Charge-spin response and collective excitations in Weyl semimetals

TL;DR

This paper derives analytical charge-spin response functions for Weyl semimetals, revealing how their unique spin-momentum locking influences collective excitations and how external fields and interactions modify these modes.

Contribution

It provides the first comprehensive analytical expressions for the charge-spin response tensor in Weyl semimetals, elucidating the effects of interactions and external fields on collective modes.

Findings

Charge-spin coupling alters zero-sound dispersion, making its velocity independent of interaction strength.

Long-range Coulomb interactions convert plasmons into spin plasmons in Weyl semimetals.

External electric and magnetic fields induce cusp singularities in collective mode frequencies.

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.