Non-centrosymmetric topological phase probed by non-linear Hall effect

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.

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.

Unconventional responses upon breaking discrete or crystal symmetries open avenues for exploring emergent physical systems and materials. By breaking inversion symmetry, a nonlinear Hall signal can be observed, even in the presence of time-reversal symmetry, quite different from the conventional Hall effects. Low-symmetry two-dimensional materials are promising candidates for the nonlinear Hall effect, but it is less known when a strong nonlinear Hall signal can be measured, in particular, its connections with the band-structure properties. By using model analysis, we find prominent nonlinear Hall signals near tilted band anticrossings and band inversions. These band signatures can be used to explain the strong nonlinear Hall effect in the recent experiments on two-dimensional WTe_{2}. This Letter will be instructive not only for analyzing the transport signatures of the nonlinear Hall effect but also for exploring unconventional responses in emergent materials.

In a system with broken inversion symmetry, a second-order nonlinear Hall effect can survive even in the presence of time-reversal symmetry. In this work, we show that a giant nonlinear Hall effect can exist in twisted bilayer WTe2 system. The Berry curvature dipole of twisted bilayer WTe2 (θ = 29.4°) can reach up to ~1400 Å, which is much larger than that in previously reported nonlinear Hall systems. In twisted bilayer WTe2 system, there exist abundant band anticrossings and band inversions around the Fermi level, which brings a complicated distribution of Berry curvature, and leads to the nonlinear Hall signals that exhibit dramatically oscillating behavior in this system. Its large amplitude and high tunability indicate that the twisted bilayer WTe2 can be an excellent platform for studying the nonlinear Hall effect.

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.

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.

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.

Electric control of magnetism at room temperature is crucial for developing next-generation high-performance spintronics. However, the intrinsic incompatibility between ferroelectricity and magnetism in crystal symmetry, along with the absence of strong magnetoelectric coupling mechanisms, continues to pose major challenges. In this work, we propose a general theoretical framework for magnon manipulation based on ferroelectric polarization switching in two-dimensional multiferroics. Our results demonstrate that, in monolayer hexagonal multiferroics, ferroelectric switching can significantly modulate the intralayer spin exchanges, enabling nonvolatile ferroelectric control of magnons. More importantly, ferroelectric polarization reversal leads to a sign change in the Berry curvature, ensuring effective control over the valley and nonlinear Hall response of magnons. Combining density functional theory calculations, we further identify a class of material candidates with Curie temperatures near room temperature. Our results provide a new way toward low-power and ferroelectrically controllable spintronics.

The nonlinear Hall effect (NLHE) can induce optical anisotropy by modifying a material's dielectric tensor, presenting opportunities for novel characterization and device applications. While the magneto-optical Kerr effect (MOKE) probes the linear Hall effect (LHE) in magnetic materials, an analogous optical probe for NLHE in nonmagnetic, time-reversal symmetric systems remains highly desirable. Here, we theoretically propose and investigate an NLHE-induced electro-optic Kerr effect (EOKE) as such a probe. Focusing on monolayer (ML) ${\mathrm{WTe}}_{2}$, a prototypical NLHE material, our analysis considers contributions from Berry curvature dipole (BCD), Drude, injection, and shift mechanisms. We demonstrate that the EOKE signal in ${\mathrm{WTe}}_{2}$ is predominantly governed by the BCD. Furthermore, the Kerr angle exhibits temporal oscillations at different optical frequencies, suggesting EOKE as a promising route for the time-resolved detection of NLHE and the dynamic investigation of material topology.

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.

We report the observation of nonlinear anomalous Hall effect (NLAHE) in the multilayered organic conductor α-(BEDT-TTF)2I3 in the charge order (CO) insulating phase just under the critical pressure for transition into two-dimensional (2D) massless Dirac fermion (DF) phase. We successfully extracted the finite nonlinear Hall voltage proportional to square current at zero magnetic field. The observed NLAHE features, current direction dependence and correlation with CO, are consistent with the previous estimation assuming 2D massive DF with a pair of tilted Dirac cones. This is the first observation of topological transport in organic conductors, and also the first example of NLAHE in the electronic phase with spontaneous symmetry breaking.

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.

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.

Recently, the linear and nonlinear planar Hall effect (PHE) on the topological insulators (TIs) surface has been extensively studied in experiments. To explain this phenomenon, various microscopic mechanisms are proposed theoretically, and one has to employ different mechanisms to separately understand the linear and nonlinear PHE even for the same system. Here, we study the planar magnetic resistance effect in TI thin film and find that a peculiar anisotropic scattering and a spin valve structure with respect to the PHE can be caused by the tilt and shift of Dirac cones, respectively, which are induced by the combination of spin-momentum locking of surface states and an in-plane magnetic field. The tilt and shift effects can act as the origin of both the linear and nonlinear PHE by distorting the spin texture of surface states or forming the spin polarization. These two mechanisms interplay and dominate, respectively, in strong coupling (thin TI) and decoupling (thick TI) between bottom and top surfaces. For thick TI film, we show that both the linear and nonlinear PHEs induced by the tilt effect can recover the results observed in recent experiments. Our theory provides a perspective to understand the origin of both linear and nonlinear PHE observed in recent experiments.

In recent years, nonreciprocal transport measurement has emerged as a probe of spin orbit interaction, spin texture, superconductivity, and other fundamental properties of materials. Here, we study the nonlinear Hall effect (NLHE) in ${\mathrm{Bi}}_{2}{\mathrm{Se}}_{3}/\mathrm{CoFeB}$ heterostructures measured by second harmonic voltage method. Magneto-optical Kerr effect measurements demonstrate the origin of the NLHE to be the asymmetric magnon scattering mechanism. Moreover, a linear relation between the nonlinear Hall resistance and the electron phase coherence length of ${\mathrm{Bi}}_{2}{\mathrm{Se}}_{3}$ is observed between 5 and 50 K. We propose a phenomenological model that explains the enhancement of the NLHE below 50 K as a result of one-dimensional antilocalization of electrons from spin disorder, enabled by spin-momentum locking and conservation of angular momentum.