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Register a new userHigher-Order Nonlinear Anomalous Hall Effects Induced by Berry Curvature Multipoles
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In recent years, it has been shown that Berry curvature monopoles and dipoles play essential roles in the anomalous Hall effect and the nonlinear Hall effect respectively. In this work, we demonstrate that Berry curvature multipoles (the higher moments of Berry curvatures at the Fermi energy) can induce higher-order nonlinear anomalous Hall (NLAH) effect. Specifically, an AC Hall voltage perpendicular to the current direction emerges, where the frequency is an integer multiple of the frequency of the applied current. Importantly, by analyzing the symmetry properties of all the 3D and 2D magnetic point groups, we note that the quadrupole, hexapole and even higher Berry curvature moments can cause the leading-order frequency multiplication in certain materials. To provide concrete examples, we point out that the third-order NLAH voltage can be the leading-order Hall response in certain antiferromagnets due to Berry curvature quadrupoles, and the fourth-order NLAH voltage can be the leading response in the surface states of topological insulators induced by Berry curvature hexapoles. Our results are established by symmetry analysis, effective Hamiltonian and first-principles calculations. Other materials which support the higher-order NLAH effect are further proposed, including 2D antiferromagnets and ferromagnets, Weyl semimetals and twisted bilayer graphene near the quantum anomalous Hall phase.
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The electronic topology is generally related to the Berry curvature, which can induce the anomalous Hall effect in time-reversal symmetry breaking systems. Intrinsic monolayer transition metal dichalcogenides possesses two nonequivalent K and K valleys, having Berry curvatures with opposite signs, and thus vanishing anomalous Hall effect in this system. Here we report the experimental realization of asymmetrical distribution of Berry curvature in a single valley in monolayer WSe2 through applying uniaxial strain to break C3v symmetry. As a result, although the Berry curvature itself is still opposite in K and K valleys, the two valleys would contribute equally to nonzero Berry curvature dipole. Upon applying electric field, the emergent Berry curvature dipole would lead to an out-of-plane orbital magnetization, which further induces an anomalous Hall effect with a linear response to E^2, known as nonlinear Hall effect. We show the strain modulated transport properties of nonlinear Hall effect in monolayer WSe2 with moderate hole-doping by gating. The second-harmonic Hall signals show quadratic dependence on electric field, and the corresponding orbital magnetization per current density can reach as large as 60. In contrast to the conventional Rashba-Edelstein effect with in-plane spin polarization, such current-induced orbital magnetization is along the out-of-plane direction, thus promising for high-efficient electrical switching of perpendicular magnetization.
Topological Weyl semimetals (WSMs) have been predicted to be excellent candidates for detecting Berry curvature dipole (BCD) and the related non-linear effects in electronics and optics due to the large Berry curvature concentrated around the Weyl nodes. And yet, linearized models of isolated tilted Weyl cones only realize a diagonal non-zero BCD tensor which sum to zero in the model of WSM with multiple Weyl nodes in the presence of mirror symmetry. On the other hand, recent textit{ab initio} work has found that realistic WSMs like TaAs-type or MoTe$_2$-type compounds, which have mirror symmetry, indeed show an off-diagonal BCD tensor with an enhanced magnitude for its non-zero components. So far, there is a lack of theoretical work addressing this contradiction for 3D WSMs. In this paper, we systematically study the BCD in 3D WSMs using lattice Weyl Hamiltonians, which go beyond the linearized models. We find that the non-zero BCD and its related important features for these WSMs do not rely on the contribution from the Weyl nodes. Instead, they are dependent on the part of the Fermi surface that lies textit{between} the Weyl nodes, in the region of the reciprocal space where neighboring Weyl cones overlap. For large enough chemical potential such Fermi surfaces are present in the lattice Weyl Hamiltonians as well as in the realistic WSMs. We also show that, a lattice Weyl Hamitonian with a non-zero chiral chemical potential for the Weyl cones can also support dips or peaks in the off-diagonal components of the BCD tensor near the Weyl nodes themselves, consistent with recent textit{ab initio} work.
We theoretically investigate the localization mechanism of quantum anomalous Hall Effect (QAHE) with large Chern numbers $mathcal{C}$ in bilayer graphene and magnetic topological insulator thin films, by applying either nonmagnetic or spin-flip (magnetic) disorders. We show that, in the presence of nonmagnetic disorders, the QAHEs in both two systems become Anderson insulating as expected when the disorder strength is large enough. However, in the presence of spin-flip disorders, the localization mechanisms in these two host materials are completely distinct. For the ferromagnetic bilayer graphene with Rashba spin-orbit coupling, the QAHE with $mathcal{C}=4$ firstly enters a Berry-curvature mediated metallic phase, and then becomes localized to be Anderson insulator along with the increasing of disorder strength. While in magnetic topological insulator thin films, the QAHE with $mathcal{C=N}$ firstly enters a Berry-curvature mediated metallic phase, then transitions to another QAHE with ${mathcal{C}}={mathcal{N}}-1$ along with the increasing of disorder strength, and is finally localized to the Anderson insulator after ${mathcal{N}}-1$ cycling between the QAHE and metallic phases. For the unusual findings in the latter system, by analyzing the Berry curvature evolution, it is known that the phase transitions originate from the exchange of Berry curvature carried by conduction (valence) bands. At the end, we provide a phenomenological picture related to the topological charges to help understand the underlying physical origins of the two different phase transition mechanisms.
The quantum anomalous Hall (QAH) effect in magnetic topological insulator (TI) represents a new state of matter originated from the interplay between topology and magnetism. The defining characteristics of the QAH ground state are the quantized Hall resistivity ($rho_{yx}$) and vanishing longitudinal resistivity ($rho_{xx}$) in the absence of external magnetic field. A fundamental question concerning the QAH effect is whether it is merely a zero-magnetic-field quantum Hall (QH) effect, or if it can host unique quantum phases and phase transitions that are unavailable elsewhere. The most dramatic departure of the QAH systems from other QH systems lies in the strong magnetic disorders that induce spatially random magnetization. Because disorder and magnetism play pivotal roles in the phase diagram of two-dimensional electron systems, the high degree of magnetic disorders in QAH systems may create novel phases and quantum critical phenomena. In this work, we perform systematic transport studies of a series of magnetic TIs with varied strength of magnetic disorders. We find that the ground state of QAH effect can be categorized into two distinct classes: the QAH insulator and anomalous Hall (AH) insulator phases, as the zero-magnetic-field counterparts of the QH liquid and Hall insulator in the QH systems. In the low disorder limit of the QAH insulator regime, we observe a universal quantized longitudinal resistance $rho_{xx} = h/e^{2}$ at the coercive field. In the AH insulator regime, we find that a magnetic field can drive it to the QAH insulator phase through a quantum critical point with distinct scaling behaviors from that in the QH phase transition. We propose that the transmission between chiral edge states at domain boundaries, tunable by disorder and magnetic fields, is the key for determining the QAH ground state.
One big achievement in modern condensed matter physics is the recognition of the importance of various band geometric quantities in physical effects. As prominent examples, Berry curvature and Berry curvature dipole are connected to the linear and the second-order Hall effects, respectively. Here, we show that the Berry connection polarizability (BCP) tensor, as another intrinsic band geometric quantity, plays a key role in the third-order Hall effect. Based on the extended semiclassical formalism, we develop a theory for the third-order charge transport and derive explicit formulas for the third-order conductivity. Our theory is applied to the two-dimensional (2D) Dirac model to investigate the essential features of BCP and the third-order Hall response. We further demonstrate the combination of our theory with the first-principles calculations to study a concrete material system, the monolayer FeSe. Our work establishes a foundation for the study of third-order transport effects, and reveals the third-order Hall effect as a tool for characterizing a large class of materials and for probing the BCP in band structure.
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