  Persistent currents (PCs) in mesoscopic rings have been a subject of intense
investigation since their proposal by B\"uttiker, Landauer, and Imry in 1983.
In this paper, we explore the behavior of PC in spin-orbit coupled rings under
the influence of a Zeeman field, 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. Our findings shed light on the
intricate interplay between spin-orbit coupling, Zeeman fields, and disorder in
mesoscopic quantum systems, offering new avenues for theoretical exploration
and experimental verification.
