te) monolayers. Our findings establish that ZnTe and CdTe monolayers exhibit a pronounced, intrinsic Berry curvature concentrated at the K and K′ valleys, arising from their robust spin–orbit coupling and inherent inversion symmetry breaking. Crucially, we uncover a significant, non-zero Berry curvature dipole (BCD) in these systems, providing compelling evidence for a robust nonlinear Hall effect under time-reversal-symmetric conditions. Such an intrinsic second-order response is highly desirable for advanced electronic functionalities. Furthermore, we demonstrate that uniaxial strain serves as an effective and versatile tool, activating the tunability of BCD components. This enables unprecedented strain-mediated control over the magnitude and vectorial direction of second-order nonlinear currents along distinct in-plane orientations. These findings position CdTe monolayers as compelling candidates for strain-tunable nonlinear transport, culminating in a proposal for a multistate neuromorphic memory device architecture that exploits vectorial current modulation.

Quantum geometry in condensed-matter physics has two components: the real part quantum metric and the imaginary part Berry curvature. Whereas the effects of Berry curvature have been observed through phenomena such as the quantum Hall effect in two-dimensional electron gases and the anomalous Hall effect (AHE) in ferromagnets, the quantum metric has rarely been explored. Here, we report a nonlinear Hall effect induced by the quantum metric dipole by interfacing even-layered MnBi2Te4 with black phosphorus. The quantum metric nonlinear Hall effect switches direction upon reversing the antiferromagnetic (AFM) spins and exhibits distinct scaling that is independent of the scattering time. Our results open the door to discovering quantum metric responses predicted theoretically and pave the way for applications that bridge nonlinear electronics with AFM spintronics.

The Hall effect occurs only in systems with broken time-reversal symmetry, such as materials under an external magnetic field in the ordinary Hall effect and magnetic materials in the anomalous Hall effect (AHE)1. Here we show a nonlinear AHE in a non-magnetic material under zero magnetic field, in which the Hall voltage depends quadratically on the longitudinal current2-6. We observe the effect in few-layer Td-WTe2, a two-dimensional semimetal with broken inversion symmetry and only one mirror line in the crystal plane. Our angle-resolved electrical measurements reveal that the Hall voltage maximizes (vanishes) when the bias current is perpendicular (parallel) to the mirror line. The observed effect can be understood as an AHE induced by the bias current, which generates an out-of-plane magnetization. The temperature dependence of the Hall conductivity further suggests that both the intrinsic Berry curvature dipole and extrinsic spin-dependent scatterings contribute to the observed nonlinear AHE.

We report on a theoretical study on the nonlinear transport in two dimensions due to both Rashba (with strength α) and Dresselhaus (with strength β) spin–orbit couplings (SOCs). Based on the Boltzmann transport formalism, we study both the magnetic control of nonreciprocal charge transport and nonlinear Hall effect using a general Hamiltonian model. It is revealed that the nonlinear conductivity is significantly anisotropic and can be strongly modulated by the direction of a magnetic field as well as by SOC strengths. We further derive the analytic formulas in the weak-field or high-density regime, in good accordance with numerical results. Intriguingly, we demonstrate that the nonlinear conductivities satisfy the symmetry relations σxxx(2)(α,β)=−σyyy(2)(β,α) and σxyy(2)(α,β)=−σyxx(2)(β,α). Based on the magnetic control of nonlinear transport, we propose a simple electrical means to quantify the ratio α/β, which is quite useful to achieve the persistent spin texture in semiconductor quantum-well structures. Our work provides valuable insights into the nonlinear transport physics and open avenues to design anisotropic rectifying devices.

Few-layer CrPS4is a two-dimensional (2D) magnetic material with excellent stability in ambient environment, which attracted significant interest in recent research. Here, via first-principles calculations, we show that 2D CrPS4hosts a variety of intriguing anomalous Hall transport phenomena, owing to its layer-dependent magnetism and symmetry character. Monolayer CrPS4can display a sizable linear anomalous Hall effect, while its nonlinear anomalous Hall response is forbidden. In contrast, bilayer CrPS4can produce pronounced intrinsic nonlinear anomalous Hall response from Berry-connection polarizability, in the absence of linear anomalous Hall effect. We clarify that the large peaks in these responses originate from gapped Dirac points in the band structure. Furthermore, we show that bilayer CrPS4also hosts a layer Hall effect, where the charge Hall current in the two layers are equal in magnitude but flow in opposite directions. This effect can be detected as an anomalous Hall signal induced by an applied gate field. Finally, even-layer CrPS4also exhibits pronounced in-plane anomalous Hall effect, where the Hall signal is linearly proportional to the applied in-plane magnetic field. Our findings unveil the rich and interesting Hall transport phenomena in 2D CrPS4magnets, suggesting its potential in electronic and spintronic device applications.