Topological responses from chiral anomaly in multi-Weyl semimetals

Abstract

Multi-Weyl semimetals are a kind of topological phase of matter with discrete Weyl nodes characterized by multiple monopole charges, in which the chiral anomaly, the anomalous nonconservation of an axial current, occurs in the presence of electric and magnetic fields. Electronic transport properties related to the chiral anomaly in the presence of both electromagnetic fields and axial electromagnetic fields in multi-Weyl semimetals are systematically studied. It has been found that the anomalous Hall conductivity has a modification linear in the axial vector potential from inhomogeneous strains. The axial electric field leads to an axial Hall current that is proportional to the distance of Weyl nodes in momentum space. This axial current may generate chirality accumulation of Weyl fermions through delicately engineering the axial electromagnetic fields even in the absence of external electromagnetic fields. Therefore, this work provides a nonmagnetic mechanism of generation of chirality accumulation in Weyl semimetals and might shed new light on the application of Weyl semimetals in the emerging field of valleytronics.Comment: 13 pages, 2 tables, 2 figures, accepted by Physical Review

Anomalous thermoelectric phenomena in lattice models of multi-Weyl semimetals

“…Here b 0 and b describe the energy and momentum-space separations between the Weyl nodes, respectively. As it turns out, without the Bardeen-Zumino term with its explicit dependence on b ν , the chiral kinetic theory cannot describe correctly the chiral magnetic effect [28,29], the anomalous Hall effect [30][31][32][33][34][35], and even some collective excitations [24] in Weyl materials.…”

Axial anomaly in multi-Weyl and triple-point semimetals

“…The derivations in [48,49] do not fully explain the quantization of the anomaly, with topological charge N Θ(α, β, γ), and, from a more fundamental point of view, do not clarify why the anomaly for multi-Weyl semimetals is proportional to the differential form F (x) ∧ F (x), in spite of the breaking of Lorentz covariance of the corresponding low energy lagrangians. In facts, doubts [62,63] have been cast upon the use of the regularization scheme of the path-integral measure exploited in the Fujikawa's method [49] in cases different from the standard Weyl theory.…”

“…In all these papers, in the expression of the anomaly -which has been derived in these articles -the Θ(α, β, γ) factor (3.10) is missing. But the absolute value of the anomaly, which has been proposed in [48,49,60], appears to be correct. The difference between the two derivations is that, in [48,49,60], the left field has been considered set since the beginning by the condition αβγ > 0.…”

“…In [48], the authors analyzed numerically the case with parallel electric and magnetic fields, and presented analytical calculations in the spirit of Nielsen and Ninomyia [14] for a system in which both fields are aligned along the direction of linear dispersion and in the presence of a full SO(2) rotational symmetry. Finally, equation (3.9) has also been verified in [49] through a field theoretical approach, based on the Fujikawa's method (see for example [56,61]), by evaluating the chiral anomaly for a double-Weyl point with SO(2) rotational symmetry. In all these papers, in the expression of the anomaly -which has been derived in these articles -the Θ(α, β, γ) factor (3.10) is missing.…”

“…In facts, doubts [62,63] have been cast upon the use of the regularization scheme of the path-integral measure exploited in the Fujikawa's method [49] in cases different from the standard Weyl theory.…”