Observation of the nonlinear Hall effect under time-reversal-symmetric conditions

Abstract

2The electrical Hall effect is the production of a transverse voltage under an out-of-plane magnetic field [1]. Historically, studies of the Hall effect have led to major breakthroughs including the discoveries of Berry curvature and the topological Chern invariants [2, 3]. In magnets, the internal magnetization allows Hall conductivity in the absence of external magnetic field [3]. This anomalous Hall effect (AHE) has become an important tool to study quantum magnets [3][4][5][6][7][8]. In nonmagnetic materials without external magnetic fields, the electrical Hall effect is rarely explored because of the constraint by time-reversal symmetry.However, strictly speaking, only the Hall effect in the linear response regime, i.e., the Hall voltage linearly proportional to the external electric field, identically vanishes due to time-reversal symmetry [9]. The Hall effect in the nonlinear response regime, on the other hand, may not be subject to such symmetry constraints [10][11][12]. Here, we report the observation of the nonlinear Hall effect (NLHE) [12] in the electrical transport of the nonmagnetic 2D quantum material, bilayer WTe 2 . Specifically, flowing an electrical current in bilayer WTe 2 leads to a nonlinear Hall voltage in the absence of magnetic field. The NLHE exhibits unusual properties sharply distinct from the AHE in metals: The NLHE shows a quadratic I -V characteristic; It strongly dominates the nonlinear longitudinal response, leading to a Hall angle of ∼ 90 • . We further show that the NLHE directly measures the "dipole moment" [12] of the Berry curvature, which arises from layer-polarized Dirac fermions in bilayer WTe 2 . Our results demonstrate a new Hall effect and provide a powerful methodology to detect Berry curvature in a wide range of nonmagnetic quantum materials in an energy-resolved way.In 1879 Edwin H. Hall observed that, when an electrical current passes through a gold film under a magnetic field, a transverse voltage develops [1]. This effect, known as the Hall effect, forms the basis of both fundamental research and practical applications such as magnetic field measurements and motion detectors. In contrast to the classical Hall effect where the Lorentz force bends the trajectory of the charge carriers, quantum mechanics describes the "bending" by the intrinsic geometry of the quantum electron wavefunctions under time-reversal symmetry breaking. This crucial theoretical understanding eventually led to the seminal discoveries of the Berry curvature and the topological Chern number, which have become pillars of modern condensed matter physics [2, 3]. One important cur-3 rent frontier is to identify AHE with quantized or topological character in unconventional magnetic quantum materials, where spin-orbit coupling (SOC), geometrical frustration and electronic correlations coexist [3][4][5][6][7][8]. These extensive studies [1,[3][4][5][6][7][8] have established a paradigm for the electrical Hall effect: (1) A non-vanishing Hall conductivity arises from the momentum-integrated Berry curva...

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