New types of topological superconductors under local magnetic symmetries

Abstract

We classify gapped topological superconducting (TSC) phases of one-dimensional quantum wires with local magnetic symmetries (LMSs), in which the time-reversal symmetry $\mathcal {T}$ is broken but its combinations with certain crystalline symmetry such as $M_x \mathcal {T}$, $C_{2z} \mathcal {T}$, $C_{4z}\mathcal {T}$, and $C_{6z}\mathcal {T}$ are preserved. Our results demonstrate that an equivalent BDI class TSC can be realized in the $M_x \mathcal {T}$ or $C_{2z} \mathcal {T}$ superconducting wire, which is characterized by a chiral Zc invariant. More interestingly, we also find two types of totally new TSC phases in the $C_{4z}\mathcal {T}$, and $C_{6z}\mathcal {T}$ superconducing wires, which are beyond the known AZ class, and are characterized by a helical Zh invariant and Zh⊕Zc invariants, respectively. In the Zh TSC phase, Z-pairs of MZMs are protected at each end. In the $C_{6z}\mathcal {T}$ case, the MZMs can be either chiral or helical, and even helical-chiral coexisting. The minimal models preserving $C_{4z}\mathcal {T}$ or $C_{6z}\mathcal {T}$ symmetry are presented to illustrate their novel TSC properties and MZMs.

Unlocking of time reversal, space-time inversion and rotation invariants in magnetic materials

“…Is it possible to further unlock the values of χ T and χ P T from the constraint χ T = χ P T ? We seek this possibility in elementary excitations in magnetically ordered lattices, the band topology of which has recently become a research focus [7][8][9][10][11][12][13][14]. While the physical time reversal is broken by magnetism, many antiferromagnetic materials preserve a symmetry in the form T → T phy t L/2 , where T phy is pure time reversal operator acting only on internal degrees of freedom, and L/2 is a lattice vector (which becomes a half-lattice vector in the magnetic unit cell) [7,8].…”

Chiral Topological superconductivity in the OAI/SC/FMI heterostructure avoiding the subband problem

“…Topological superconductivity (TSC) has attracted intensive interest for its ability to host the Majorana states (MSs) and its implementation of topological quantum computations [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16]. The initial system to realize TSC involves the p-wave pairing superconductor (SC) [17][18][19][20].…”

Prediction of topological superconductivity in 1$T$-TiTe$_2$ under pressure

“…Introduction -As one of the most intriguing systems to host the Majorana zero modes (MZMs), topological superconductors (TSCs) play important roles in both the condensed matter physics and the topological quantum computations [1][2][3], which have attracted growing interest in the past decade [4][5][6]. Since natural TSC is very rare [7], a variety of architectures have been proposed in one-, two-and three-dimension for the realization of the TSC and MZMs [8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25]. In particular, Gang Xu et al proposed that TSC can be realized in the vortex of superconducting topological metallic materials such as the iron-based superconductor FeSe 0.5 Te 0.5 .…”