${\mathrm{CaFeAs}}_2$: A staggered intercalation of quantum spin Hall and high-temperature superconductivity

We predict that ${\mathrm{CaFeAs}}_2$, a newly discovered iron-based high-temperature $\left(T_c\right)$ superconductor, is a staggered intercalation compound that integrates topological quantum spin Hall (QSH) and superconductivity (SC). ${\mathrm{CaFeAs}}_2$ has a structure with staggered CaAs and FeAs layers. While the FeAs layers are known to be responsible for high $T_c$ superconductivity, we show that with spin orbital coupling each CaAs layer is a $Z_2$ topologically nontrivial two-dimensional QSH insulator and the bulk is a three-dimensional weak topological insulator. In the superconducting state, the edge states in the CaAs layer are natural one-dimensional topological superconductors. The staggered intercalation of QSH and SC provides us a unique opportunity to realize and explore physics, such as Majorana modes and Majorana fermion chains.

Figure 1

(a) Schematic view of the crystal structure of ${\mathrm{Ca}}_{1-x}{\mathrm{La}}_x{\mathrm{FeAs}}_2$. (b) Fermi surfaces (FSs) for ${\mathrm{CaFeAs}}_2$. The green circles and ellipses FSs are contributed by the FeAs layers. The red circle FS is attributed to $p_z$ orbitals of As-1 and $d$ orbitals of Ca. The orange circles FSs are attributed to $p_x$ and $p_y$ orbitals of As-1. (c) Lattice model for the As layer in ${\mathrm{CaFeAs}}_2$.

Figure 2

Band structures for As layers and ${\mathrm{CaFeAs}}_2$. (a) Band structure without SOC. The zoom-in band structure near the Fermi level (b) without SOC and (c) with SOC. The strength of SOC is 0.19 eV. (d) The LDA band structure of ${\mathrm{CaFeAs}}_2$ with SOC. The Dirac cone is gapped by SOC and the gap is about 0.1 eV. The sizes of the green circles are proportional to the weights of the $p_x$ and $p_y$ orbitals.

Figure 3

The evolution of Wannier function centers [(a) and (b)] and edge states [(c) and (d)] for our tight-binding model. (a), (c) $\lambda =0.19$ eV and ${\lambda }_{\nu }=0$. The vertical axis shows the Wannier centers of the four occupied bands. (b), (d) $\lambda =0.19$ eV and ${\lambda }_{\nu }=0.19$ eV. The red and green lines denote edge states from different edges.

Figure 4

The topological phase diagram in the $\lambda \text{−}{\lambda }_{\nu }$ plane for possible material systems. The inset shows the phase diagram in the whole parameter space.

Figure 5

Schematic picture of the proposed setup for the realization of Majorana fermions. (a) Two Majorana modes. (b) A Majorana chain realization. The green circles denote Majorana modes and the blue rectangles denote a ferromagnetic insulator (FMI).