Persistent currents in mesoscopic spin-orbit coupled rings due to an applied Zeeman field

Persistent currents (PCs) in mesoscopic rings have been a subject of intense investigation since their proposal by B"uttiker, Landauer, and Imry in 1983 [Phys. Lett. A 96, 365 (1983).]. In this paper, we explore the behavior of PC in spin-orbit coupled rings under the influence of a Zeeman field (without a need for a flux threading the ring), contrasting it with traditional PC observed in rings threaded by magnetic flux. Our study reveals that the emergence of PC in our setup crucially depends on nonzero values of spin-orbit coupling and the Zeeman field. Through theoretical analysis and numerical calculations, we uncover several intriguing phenomena. Specifically, in ballistic rings, we observe an inverse proportionality between PC and system size, with PC being zero at half filling for even numbers of sites. Additionally, the introduction of on-site disorder leads to the suppression of PC, with exponential decay observed for large disorder strengths and quadratic decay for smaller disorder strengths. Notably, disorder can enhance PC in individual samples, albeit with a configuration-averaged PC of zero. Furthermore, we find that the standard deviation of PC increases with disorder strength, reaching a maximum before decreasing to zero at high disorder strengths. We study the case of PC when the Zeeman field and the spin-orbit field are noncollinear. We also study persistent spin current, which shows behavior similar to that of PC except that at half filling, it is not zero. Our findings shed light on the intricate interplay between spin-orbit coupling, Zeeman fields, and disorder in mesoscopic quantum systems, offering different avenues for theoretical exploration and experimental verification.