Collective modes of a helical liquid

TL;DR

This paper investigates the collective excitations and transport phenomena on the surface of topological insulators, revealing a coupled spin-wave and plasmon mode unique to helical metals.

Contribution

It establishes an exact relation between electrical and spin dynamics, predicting a hybridized spin-plasmon mode specific to helical liquids.

Findings

Existence of an undamped spin wave accompanying the sound mode.

Coupling of surface plasmon to spin wave forming a spin-plasmon mode.

Quantitative predictions for spin-plasmon in Bi2Se3 and experimental detection proposals.

Abstract

We study low energy collective modes and transport properties of the "helical metal" on the surface of a topological insulator. At low energies, electrical transport and spin dynamics at the surface are exactly related by an operator identity equating the electric current to the in-plane components of the spin degrees of freedom. From this relation it follows that an undamped spin wave always accompanies the sound mode in the helical metal -- thus it is possible to `hear' the sound of spins. In the presence of long range Coulomb interactions, the surface plasmon mode is also coupled to the spin wave, giving rise to a hybridized "spin-plasmon" mode. We make quantitative predictions for the spin-plasmon in ${\rm Bi}_2{\rm Se}_3$, and discuss its detection in a spin-grating experiment.