Modulation of quantum geometry and its coupling to pseudo-electric field by dynamic strain.

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.

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 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.

It has recently been realized that the first-order moment of the Berry curvature, namely, the Berry curvature dipole (BCD), can give rise to nonlinear current in a wide variety of time-reversal invariant and non-centrosymmetric materials. While the BCD in two-dimensional Dirac systems is known to be finite only in the presence of either substantial spin-orbit coupling where low-energy Dirac quasiparticles form tilted cones or higher order warping of the Fermi surface, we argue that the low-energy Dirac quasiparticles arising from the merging of a pair of Dirac points without any tilt or warping of the Fermi surface can lead to a nonzero BCD. Remarkably, in such systems, the BCD is found to be independent of Dirac velocity as opposed to the Dirac dispersion with a tilt or warping effects. We further show that the proposed systems can naturally host helicity-dependent photocurrent due to their linear momentum-dependent Berry curvatures. Finally, we discuss an important byproduct of this work, i.e., nonlinear anomalous Nernst effect as a second-order thermal response.

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 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.

Quantum geometry characterizes the geometric properties of Bloch electrons in the wave space, represented by the quantum metric and the Berry curvature. Recent studies have revealed that the quantum geometry plays a major role in various physical phenomena, from multipole to non-Hermitian physics. For superconductors, the quantum geometry is clarified to appear in the superfluid weight, an essential quantity of superconductivity. Although the superfluid weight was considered to be determined by the Fermi-liquid contribution for a long time, the geometric contribution is not negligible in some superconductors such as artificial flat-band systems and monolayer FeSe. While the superfluid weight is essential for many superconducting phenomena related to the center of mass momenta of Cooper pairs (CMMCP), the full scope of the quantum geometric effect on superconductivity remains unresolved. In this paper, we study the quantum geometric effect on the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state acquiring a finite CMMCP in equilibrium. As a benchmark, the phase diagrams of effective models for monolayer FeSe in an in-plane magnetic field are calculated. In the case of the isotropic $s$-wave pairing, the quantum geometry stabilizes the BCS state, and a metastable BCS state appears in the high-magnetic-field region. In addition, the quantum geometry induces the phase transition from the FFLO state to the BCS state with increasing temperature. However, for the intersublattice pairing, the quantum geometry gives a negative contribution to the superfluid weight; this can induce the FFLO superconductivity in particular parameter sets.

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.

Water flow through a carbon nanotube: A comparison between static and terahertz electric fields

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 jellium model is a paradigmatic problem in condensed matter physics, exhibiting a phase transition between metallic and Wigner crystal phases. However, its vanishing Berry curvature makes it ill suited for studying recent experimental platforms that combine strong interactions with nontrivial quantum geometry. These experiments inspired the anomalous Hall crystal (AHC)-a topological variant of the Wigner crystal. The AHC spontaneously breaks continuous translation symmetry but has a nonzero Chern number. In this Letter, we introduce λ-jellium, a minimal extension of the two-dimensional jellium model. Its Berry curvature distribution is controlled by a single parameter λ, where λ=0 corresponds to the standard jellium model. This setup facilitates the systematic exploration of Berry curvature's impact on electron crystallization. The phase diagram of this model, established using self-consistent Hartree Fock calculations, reveals several interesting features: (i)The AHC phase occupies a large region of the phase diagram. (ii)Two distinct Wigner crystal phases, the latter enabled by quantum geometry, and two distinct Fermi liquid phases are present. (iii)A continuous phase transition separates the AHC and one of the Wigner crystal phases. (iv)In some parts of the AHC phase, the lattice geometry is nontriangular, unlike in the classical Wigner crystal. In addition to elucidating the physics of correlated electrons with nonzero Berry curvature, we expect that the simplicity of the model makes it an excellent starting point for more advanced numerical methods.

We demonstrate robust and reversible electric-current control of the anomalous Hall effect (AHE) in a two-dimensional WTe₂/Fe₃GeTe₂ (FGT) stack. Applying a current through Td-WTe₂ leads to a giant modulation of the AHE of the adjacent FGT layer, with the relative change of the AHE conductivity exceeding 180%. Control experiments show that i) the observed effect is absent in pure FGT, ii) the modulation weakens in thicker FGT films, confirming its interfacial origin, and iii) the modulation peaks for bilayer WTe₂, indicating that the Berry-curvature dipole (BCD) plays the dominant role in the modulation. We propose that the charge current I generates an out-of-plane magnetization Mz via BCD in WTe₂ and Mz modifies the exchange splitting of FGT via the inverse magnetic proximity effect, thereby altering its Berry curvature and nontrivially influencing the AHE. The demonstrated method of AHE control offers new possibilities for magnetism control, i.e., for the study of AHE-transistors as well as electric-current control of quantum magnets, especially magnetic insulators.

During the past two decades, it has been established that a non-trivial electron wave-function topology generates an anomalous Hall effect (AHE), which shows itself as a Hall conductivity non-linear in magnetic field. Here, we report on an unprecedented case of field-linear AHE. In Mn3Sn, a kagome magnet, the out-of-plane Hall response, which shows an abrupt jump, was discovered to be a case of AHE. We find now that the in-plane Hall response, which is perfectly linear in magnetic field, is set by the Berry curvature of the wavefunction. The amplitude of the Hall response and its concomitant Nernst signal exceed by far what is expected in the semiclassical picture. We argue that magnetic field induces out-of-plane spin canting and thereafter gives rise to nontrivial spin chirality on the kagome lattice. In band structure, we find that the spin chirality modifies the topology by gapping out Weyl nodal lines unknown before, accounting for the AHE observed. Our work reveals intriguing unification of real-space Berry phase from spin chirality and momentum-space Berry curvature in a kagome material.

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.