Quantum criticality in the 122 iron pnictide superconductors emerging from orbital-selective Mottness

The twin issues of the nature of the “normal” state and competing order(s) in the iron arsenides are central to understanding their unconventional, high-$T_c$ superconductivity. We use a combination of transport anisotropy measurements on detwinned $\mathrm{Sr}{\left({\mathrm{Fe}}_{1-x}{\mathrm{Co}}_x\right)}_2{\mathrm{As}}_2$ single crystals and local density approximation plus dynamical mean field theory (LDA + DMFT) calculations to revisit these issues. The peculiar resistivity anisotropy and its evolution with $x$ are naturally interpreted in terms of an underlying orbital-selective Mott transition (OSMT) that gaps out the $d_{xz}$ or $d_{yz}$ states. Further, we use a Landau-Ginzburg approach using LDA + DMFT input to rationalize a wide range of anomalies seen up to optimal doping, providing strong evidence for secondary electronic nematic order. These findings suggest that strong dynamical fluctuations linked to a marginal quantum-critical point associated with this OSMT and a secondary electronic nematic order constitute an intrinsically electronic pairing mechanism for superconductivity in Fe arsenides.

Figure 1

Measurements showing the variation of resistivity along the orthogonal $a$ and $b$ directions, with temperature, for various Co dopings. For the undoped ${\mathrm{SrFe}}_2{\mathrm{As}}_2,$ although the resistivities are different along the two directions below the SDW transition, they are both still metallic. With doping the transition is shifted to lower temperatures and vanishes beyond a doping of 8.1%, whereas superconductivity appears around 7.6%. The resistivity along the $b$ direction shows an insulating temperature dependence for intermediate dopings. See the text for theoretical analysis.

Figure 2

Evolution of the anisotropy in resistivity, defined as $[{\rho }_b/{\rho }_a]$ as a function of Co doping in ${\mathrm{SrFe}}_2{\mathrm{As}}_2.$ The parent compound has a $T_{\text{SDW}}\sim 200$ K which gradually decreases with increasing electron doping. SC and SDW co-exist for 7.6 % and 8.1 % Co doping [12]. The anisotropy becomes maximum just prior to the onset of SC and the value is very similar to that obtained in the Ba analog (see Ref. [3] for a comparison). However the splitting between the structural and SDW is not prominent as other cases.

Figure 3

Variation of the imaginary part of the self-energy corresponding to the $d_{xz}, d_{yz}, d_{xy}$, and $d_{x^2-y^2}$ orbitals with energy. $x$ is the theoretical doping and $\left(\delta \right)$ refers to the energy associated with the splitting of the $d_{xz}$ and the $d_{yz}$ bands. As is evident, the self-energy for the $d_{xz}$ band develops a sharp negative pole near Fermi energy, though slightly shifted, implying the onset of the Mott localization.

Figure 4

Variation of the resistivity along the two orthogonal $a$ and $b$ directions with temperature calculated from DMFT. For the parent $(x=0)$ system, although there is a split in the response both the directions show metallic behavior as is also noticed in experiments. The inset shows the resistivity for different values of doping in the absence of the OSMT [19].

Figure 5

Halperin-Nelson fits (see text) to the resistivity across the SDW/SC regimes for Co dopings corresponding to 7.6% and 8.1%. Application of magnetic field of 15 T lowers the $T_c$ as can be seen in the bottom panel, and simultaneously increases the insulating behavior.

Figure 6

Phases on the $b_m$ vs $\alpha$ plane where $b_m$ is the parameter which changes sign at the Lifshitz QCP (in the absence of superconductivity) and $\alpha$ is the coefficient of the quadratic term in the free energy of the superconductor. The phase diagram is for the case $c_m>0$ which is supported by our DMFT calculations. Here ${\tilde{b}}_m=b_m-u\alpha /2\beta$ and ${\tilde{d}}_m=d_m-u^2/4\beta .$ SC, EN, and D refer to superconducting, electron nematic and disordered phases respectively. The solid lines indicate a first-order transition and dashed lines indicate second-order transitions. The dotted line is the limit of metastability of the nonnematic phases: beyond this line a transition to nematic phases (EN or SC + EN) is inevitable. Lifshitz transitions correspond to ${\tilde{b}}_m=0$ in the coexistence phase and $b_m=0$ otherwise (line $N^{\prime }{O}^{\prime }{B}^{\prime }{X}^{\prime }{A}^{\prime }$).