biostudies-literatureZou JNational Natural Science Foundation of ChinaNational Key Research and Development Program of Chinanwaa169https://www.ebi.ac.uk/biostudies/studies/S-EPMC8288464biostudies-literatureUnknown8(5)We classify gapped topological superconducting (TSC) phases of one-dimensional quantum wires with local magnetic symmetries, in which the time-reversal symmetry [Formula: see text] is broken, but its combinations with certain crystalline symmetries, such as [Formula: see text], [Formula: see text], [Formula: see text] and [Formula: see text], are preserved. Our results demonstrate that an equivalent BDI class TSC can be realized in the [Formula: see text] or [Formula: see text] superconducting wire, which is characterized by a chiral <i>Z</i> ^<i>c</i> invariant. More interestingly, we also find two types of totally new TSC phases in the [Formula: see text] and [Formula: see text] superinducting wires, which are beyond the known AZ class, and are characterized by a helical <i>Z</i> ^<i>h</i> invariant and <i>Z</i> ^<i>h</i> ⊕<i>Z</i> ^<i>c</i> invariants, respectively. In the <i>Z</i> ^<i>h</i> TSC phase, <i>Z</i> pairs of Majorana zero modes (MZMs) are protected at each end. In the [Formula: see text] case, the MZMs can be either chiral or helical, and even helical-chiral coexisting. The minimal models preserving [Formula: see text] or [Formula: see text] symmetry are presented to illustrate their novel TSC properties and MZMs.National science reviewNew types of topological superconductors under local magnetic symmetries.PMC82884642018YFA030700011874022Zou JXie QXu GSong ZfalseNew types of topological superconductors under local magnetic symmetries.We classify gapped topological superconducting (TSC) phases of one-dimensional quantum wires with local magnetic symmetries, in which the time-reversal symmetry [Formula: see text] is broken, but its combinations with certain crystalline symmetries, such as [Formula: see text], [Formula: see text], [Formula: see text] and [Formula: see text], are preserved. Our results demonstrate that an equivalent BDI class TSC can be realized in the [Formula: see text] or [Formula: see text] superconducting wire, which is characterized by a chiral <i>Z</i> ^<i>c</i> invariant. More interestingly, we also find two types of totally new TSC phases in the [Formula: see text] and [Formula: see text] superinducting wires, which are beyond the known AZ class, and are characterized by a helical <i>Z</i> ^<i>h</i> invariant and <i>Z</i> ^<i>h</i> ⊕<i>Z</i> ^<i>c</i> invariants, respectively. In the <i>Z</i> ^<i>h</i> TSC phase, <i>Z</i> pairs of Majorana zero modes (MZMs) are protected at each end. In the [Formula: see text] case, the MZMs can be either chiral or helical, and even helical-chiral coexisting. The minimal models preserving [Formula: see text] or [Formula: see text] symmetry are presented to illustrate their novel TSC properties and MZMs.2021-01-01T00:00:00Z2021 May2026-07-16T13:33:41.963Z2025-06-01T03:27:26.863ZS-EPMC82884643469163310.1093/nsr/nwaa169