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Register a new userRevealing the Boundary Weyl Physics of the 4D Hall Effect via Phason Engineering in Metamaterials
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Quantum Hall effect (QHE) has been theoretically predicted in 4-dimensions and higher. In hypothetical $2n$-dimensions, the topological characters of both the bulk and the boundary are manifested as quantized non-linear transport coefficients that relate to higher Chern numbers of the bulk gap projection and winding numbers of the Weyl spectral singularities on the $(2n-1)$-dimensional boundaries. Here, we introduce the concept of phason engineering in metamaterials and use it to access QHE in arbitrary dimensions. We fabricate a re-configurable 2-dimensional aperiodic acoustic crystal displaying the 4D QHE and we supply a direct experimental confirmation that the topological boundary spectrum assembles in a Weyl singularity when mapped as function of the quasi-momenta. We also demonstrate novel topological wave steering enabled by this Weyl singularity.
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Weyl semimetals are intriguing topological states of matter that support various anomalous magneto-transport phenomena. One such phenomenon is a negative longitudinal ($mathbf{ abla} T parallel mathbf{B}$) magneto-thermal resistivity, which arises due to chiral magnetic effect (CME). In this paper we show that another fascinating effect induced by CME is the planar thermal Hall effect (PTHE), i.e., appearance of an in-plane transverse temperature gradient when the current due to $mathbf{ abla} T$ and the magnetic field $mathbf{B}$ are not aligned with each other. Using semiclassical Boltzmann transport formalism in the relaxation time approximation we compute both longitudinal magneto-thermal conductivity (LMTC) and planar thermal Hall conductivity (PTHC) for a time reversal symmetry breaking WSM. We find that both LMTC and PTHC are quadratic in B in type-I WSM whereas each follows a linear-B dependence in type-II WSM in a configuration where $mathbf{ abla} T$ and B are applied along the tilt direction. In addition, we investigate the Wiedemann-Franz law for an inversion symmetry broken WSM (e.g., WTe$_{2}$) and find that this law is violated in these systems due to both chiral anomaly and CME.
The manifestation of chiral anomaly in Weyl semimetals typically relies on the observation of longitudinal magnetoconductance (LMC) along with the planar Hall effect, with a specific magnetic field and angle dependence. Here we solve the Boltzmann equation in the semiclassical regime for a prototype of a Weyl semimetal, allowing for both intravalley and intervalley scattering, along with including effects from the orbital magnetic moment (OMM), in a geometry where the electric and magnetic fields are not necessarily parallel to each other. We construct the phase diagram in the relevant parameter space that describes the shift from positive to negative LMC in the presence of OMM and sufficiently strong intervalley scattering, as has been recently pointed out for only parallel electric and magnetic fields. On the other hand, we find that the chiral anomaly contribution to the planar Hall effect always remains positive (unlike the LMC) irrespective of the inclusion or exclusion of OMM, or the strength of the intervalley scattering. Our predictions can be directly tested in experiments, and may be employed as new diagnostic procedures to verify chiral anomaly in Weyl systems.
Transient optical heating provides an efficient way to trigger phase transitions in naturally occurring media through ultrashort laser pulse irradiation. A similar approach could be used to induce topological phase transitions in the photonic response of suitably engineered artificial structures known as metamaterials. Here, we predict a topological transition in the isofrequency dispersion contours of a layered graphene metamaterial under optical pumping. We show that the contour topology transforms from elliptic to hyperbolic within a subpicosecond timescale by exploiting the extraordinary photothermal properties of graphene. This new phenomenon allows us to theoretically demonstrate applications in engineering the decay rate of proximal optical emitters, ultrafast beam steering, and dynamical far-field subwavelength imaging. Our study opens a disruptive approach toward ultrafast control of light emission, beam steering, and optical image processing.
The ordinary Hall effect refers to generation of a transverse voltage upon exertion of an electric field in the presence of an out-of-plane magnetic field. While a linear Hall effect is commonly observed in systems with breaking time-reversal symmetry via an applied external magnetic field or their intrinsic magnetization1, 2, a nonlinear Hall effect can generically occur in non-magnetic systems associated with a nonvanishing Berry curvature dipole3. Here we report, observations of a nonlinear optical Hall effect in a Weyl semimetal WTe2 without an applied magnetic field at room temperature. We observe an optical Hall effect resulting in a polarization rotation of the reflected light, referred to as the nonlinear Kerr rotation. The nonlinear Kerr rotation linearly depends on the charge current and optical power, which manifests the fourth-order nonlinearity. We quantitatively determine the fourth-order susceptibility, which exhibits strong anisotropy depending on the directions of the charge current and the light polarization. Employing symmetry analysis of Berry curvature multipoles, we demonstrate that the nonlinear Kerr rotations can arise from the Berry curvature hexapole allowed by the crystalline symmetries of WTe2. There also exist marginal signals that are incompatible with the symmetries, which suggest a hidden phase associated with the nonlinear process.
We investigate the electric and thermal transport properties in a disordered Weyl ferromagnet on an equal footing by using the Keldysh formalism in curved spacetime. In particular, we calculate the anomalous thermal Hall conductivity, which consists of the Kubo formula and the heat magnetization, without relying on the Wiedemann-Franz law. We take nonmagnetic impurities into account within the self-consistent $T$-matrix approximation and reproduce the Wiedemann-Franz law for the extrinsic Fermi-surface and intrinsic Fermi-sea terms, respectively. This is the first step towards a unified theory of the anomalous Hall effect at finite temperature, where we should take into account both disorder and interactions.
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