Probing pure spin-rotation quantum geometry in persistent spin textures via nonlinear transport

Abstract: Persistent spin textures (PST) are spin-orbit coupled states in which Bloch spinors become momentum independent due to an underlying symmetry constraint, leading to the complete suppression of conventional and Zeeman quantum geometric quantities. This makes accessing their intrinsic geometric structure experimentally challenging. Here, we show that the spin-rotation quantum geometric tensor (SRQGT) provides the missing probe. Using a two-dimensional electron gas and a cubic spin-splitting system as representative PST platforms, we demonstrate that the SRQGT remains finite and momentum independent and generates a measurable nonlinear gyrotropic current. The smoking-gun signature of PST is a fully direction-independent nonlinear gyrotropic response: magnetic currents coincide in magnitude and display identical parametric variations. These results establish PST systems as minimal platforms for isolating pure spin-rotation quantum geometry.