In a 2D model Hamiltonian, orbital Hall conductivity quantizes when altermagnetism exceeds sp-hybridization while spin Hall quantizes when Rashba SOC is weaker, with both independent of the other coupling and arising from Fermi-surface Berry curvature.
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Quantized orbital and spin Hall transport: interplay between $sp$-hybridization, altermagnetism and spin-orbit coupling
In a 2D model Hamiltonian, orbital Hall conductivity quantizes when altermagnetism exceeds sp-hybridization while spin Hall quantizes when Rashba SOC is weaker, with both independent of the other coupling and arising from Fermi-surface Berry curvature.