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Register a new userMixed axial-torsional anomaly in Weyl semimetals
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We show that Weyl semimetals exhibit a mixed axial-torsional anomaly in the presence of axial torsion, a concept exclusive of these materials with no known natural fundamental interpretation in terms of the geometry of spacetime. This anomaly implies a nonconservation of the axial current---the difference in current of left- and right-handed chiral fermions---when the torsion of the spacetime in which the Weyl fermions move couples with opposite sign to different chiralities. The anomaly is activated by driving transverse sound waves through a Weyl semimetal with a spatially varying tilted dispersion, which can be engineered by applying strain. This leads to sizable alternating current in presence of a magnetic field that provides a clear-cut experimental signature of our predictions.
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A space-time dependent node separation in Weyl semimetals acts as an axial vector field. Coupled with domain wall motion in magnetic Weyl semimetals, this induces axial electric and magnetic fields localized at the domain wall. We show how these fields can activate the axial (chiral) anomaly and provide a direct experimental signature of it. Specifically, a domain wall provides a spatially dependent Weyl node separation and an axial magnetic field $textbf{B}_5$, and domain wall movement, driven by an external magnetic field, gives the Weyl node separation a time dependence, inducing an axial electric field $textbf{E}_5$. At magnetic fields beyond the Walker breakdown, $textbf{E}_5cdottextbf{B}_5$ becomes nonzero and activates the axial anomaly that induces a finite axial charge density -- imbalance in the number of left- and right-handed fermions -- moving with the domain wall. This axial density, in turn, produces, via the chiral magnetic effect, an oscillating current flowing along the domain wall plane, resulting in a characteristic radiation of electromagnetic waves emanating from the domain wall. A detection of this radiation would constitute a direct measurement of the axial anomaly induced by axial electromagnetic fields.
We suggest the possibility of a linear magnetochiral effect in time reversal breaking Weyl semimetals. Generically the magnetochiral effect consists in a simultaneous linear dependence of the magnetotransport coefficients with the magnetic field and a momentum vector. This simultaneous dependence is allowed by the Onsager reciprocity relations, being the separation vector between the Weyl nodes the vector that plays such role. As a side consequence, we find a non vanishing positive longitudinal magnetoconductivity at Fermi energies above the point where the chirality of the Weyl nodes is globally lost.
Weyl semimetals are well-known for hosting topologically protected linear band crossings, serving as the analog of the relativistic Weyl Fermions in the condensed matter context. Such analogy persists deeply, allowing the existence of the chiral anomaly under parallel electric and magnetic field in Weyl semimetals. Different from such picture, here we show that, a unique mechanism of the chiral anomaly exists in Weyl semimetals by injecting a spin current with parallel spin polarization and flow direction. The existence of such a chiral anomaly is protected by the topological feature that each Weyl cone can also be a source or drain of the spin field in the momentum space. It leads to measurable experimental signals, such as an electric charge current parallel with an applied magnetic field in the absence of the electric field, and a sharp peak at certain resonant frequency in the injection current in achiral Weyl semimetals through the circular photogalvanic effect. Our work shows that the topological implication of Weyl semimetals goes beyond the link with relativistic Weyl Fermions, and offers a promising scenario to examine the interplay between topology and spin.
We report on exotic response properties in 3D time-reversal invariant Weyl semimetals with mirror symmetry. Despite having a vanishing anomalous Hall coefficient, we find that the momentum-space quadrupole moment formed by four Weyl nodes determines the coefficient of a mixed emph{electromagnetic charge-stress} response, in which momentum flows perpendicular to an applied electric field, and electric charge accumulates on certain types of lattice defects. This response is described by a mixed Chern-Simons-like term in 3 spatial dimensions, which couples a rank-2 gauge field to the usual electromagnetic gauge field. On certain 2D surfaces of the bulk 3D Weyl semimetal, we find what we will call rank-2 chiral fermions, with $omega =k_x k_y$ dispersion. The intrinsically 2D rank-2 chiral fermions have a mixed charge-momentum anomaly which is cancelled by the bulk of the 3D system.
After the experimental realization, the Berry curvature dipole (BCD) induced nonlinear Hall effect (NLHE) has attracted tremendous interest to the condensed matter community. Here, we investigate another family of Hall effect, namely, chiral anomaly induced nonlinear Hall effect (CNHE) in multi-Weyl semimetal (mWSM). In contrast to the BCD induced NLHE, CNHE appears because of the combination of both chiral anomaly and anomalous velocity due to non-trivial Berry curvature. Using the semiclassical Boltzmann theory within the relaxation time approximation, we show that, in contrast to the chiral anomaly induced linear Hall effect, the magnitude of CNHE decreases with the topological charge n. Interestingly, we find that unlike the case of n=1, the CNHE has different behaviors in different planes. Our prediction on the behavior of CNHE in mWSM can directly be checked in experiments.
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