Nonmonotonic quantum phase gathering in curved spintronic circuits

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