Hidden Zeeman Field in Odd-Parity Magnets: An Ideal Platform for Topological Superconductivity

Abstract: Odd-parity magnets (OPMs) have emerged as a fundamental class of unconventional magnetisms, characterized by time-reversal-preserving non-relativistic spin splitting (NSS). Despite growing interest, the fundamental understanding of OPMs remains critically incomplete, as previous studies have focused exclusively on NSS while overlooking the intrinsically broken time-reversal symmetry ($\mathcal{T}$) inherent to magnetic order. In this work, we reveal that OPMs universally host a hidden Zeeman field rooted in this $\mathcal{T}$-breaking, which fundamentally reshapes their band structure. Through an analytical $f$-wave magnet model, we show that NSS microscopically originates from an emergent gauge field, manifesting as a real-space spin loop current order. Crucially, the large NSS (eV scale) enables conventional superconductivity to coexist robustly with the hidden Zeeman field, with Zeeman splitting reaches hundreds of meV. This unique band structure establishes OPMs as an ideal platform for topological superconductors (TSCs), supporting large topological regions. Based on OPMs, we engineer a series of TSCs hosting distinct Majorana boundary modes, including unidirectional Majorana edge states. Our work corrects a fundamental misconception about OPMs and establishes them as a versatile platform for field-free and robust TSCs.