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...

Time reversal and spatial inversion are two key symmetries for conventional Bardeen-Cooper-Schrieffer (BCS) superconductivity . Breaking inversion symmetry can lead to mixed-parity Cooper pairing and unconventional superconducting properties. Two-dimensional (2D) NbSe has emerged as a new non-centrosymmetric superconductor with the unique out-of-plane or Ising spin-orbit coupling (SOC). Here we report the observation of an unusual continuous paramagnetic-limited superconductor-normal metal transition in 2D NbSe. Using tunelling spectroscopy under high in-plane magnetic fields, we observe a continuous closing of the superconducting gap at the upper critical field at low temperatures, in stark contrast to the abrupt first-order transition observed in BCS thin-film superconductors. The paramagnetic-limited continuous transition arises from a large spin susceptibility of the superconducting phase due to the Ising SOC. The result is further supported by self-consistent mean-field calculations based on the ab initio band structure of 2D NbSe. Our findings establish 2D NbSe as a promising platform to explore novel spin-dependent superconducting phenomena and device concepts , such as equal-spin Andreev reflection and topological superconductivity.

Two-dimensional transition metal dichalcogenides (TMDs) have been attracting significant interest 1-8 due to a range of properties, such as layer-dependent inversion symmetry, valleycontrasted Berry curvatures, and strong spin-orbit coupling (SOC). Of particular interest is niobium diselenide (NbSe 2 ), whose superconducting state in few-layer samples is profoundly affected by an unusual type of SOC called Ising SOC 7 . Combined with the reduced dimensionality, the latter stabilizes the superconducting state against magnetic fields up to ~35 T and could lead to other exotic properties such as nodal and crystalline topological superconductivity 9-14 . Here, we report transport measurements of few-layer NbSe 2 under inplane external magnetic fields, revealing an unexpected two-fold rotational symmetry of the superconducting state. In contrast to the three-fold symmetry of the lattice, we observe that