Model of Vortex States in Hole-Doped Iron-Pnictide Superconductors

Based on a phenomenological model with competing spin-density-wave (SDW) and extended $s$-wave superconductivity, the vortex states in ${\mathrm{Ba}}_{1-x}{\mathrm{K}}_x{\mathrm{Fe}}_2{\mathrm{As}}_2$ are investigated by solving Bogoliubov–de Gennes equations. Our result for the optimally doped compound without induced SDW is in qualitative agreement with recent scanning tunneling microscopy experiment. We also propose that the main effect of the SDW on the vortex states is to reduce the intensity of the in-gap peak in the local density of states and transfer the spectral weight to form additional peaks outside the gap.

Figure 1

Spatial variations of (a) the reduced ES order parameter ${\Delta }_{j\beta }^R$, (b) electron density $n_j$, and (c) ZE LDOS map plotted on a $24\times 24$ lattice. (d) The LDOS at four typical positions along the black cut in (c) at site (11, 12) very close to the vortex center [the latter is in the center of the plaquette enclosed by sites (11, 12), (12, 12), (12, 11), and (11, 11)]; within the vortex core while away from the center (10, 12); around the edge of a vortex (5, 12); and far outside a vortex (0, 12). The curves in (d) are displaced vertically for clarity and the gray dashed line indicates the position of zero energy. The doping concentration is $x=0.4$ and $J_H=0.2U$.

Figure 2

(a) and (b) are similar to Figs. 1a, 1b, respectively, but are plotted on a $48\times 24$ lattice. (c) is the same as Fig. 1c. (d) The staggered magnetization $M_j^s$ plotted on a $48\times 24$ lattice. (e) The LDOS at four typical positions along the black cut in (c). (f) is similar to (e), but is plotted along the white cut. The doping concentration is $x=0.4$ and $J_H=0.23U$.

Figure 3

(a) and (b) are the same as Figs. 2a, 2b, respectively. (c) is similar to Fig. 2, but is plotted on a $48\times 24$ lattice. (d) is the same as Fig. 2d. (e) The LDOS along the black cut in (c). (f) is similar to (e), but is plotted along the white cut. The doping concentration is $x=0.3$ and $J_H=0.32U$.