Anisotropy of the dc conductivity due to orbital-selective spin fluctuations in the nematic phase of iron superconductors

We study the dc conductivity of iron-based superconductors within the orbital-selective spin fluctuation scenario. Within this approach, the anisotropy of spin fluctuations below the spin-nematic transition at $T_S$ is also responsible for the orbital ordering, induced by nematic self-energy corrections to the quasiparticle dispersion. As a consequence, the anisotropy of the dc conductivity below $T_S$ is determined not only by the anisotropy of the scattering rates as expected within a spin-nematic scenario, but also by the modification of the Fermi velocity due to the orbital reconstruction. More interestingly, it turns out that these two effects contribute to the dc-conductivity anisotropy with opposite signs. By using realistic band-structure parameters we compute the conductivity anisotropy for both 122 and FeSe compounds, discussing the possible origin of the different dc-conductivity anisotropy observed experimentally in these two families of iron-based superconductors.

Figure 1

General sketch of the orbital content of the Fermi surface of the four-pocket model for iron superconductors. The green and red arrows show the OSSF with $yz$ content in the $x$ direction and $xz$ content in the $y$ direction. Cold spots, where the scattering rate is minimum, are shown by a circle and they are found on the $xy$ and $xz$ orbitals in the nematic phase due to anisotropic self-energy corrections. See the text.

Figure 2

Numerical computation of FS wave vectors and velocity components for 122 system parameters in the tetragonal and nematic phase. ${\mathrm{\Phi }}_h={\mathrm{\Phi }}_e=4$ meV, the spin-orbit interaction is 5 meV, other band parameters are detailed in Appendix pp3. The $k_F$ are measured in units $1/a\sim 0.375\AA$, where $a=a_{\mathrm{FeFe}}$ is the lattice constant of the 1-Fe unit cell. The velocities are in eV.

Figure 3

Renormalized scattering rate (in meV) computed using realistic 122 system parameters. Here ${\mathrm{\Gamma }}_0^h=3$ meV and ${\mathrm{\Gamma }}_0^e=2$ meV. We fix $\mathrm{\Delta }{\mathrm{\Gamma }}^h$ and $\mathrm{\Delta }{\mathrm{\Gamma }}^e$ considering the imaginary part of the self-energy for each pocket changing proportionally to the real part in the nematic phase (Appendix pp3).

Figure 4

Numerical computation of the velocity contribution to the dc conductivity anisotropy $\mathrm{\Delta }{\sigma }_V$ and of the total dc conductivity anisotropy $\mathrm{\Delta }\sigma$ for realistic parameter for 122. In (a) and (b) we renormalized the pocket contributions to their value in the tetragonal phase, i.e., $\mathrm{\Delta }{\sigma }_V^{l_{\pm }}({\mathrm{\Phi }}^{h/e}=0)$ and analogously in (d) and (e). In (c) and (f) instead we renormalize the h and e contributions to the total tetragonal values, i.e., ${\sigma }_{V\text{tot}}={\sigma }_V({\mathrm{\Phi }}^{h/e}=0)$ and ${\sigma }_{\text{tot}}=\sigma ({\mathrm{\Phi }}^{h/e}=0)$.

Figure 5

Numerical computation of the tetragonal and nematic FS and Fermi velocity components for FeSe parameters. ${\mathrm{\Phi }}_h={\mathrm{\Phi }}_e=15$ meV, the spin-orbit interaction is 20 meV, the other band parameters are detailed in Appendix pp3.

Figure 6

Renormalized scattering rate for FeSe. ${\mathrm{\Gamma }}_0^h=5$ meV and ${\mathrm{\Gamma }}_0^e=2.5$ meV. $\mathrm{\Delta }{\mathrm{\Gamma }}^h$ and $\mathrm{\Delta }{\mathrm{\Gamma }}^e$ are considered as proportional to the nematic variation of the real parts (Appendix pp3).

Figure 7

Numerical computation of the velocity contribution to the dc conductivity anisotropy and of the total dc conductivity anisotropy for a realistic parameter for FeSe. All the pockets show consistent deviations of the dc anisotropy with respect the analytical expectations Eqs. (28) and (31).