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Register a new userBerry connection polarizability tensor and third-order Hall effect
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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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n this paper, we employ a fully microscopic approach to the study of interlayer excitons in layered materials. We discuss the utilization of Fowlers and Karplus method to access the dynamical polarizability of non--interacting interlayer excitons in a $mathrm{WSe}_{2}/mathrm{WS}_{2}$--based van der Waals heterostructure. Following from the calculation of the linear polarizability, we consider Svendsens variational method to the dynamic third--order polarizability. With this variational method, we study both two--photon absorption and third--harmonic generation processes for interlayer excitons in a $mathrm{WSe}_{2}/mathrm{WS}_{2}$ hetero--bilayer, discussing the various intra--excitonic energy level transitions observed.
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.
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.
We propose theoretically a reconfigurable two-dimensional (2D) hexagonal sonic crystal with higher-order topology protected by the six-fold, $C_6$, rotation symmetry. The acoustic band gap and band topology can be controlled by rotating the triangular scatterers in each unit-cell. In the nontrivial phase, the sonic crystal realizes the topological spin Hall effect in a higher-order fashion: (i) The edge states emerging in the bulk band gap exhibits partial spin-momentum locking and are gapped due to the reduced spatial symmetry at the edges. (ii) The gapped edge states, on the other hand, stabilize the topological corner states emerging in the edge band gap. The partial spin-momentum locking is manifested as pseudo-spin-polarization of edge states away from the time-reversal invariant momenta, where the pseudospin is emulated by the acoustic orbital angular momentum. We reveal the underlying topological mechanism using a corner topological index based on the symmetry representation of the acoustic Bloch bands.
Response properties that are purely intrinsic to physical systems are of paramount importance in physics research, as they probe fundamental properties of band structures and allow quantitative calculation and comparison with experiment. For anomalous Hall transport in magnets, an intrinsic effect can appear at the second order to the applied electric field. We show that this intrinsic second-order anomalous Hall effect is associated with an intrinsic band geometric property -- the dipole moment of Berry-connection polarizability (BCP) in momentum space. The effect has scaling relation and symmetry constraints that are distinct from the previously studied extrinsic contributions. Particularly, in antiferromagnets with $mathcal{PT}$ symmetry, the intrinsic effect dominates. Combined with first-principles calculations, we demonstrate the first quantitative evaluation of the effect in the antiferromagnet Mn$_{2}$Au. We show that the BCP dipole and the resulting intrinsic second-order conductivity are pronounced around band near degeneracies. Importantly, the intrinsic response exhibits sensitive dependence on the N{e}el vector orientation with a $2pi$ periodicity, which offers a new route for electric detection of the magnetic order in $mathcal{PT}$-invariant antiferromagnets.
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