Impact of spin-orbit coupling on electron correlation corrections to the density of states in anisotropic conductors

Abstract

We study Altshuler-Aronov-type interaction corrections to the single-particle density of states (DOS) in a strongly anisotropic 2D conductor with an open Fermi surface (FS) and weak disorder, in the presence of coexisting Rashba and Dresselhaus spin-orbit couplings (SOCs) constrained to the longitudinal direction. The low-energy band consists of two warped sheets weakly tunnel-coupled transversely; SOC splits the sheets into helicity branches with a fixed spin axis. Working in a Matsubara space, we compute the exchange contribution in the diffusion channel with dynamically screened Coulomb interaction and an impurity ladder. The resulting DOS anomaly exhibits a dimensional crossover governed by the transverse coupling scale ${\epsilon }_c$. Close to the Fermi level ($|\epsilon -{\epsilon }_F|<{\epsilon }_c$), the system behaves two-dimensionally, featuring a logarithmic DOS dip whose magnitude is enhanced by intrinsic SOCs. Further from the Fermi level ($|\epsilon -{\epsilon }_F|>{\epsilon }_c$), the system behaves quasi-one-dimensionally, featuring a sharper square-root singularity whose amplitude is remarkably enhanced by the SOCs. Notably, we identify a critical SOC strength at which these spin-orbit effects exactly cancel the electron-correlation correction, perfectly restoring the unperturbed density of states. Furthermore, increasing the SOC beyond this critical point inverts the sign of the anomaly entirely, yielding a positive DOS correction. This sign reversal fundamentally alters the energy dependence, such that at energies beyond ${\epsilon }_F+{\epsilon }_c$, the positive correction decays to smaller values as energy increases, opposite to the standard negative correction. This contrasting trend provides a distinct spectroscopic signature of SOC-modulated correlation effects.

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