The Hall effect occurs only in systems with broken time-reversal symmetry, such as solids under an external magnetic field in the ordinary Hall effect and magnetic materials in the anomalous Hall effect (AHE) 1 . Here we show a new Hall effect in a nonmagnetic material under zero magnetic field, in which the Hall voltage depends quadratically on the longitudinal current 2-6 . We observe the effect (referred to as nonlinear AHE) in two-dimensional Td-WTe2, a semimetal with broken inversion symmetry and only one mirror line in the crystal plane. Our angle-resolved electrical measurements reveal that the Hall voltage changes sign when the bias current reverses direction; it 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 intrinsic Berry curvature dipole and extrinsic spin-dependent scatterings contribute to the observed nonlinear AHE. Our results open the possibility of exploring the intrinsic Berry curvature effect in nonlinear electrical transport in solids 3-7 .Unlike the linear Hall effect that has to vanish to satisfy the Onsager's reciprocity relation in a time-reversal invariant system, in principle, the nonlinear Hall effect does not have to vanish 8 . On the other hand, a second-order nonlinear effect occurs only in systems with broken inversion symmetry 9 . Atomically thin Td-WTe2 possesses all the right symmetries to realize the second-order nonlinear anomalous Hall effect (AHE) with an in-plane Hall conductivity under an in-plane bias current. Monolayer WTe2 of the Td/T' polytype consists of a layer of W atoms sandwiched between two layers of Te atoms in a distorted octahedral coordination 10 ( Fig. 1a). It is centrosymmetric with one mirror line (dashed line, Fig. 1a) along the crystal b-axis. Multilayer Td-WTe2 is formed by stacking monolayers with rotated alternating layers by 180 degrees 10 ( Fig. 1a). It is non-centrosymmetric and has point group (Ref. 11 ). In contrast to the bulk (point group 2 1 ) 10 , the screw-axis and glide plane symmetries are broken at the surfaces to allow an in-plane polar axis along the mirror line. Pristine Td-WTe2 is a semimetal with nearly compensated electron and hole densities down to a thickness of three layers [12][13][14][15] . An array of quantum revelations has been recently reported in this system including a two-dimensional (2D) topological insulator in the monolayer limit [16][17][18][19] , superconductivity induced by electrostatic doping in monolayers 20, 21 , and a switchable ferroelectric metal 2 in two-and three-layers 22 . Here we investigate the nonlinear electrical properties of atomically thin Td-WTe2.In our experiment, Td-WTe2 samples with a thickness of 4 -8 layers have been studied. They were fabricated by mechanical exfoliation from bulk crystals (HQ Graphene) and were capped by hexagonal boron nitride th...

Exploiting the valley degree of freedom to store and manipulate information provides a novel paradigm for future electronics. A monolayer transition-metal dichalcogenide (TMDC) with a broken inversion symmetry possesses two degenerate yet inequivalent valleys, which offers unique opportunities for valley control through the helicity of light. Lifting the valley degeneracy by Zeeman splitting has been demonstrated recently, which may enable valley control by a magnetic field. However, the realized valley splitting is modest (∼0.2 meV T). Here we show greatly enhanced valley spitting in monolayer WSe, utilizing the interfacial magnetic exchange field (MEF) from a ferromagnetic EuS substrate. A valley splitting of 2.5 meV is demonstrated at 1 T by magnetoreflectance measurements and corresponds to an effective exchange field of ∼12 T. Moreover, the splitting follows the magnetization of EuS, a hallmark of the MEF. Utilizing the MEF of a magnetic insulator can induce magnetic order and valley and spin polarization in TMDCs, which may enable valleytronic and quantum-computing applications.

The interaction induced localization of electrons -the Mott transition -is expected to occur in the half-filled Hubbard model [1][2][3]24,25 . The ground state is a metal with a sharply defined electronic Fermi surface when the kinetic energy of the electrons -characterized by the bandwidth 𝑊far exceeds their interaction energy -characterized by the on-site Coulomb repulsion 𝑈 . Conversely, when 𝑈 ≫ 𝑊, the ground state is an electrical insulator with a charge-gap. The system undergoes a MIT when 𝑈 and 𝑊 become comparable. Although this picture is widely accepted from the seminal works of Mott and Hubbard, the nature of the transition remains poorly understood. In most materials, the transitions are driven first-order and often accompanied by simultaneous magnetic, structural or other forms of ordering 1,3 . Continuous MIT, which exhibits no symmetry