Effects of Lifshitz Transition on Charge Transport in Magnetic Phases of Fe-Based Superconductors

The unusual temperature dependence of the resistivity and its in-plane anisotropy observed in the Fe-based superconducting materials, particularly ${\mathrm{Ba}({\mathrm{Fe}}_{1-x}{\mathrm{Co}}_x)}_2{\mathrm{As}}_2$, has been a long-standing puzzle. Here, we consider the effect of impurity scattering on the temperature dependence of the average resistivity within a simple two-band model of a dirty spin density wave metal. The sharp drop in resistivity below the Néel temperature $T_N$ in the parent compound can only be understood in terms of a Lifshitz transition following Fermi surface reconstruction upon magnetic ordering. We show that the observed resistivity anisotropy in this phase, arising from nematic defect structures, is affected by the Lifshitz transition as well.

Figure 1

(a) Fit (red line) of resistivity data (black dots) from Ref. [35] in the high-$T$ paramagnetic phase with ${\rho }_{\text{avg}}=2.5\times {10}^{-1}+9.1\times {10}^{-7}{T}^2$. (b) $T$ evolution of the total density of states and the $c$- and $f$-electron scattering rates. Insets: Fermi surface evolution due to $T$ dependence of SDW potential. $T_N$, $T_e^{*}$, $T_h^{*}$ are defined in text. (c) $T$ dependence of average resistivity for various total scattering rates $\mathrm{\Gamma }$. ${\rho }_n\equiv {\rho }_{\text{avg}}(T=T_N)$. (d) $\mathrm{\Delta }{\rho }_{\text{avg}}$ (defined in text) dependence on $W_0$ and $\mathrm{\Gamma }$.

Figure 2

Main panel: ${\rho }_{\text{ani}}$ vs. SDW gap $W_0$ for ${\mathrm{\Gamma }}_1=0.5\mathrm{\Gamma }$. Curves for ellipticity ${\xi }_e=\pm 2$ at $T=T_0=0$ (upward or downward triangles, respectively) and at $T=T_N$ (dots or circles, respectively), and for the average of two-plane model (dashed line). The dash-dotted line indicates ${\rho }_{\text{ani}}=0$. $W_e^{*}$, $W_h^{*}$ are defined in text. Bottom inset: same quantities for ${\mathrm{\Gamma }}_1=0$. Top inset: cartoon of extended impurity potential aligned along antiferromagnetic axis $a$.

Figure 3

(a) Resistivity ${\rho }_{a,b}$ at $k_z=\pi$ for a two-plane model with isotropic scatterers. (b)–(c) Same at $k_z=\pi ,0$, respectively, for a two-plane model with anisotropic scatterers. (d) Average of (b) and (c).