Charge-spin response and collective excitations in Weyl semimetals

Abstract

Weyl semimetals are characterized by unconventional electromagnetic response. We present analytical expressions for all components of the frequency-and wave-vector-dependent charge-spin linear-response tensor of Weyl fermions. The spin-momentum locking of the Weyl Hamiltonian leads to a coupling between charge and longitudinal spin fluctuations, while transverse spin fluctuations remain decoupled from the charge. A real Weyl semimetal with multiple Weyl nodes can show this charge-spin coupling in equilibrium if its crystal symmetry is sufficiently low. All Weyl semimetals are expected to show this coupling if they are driven into a non-equilibrium stationary state with different occupations of Weyl nodes, for example by exploiting the chiral anomaly. Based on the response tensor, we investigate the low-energy collective excitations of interacting Weyl fermions. For a local Hubbard interaction, the charge-spin coupling leads to a dramatic change of the zero-sound dispersion: its velocity becomes independent of the interaction strength and the chemical potential and is given solely by the Fermi velocity. In the presence of long-range Coulomb interactions, the coupling transforms the plasmon modes into spin plasmons. For real Weyl semimetals with multiple Weyl nodes, the collective modes are strongly affected by the presence of parallel static electric and magnetic fields, due to the chiral anomaly. In particular, the zero-sound frequency at fixed momentum and the spin content of the spin plasmons go through cusp singularities as the chemical potential of one of the Weyl cones is tuned through the Weyl node. We discuss possible experiments that could provide smoking-gun evidence for Weyl physics. arXiv:1810.12560v2 [cond-mat.mes-hall]

Dynamical density and spin response of Fermi arcs and their consequences for Weyl semimetals

“…The rather lengthy expressions for bulk response functions for our model are given in Appendix D. They are similar to the ones presented in Ref. [45].…”

“…The zero-temperature dynamical density and spin response of the bulk states has been calculated in Ref. [44,45] using a k · p Hamiltonian. For the sake of completeness and to explore its orbital structure, we calculate the bulk response tensor for our model.…”

“…In the presence of non-orthogonal E and B fields, the plasmons carry spin, which can be probed by optical pump-probe spectroscopy as discussed in Ref. [45].…”

“…The electromagnetic and transport properties exhibited by WSMs has been studied theoretically using semi- * carsten.timm@tu-dresden.de classical transport theory [22,[36][37][38], field-theoretic approaches [21,39], and the Kubo formalism [40][41][42]. The dynamical density, spin, and current responses to inhomogenous and time-dependent external fields have been investigated for Weyl fermions in the bulk, using Kohn-Luttinger-type (k · p) models [43][44][45]. The dynamical current response provides information about transport properties such as the chiral magnetic effect and the optical conductivity [44].…”

“…The dynamical current response provides information about transport properties such as the chiral magnetic effect and the optical conductivity [44]. On the other hand, exploring the coupled density and spin response reveals the existence of novel collective excitations, i.e, spin plasmons, which provide another experimental signature of WSMs [45]. While the surface plasmon excitations of the FA states have been investigated [46][47][48][49][50], an unified study of the density, spin, and current response of the FA states has been lacking but is desirable as it reflects the rich physics of the FA states.…”