Superconductivity and local noncentrosymmetricity in crystal lattices

Symmetry of the crystal lattice can be a determining factor for the structure of Cooper pairs in unconventional superconductors. In this study we extend the discussion of superconductivity in noncentrosymmetric materials to the case when inversion symmetry is missing locally, but is present on a global level. Concretely, we investigate the staggered noncentrosymmetricity within a regular sublattice structure, in some analogy to the discussion of superconductivity in antiferromagnetic systems. Three crystal structures are analyzed in detail as illustrative examples for the extended classification of Cooper-pairing channels. One of the cases may be relevant for the class of iron-pnictide superconductors.

Figure 1

The two example crystal structures analyzed in detail in Secs. 3 and 4. (a) Inversion-symmetry-lacking layers that are stacked along the $z$ direction in a staggered way. The symmetry center lies between the layers and the crystal has a symmorphic structure. (b) Top view of the crystal structure with O${}_6$ octahedra rotated around the $c$ axis leading to a doubling of the unit cell. While both sublattices still retain inversion symmetry, the bonds do not, as the rotation shifts the O ions off the bonds. This crystal structure with its symmetry center on one of the sublattices is nonsymmorphic.

Figure 2

Suppression of the transition temperature of the intraband gaps due to the antisymmetric SOC. With increasing interlayer coupling, the suppression is weakened, $t_z=0$, $0.1t$, and $0.2t$ from bottom to top.

Figure 3

Change in the transition temperature of the interband gap with ${\vec{d}}_1\left(\mathbf{k}\right)=\widehat{x}\sin k_y-\widehat{y}\sin k_x$ as a function of the interlayer hopping $t_z$ for different spin-orbit coupling strengths.

Figure 4

(a) Top view of the basic FeAs crystal structure. The open circles denote As ions lying below the plane while the crosses denote ions above the plane. (b) Top view of one of the sublattices rotated by 45${}^{\circ }$ for an easier analysis of the hopping Hamiltonian.