Enhanced lifetimes of spin chains coupled to chiral edge states

We consider spin relaxation of finite-size spin chains exchanged coupled with a one dimensional (1D) electron gas at the edge of a Quantum Spin Hall (QSH) insulator. Spin lifetimes can be enhanced due to two independent mechanisms. First, the suppression of spin-flip forward scattering inherent in the spin momentum locking of the QSH edges. Second, the reduction of spin-flip backward scattering due to destructive interference of the quasiparticle exchange, modulated by $k_{F}d$, where $d$ is the inter-spin distance and $k_F$ is the Fermi wavenumber of the electron gas. We show that the spin lifetime of the $S=1\mathrm{/}2$ ground state of odd-numbered chains of antiferromagnetically (AFM) coupled $S=1\mathrm{/}2$ spins can be increased more than 4 orders of magnitude by properly tuning the product $k_{F}d$ and the spin size $N$, in strong contrast with the 1D case. Possible physical realizations together with some potential issues are also discussed.