论文标题
$ \ Mathcal {c} _4 $ -smmetric Dirac Semimetal的节点高阶拓扑超导性
Nodal higher-order topological superconductivity from a $\mathcal{C}_4$-symmetric Dirac semimetal
论文作者
论文摘要
我们分析了从CD $ _3 $中出现的可能超导状态的拓扑特性，为$ _2 $ - 类似，$ \ Mathcal {C} _4 $ - 符合的dirac半明确，并在$ k_z $方向上分开了两个四倍的变性零件。与最简单的Weyl半学上，所有配对顺序在拓扑上都被阻塞和节点，我们表明，在狄拉克半光中配对的拓扑障碍物至关重要，仅对某些配对对称性存在至关重要。特别是，我们专注于奇数$ b_ {1u} $和$ b_ {2u} $配对状态，这两种状态都可以通过Ising铁磁波动来诱导。 $ b_ {1u} $和$ b_ {2u} $配对状态继承了正常状态的拓扑障碍，这表明这些状态必然容纳了四个Bogolibov- de Gennes（BDG）DIRAC点节点，该节点受$ \ Mathbb {Z} _2 _2 $ Monopole的电荷保护。通过Wannier状态分析，我们表明超导状态的拓扑阻塞具有较高的性质。结果，在带有间隙表面的杆几何形状中，在BDG DIRAC点之间的铰链的某些$ k_z $区域中存在高阶Majorana零模式的弧。与Weyl半金属中的费米弧不同，高阶Majorana弧稳定，因为额外的$ \ Mathbb {Z} $ - 由$ \ Mathcal {c} _4 _4 $ Symmetry Symmetry的BDG DIRAC点的额外估价单极收费。 We find that the same $\mathbb{Z}$-valued charge is also carried by $B_{1g}$ and $B_{2g}$ channels, where the BdG spectrum hosts bulk ``nodal cages", i.e., cages formed by nodal lines, that are stable against symmetry preserving perturbations.
We analyze the topological properties of the possible superconducting states emerging from a Cd$_3$As$_2$-like, $\mathcal{C}_4$-symmetric Dirac semimetal, with two four-fold degenerate Dirac points separated in the $k_z$ direction. Unlike the simplest Weyl semimetal for which all pairing orders are topologically obstructed and nodal, we show that the topological obstruction for pairing in Dirac semimetals crucially only exists for certain pairing symmetries. In particular, we focus on odd-parity $B_{1u}$ and $B_{2u}$ pairing states, both of which can be induced by Ising ferromagnetic fluctuations. The $B_{1u}$ and $B_{2u}$ pairing states inherit the topological obstruction from the normal state, which dictates that these states necessarily hosts four Bogolibov- de Gennes (BdG) Dirac point nodes protected by a $\mathbb{Z}_2$ monopole charge. By a Wannier state analysis, we show that the topological obstruction in the superconducting states is of higher-order nature. As a result, in a rod geometry with gapped surfaces, arcs of higher-order Majorana zero modes exist in certain $k_z$ regions of the hinges between the BdG Dirac points. Unlike Fermi arcs in Weyl semimetals, the higher-order Majorana arcs are stable against self-annihilation due to an additional $\mathbb{Z}$-valued monopole charge of the BdG Dirac points protected by $\mathcal{C}_4$ symmetry. We find that the same $\mathbb{Z}$-valued charge is also carried by $B_{1g}$ and $B_{2g}$ channels, where the BdG spectrum hosts bulk ``nodal cages", i.e., cages formed by nodal lines, that are stable against symmetry preserving perturbations.
