Manipulation of Gap Nodes by Uniaxial Strain in Iron-Based Superconductors

In the iron pnictides and chalcogenides, multiple orbitals participate in the superconducting state, enabling different gap structures to be realized in distinct materials. Here we argue that the spectral weights of these orbitals can, in principle, be controlled by a tetragonal symmetry-breaking uniaxial strain, due to the enhanced nematic susceptibility of many iron-based superconductors. By investigating multiorbital microscopic models in the presence of orbital order, we show that not only $T_c$ can be enhanced, but pairs of accidental gap nodes can be annihilated and created in the Fermi surface by an increasing external strain. We explain our results as a mixture of nearly degenerate superconducting states promoted by strain, and show that the annihilation and creation of nodes can be detected experimentally via anisotropic penetration depth measurements. Our results provide a promising framework to externally control the superconducting properties of iron-based materials.

Figure 1

(a) Change of the FS by orbital order. The solid (dashed) lines describe the FS for ${\mathrm{\Delta }}_{oo}=0$ (${\mathrm{\Delta }}_{oo}=80\mathrm{meV}$). Different colors represent the dominant $3d$ orbital component on the FS. (b) Enhancement of $T_c\propto e^{-1/{\lambda }_{\alpha }}$ (in units of its value in the tetragonal phase $T_{c_0}$) as a function of the orbital order parameter ${\mathrm{\Delta }}_{oo}$.

Figure 2

Evolution of gap structure at $T_c$ for increasing orbital order parameter ${\mathrm{\Delta }}_{oo}$. The four panels in (a) show the angular dependencies of the gaps of each pocket in the presence (blue lines) and in the absence (red lines) of orbital order. The angles are measured relative to the $x$ axis. (b) Schematic illustration of the motion of nodes as a function of increasing ${\mathrm{\Delta }}_{oo}$. While nodes are created in the hole pockets, emerging along both the $x$ and $y$ directions (white dots), the electron pockets’ nodes are annihilated, merging along the $x$ direction (black dots). Green (yellow) lines denote positive (negative) gap values.

Figure 3

Angular dependence of the gaps on the hole ($h_1$) and electron ($e_{x/y}$) pockets at $T_c$ (dashed red line) and at $T=0$ (solid blue line) within our effective three-band model. The gaps are normalized by their absolute average values. The parameters used are $v=0.30$, $w=0.25$, ${\beta }_e=2{\beta }_h=0.40$.

Figure 4

Anisotropic penetration depth ${\lambda }_{xx}-{\lambda }_{yy}$, as a function of the mixing parameter $\gamma \propto {\partial }_x{u}_x-{\partial }_y{u}_y$ in Eq. (3), for $T/{\mathrm{\Delta }}_0=0.01$. Arrows denote the peaks and troughs reflecting the annihilation and creation of nodes in the Fermi pockets.