Dynamical spin susceptibility of a Fermi liquid without conservation law

Galilean invariance along with the conservation of charge and total spin guarantees that the corresponding susceptibilities vanish at an infinitely long wavelength (q=0) and finite frequency. But the susceptibility of nematic fluctuations or that of spin fluctuations in the presence of spin-orbit interaction (SOI) is not protected by any conservation laws and hence leads to finite spectral weight outside the particle-hole continuum even at q=0 and finite ω [1,2]. Finite width of the chiral spin modes for a Fermi liquid (FL) with Rashba SOI was studied at q=0 by Maiti and Maslov [3]. Here, we study the effect of residual interaction on the chiral spin modes of a FL with weak Rasbha SOI for a model of dynamic screened Coulomb potential at finite q by going beyond the random phase approximation(RPA). We also study the interplay between the plasmon and chiral spin modes due to their coupling for the non-RPA corrections.

[1] V. Zyuzin, P. Sharma, and D. L. Maslov, Phys. Rev. B 98, 115139 (2018).
[2] A. Klein, S. Lederer, D. Chowdhury, E. Berg, and A. Chubukov, Phys. Rev. B 97, 155115 (2018).
[3] S. Maiti and D.L. Maslov, PRL 114,156803 (2015).