Odd-Parity Altermagnetism Originated from Orbital Orders

Abstract: Odd-parity spin-splitting plays a central role in spintronics and unconventional superconductivity, yet its microscopic realization in collinear magnetic systems remains elusive. We propose a general symmetry-based strategy for realizing odd-parity altermagnetism by stacking two noncentrosymmetric monolayers in an interlayer antiferromagnetic configuration and applying an in-plane layer-flip operation. In this setting, odd-parity spin-splitting originates from nonrelativistic orbital orders rather than spin-orbit coupling, and is protected by an effective time-reversal symmetry despite the explicit time-reversal symmetry being broken. By exploiting lattice symmetries, our framework enables the realization of both $p$- and $f$-wave altermagnets. The resulting models generically host quantum spin Hall insulator phases, featuring topologically protected helical edge states and quantized spin Hall conductance. Our work expands the landscape of altermagnetic phases and opens a pathway toward spintronics and unconventional superconductivity in altermagnetic systems.