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.

Figures (5)

• Figure 1: Nonlinear Gyrotropic Magnetic Response in Persistent Spin Textures: Schematic of a persistent spin textures-hosting material subjected to a time-dependent magnetic field, where the leading response is a purely second-order gyrotropic magnetic current response arising entirely from the spin-rotation quantum geometry.
• Figure 2: Spin Textures on Fermi Contours of a Rashba–Dresselhaus Two-Dimensional Electron Gas: (a,f) Energy dispersions for $\alpha>\beta$ and $\alpha=\beta$. For $\alpha = 0.6~\mathrm{eV.\mathring{A}}$ and $\beta = 0.2~\mathrm{eV.\mathring{A}}$, an isolated band-touching point lies on the zero-energy plane (orange). At $\alpha=\beta=0.6~\mathrm{eV.\mathring{A}}$, a nodal line forms with its minimum touching the zero-energy plane. (b,d) Spin textures at fixed energy $\mu = 0.03~\mathrm{eV}$ for $\alpha>\beta$ and $\alpha=\beta$. (c,e) Corresponding spin textures at $\mu = -0.03~\mathrm{eV}$.
• Figure 3: Spin Textures on Fermi Contours of a Rashba–Dresselhaus Two-Dimensional Electron Gas with Finite Tilt: (a,f) Energy dispersions and spin textures in the presence of a tilt $\delta = 0.25~\mathrm{eV.\mathring{A}}$ applied along $k_x$. (b,d) Spin textures at $\mu = 0.03~\mathrm{eV}$ for $\alpha>\beta$ and $\alpha=\beta$; (c,e) corresponding spin textures at $\mu = -0.03~\mathrm{eV}$, showing that the tilt does not destroy the persistent spin textures.
• Figure 4: Displacement and Conduction Nonlinear Gyrotropic Magnetic Conductivity of Two-Dimensional Electron Gas: (a, b) Only two of the non-vanishing displacement nonlinear gyrotropic magnetic conductivity components $\chi^{D}_{xxz}$ and $\chi^{D}_{xyz}$ are shown for $\alpha>\beta$ and $\alpha=\beta$, respectively. (c, d) The conduction nonlinear gyrotropic magnetic conductivity components $\chi^{C}_{xxx}$ and $\chi^{C}_{yxx}$ for $\alpha>\beta$ and $\alpha=\beta$, respectively in presence of tilt. We consider $T = 50~\text{K}$, $\omega = 10 ^{13} \text{Hz}$ and $\chi_0 = \left(\frac{g\mu_B}{2}\right)^2 \,\mathrm{A^{-1}\,m\,T^{2}}$.
• Figure 5: Spin Textures and Displacement Magnetic Current Response in a System with Purely Cubic Spin Splittings: (a) Energy dispersion. (b) Two of the nonvanishing components of the displacement nonlinear gyrotropic magnetic conductivity, $\chi_{xxy}^D$ and $\chi_{xyx}^D$; inset: spin textures along the Fermi contours. Parameters: $E_0 = 2.13~\mathrm{eV}$, $\Delta = 1.27~\mathrm{eV\!\cdot\!\mathring{A}^2}$, $\zeta = -5.24~\mathrm{eV\!\cdot\!\mathring{A}^3}$, $\lambda = -3.43~\mathrm{eV\!\cdot\!\mathring{A}^3}$, $T = 50~\text{K}$ and $\omega = 10 ^{13} \text{Hz}$.