Structured-Light Control of Goniopolar Thermoelectricity in NaSn\texorpdfstring{${}_2$}{2}As\texorpdfstring{${}_2$}{2}

Abstract

Goniopolar metals exhibit opposite thermoelectric polarities along different crystallographic directions, enabling zero-field transverse thermoelectricity but offering few means for external control. Here we show that a spatially structured Laguerre--Gaussian vector potential can programmably reconstruct the goniopolar phase space of NaSn${}_2$As${}_2$. First-principles-derived Wannier transport with bond-dependent Peierls coupling reveals two OAM-dependent spatial scaling laws: the radial response follows the Laguerre--Gaussian radius $r_{\max }\propto \sqrt{|\ell |}$, while calculations for $|\ell |=2$--5 yield a dominant angular harmonic $m_{\mathrm{dom}}=2|\ell |$, encoding the optical winding in a frequency-doubled thermoelectric response. Increasing $|\ell |$ simultaneously reconstructs pre-existing goniopolar windows, enhancing a representative window by approximately 17\% at $|\ell |=5$. By contrast, reversing $\ell$ at fixed polarization produces only a small correction that approximately interchanges upon polarization reversal. Energy-resolved transport reveals that the structured field redistributes in-plane and cross-plane electronic velocities, shifting the directional Seebeck-zero boundaries that define the goniopolar state. These results establish vortex position and OAM magnitude as programmable control coordinates for goniopolar thermoelectricity.

6 pages, 4 figures