Unusual spin dynamics in topological insulators

The dynamic spin susceptibility (DSS) has a ubiquitous Lorentzian form around the Zeeman energy in conventional materials with weak spin orbit coupling, whose spectral width characterizes the spin relaxation rate. We show that DSS has an unusual non-Lorentzian form in topological insulators, which are characterized by strong SOC, and the anisotropy of the DSS reveals the orientation of the underlying spin texture of topological states. At zero temperature, the high frequency part of DSS is universal and increases in certain directions as ω(d-1) with d = 2 and 3 for surface states and Weyl semimetals, respectively, while for helical edge states, the interactions renormalize the exponent as d = 2K - 1 with K the Luttinger-liquid parameter. As a result, spin relaxation rate cannot be deduced from the DSS in contrast to the case of usual metals, which follows from the strongly entangled spin and charge degrees of freedom in these systems.