Nonmonotonic quantum phase gathering in curved spintronic circuits

Spin carriers propagating along quantum circuits gather spin phases depending on the circuit's size, shape, and spin-orbit coupling (SOC) strength. These typically grow monotonically with SOC strength, as found in Rashba wires rings. In this work we show that spin-phase gathering can be engineered by geometric means, viz., curvature of circuits, to nonmonotonic. We demonstrate peculiar property using one-dimensional polygonal models where flat segments alternate highly curved vertices. The complex interplay between dynamic components---triggered a series emergent degeneracy points---leads bounded, global phases. Moreover, particulars have observable consequences Aharonov-Casher conductance loops, connection passed unnoticed previous works.