Universal giant spin Hall effect in moiré metal

Abstract While moiré phenomena have been extensively studied in low-carrier-density systems such as semiconductors, their implications for metallic systems with large Fermi surfaces remain largely unexplored. Using GPU-accelerated large-scale ab-initio quantum transport simulations, we investigate spin transport in two distinct platforms: twisted bilayer MoTe 2 (semiconductor) and NbX 2 ( X = S, Se; metals). In twisted MoTe 2 , the spin Hall conductivity (SHC) evolves from $$4\frac{e}{4\pi }$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mn>4</mml:mn> <mml:mfrac> <mml:mrow> <mml:mi>e</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>4</mml:mn> <mml:mi>π</mml:mi> </mml:mrow> </mml:mfrac> </mml:mrow> </mml:math> at 5.09° to $$10\frac{e}{4\pi }$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mn>10</mml:mn> <mml:mfrac> <mml:mrow> <mml:mi>e</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>4</mml:mn> <mml:mi>π</mml:mi> </mml:mrow> </mml:mfrac> </mml:mrow> </mml:math> at 1.89°. Remarkably, in heavily doped metallic regimes where isolated Chern bands are absent, we observe a universal amplification of the SHC arising from Fermi surface reconstruction under a long-wavelength potential, with the peak SHC tripling from $$6\frac{e}{4\pi }$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mn>6</mml:mn> <mml:mfrac> <mml:mrow> <mml:mi>e</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>4</mml:mn> <mml:mi>π</mml:mi> </mml:mrow> </mml:mfrac> </mml:mrow> </mml:math> at 5.09° to $$17\frac{e}{4\pi }$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mn>17</mml:mn> <mml:mfrac> <mml:mrow> <mml:mi>e</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>4</mml:mn> <mml:mi>π</mml:mi> </mml:mrow> </mml:mfrac> </mml:mrow> </mml:math> at 3.89°. For moiré metals like twisted NbX 2 , we identify a record SHC of −5200 ( ℏ / e )S/cm, surpassing all known bulk materials.