Fractional power-law behavior and its origin in iron-chalcogenide and ruthenate superconductors: Insights from first-principles calculations

We perform realistic first-principles calculations of iron chalcogenides and ruthenate-based materials to identify experimental signatures of Hund's-coupling-induced correlations in these systems. We find that FeTe and K${}_x$Fe${}_{2-y}$Se${}_2$ display unusual orbital-dependent fractional power-law behavior in their quasiparticle self-energy and optical conductivity, a phenomenon first identified in SrRuO${}_3$. Strong incoherence in the paramagnetic state of these materials results in electronic states hidden to angle-resolved photoemission spectroscopy which reemerge at low temperatures. We identify the effective low-energy Hamiltonian describing these systems and show that these anomalies are not controlled by the proximity to a quantum critical point but result from coexistence of fast quantum mechanical orbital fluctuations and slow spin fluctuations.

Figure 1

Fractional power law in (a) theoretical self-energy and (b) experimental optical conductivity in iron chalcogenides and ruthenates. Experimental data are taken from Ref. 42 for FeTe${}_{0.91}$ and FeTe${}_{0.7}$Se${}_{0.3}$, Ref. 43 for Fe${}_{1.06}$Te${}_{0.88}$S${}_{0.14}$, Ref. 28 for Sr${}_2$RuO${}_4$, and Ref. 29 for SrRuO${}_3$.

Figure 2

Incoherence-coherence crossover in FeTe. $A(\mathbf{k},\omega )$ along the path $\Gamma \to X\to M\to \Gamma \to Z\to R\to A\to Z$ for FeTe at (a) 232 K, (b) 116 K, and (c) 58 K and for (d) FeSe at 116 K in the PM states. (e), (f) $A\left(\omega \right)$ for the Fe $3d$ $xy$ and the $xz$ and $yz$ orbitals at 387, 232, 116, and 58 K in PM FeTe. (g), (h) Color-coded Fermi surface in the $\Gamma$ plane for PM FeTe and FeSe, respectively. Red, green, and blue colors correspond to $xy$, $xz$, and $yz$ orbital character, respectively. Due to the incoherent nature of the $xy$ orbital above $T_N$, the outer hole pocket around $\Gamma$ is not easy to detect in ARPES experiments.

Figure 3

Quasiparticle self-energies for a three-band model with $J_H=2.0$ at different fillings $n_d=1.75$, 2.00, and 2.26. (a) The self-energies at two temperatures $T=0.01$ and 0.001 25 show the incoherence-coherence crossover with decreasing temperature. (b) The self-energies plotted in log${}_{10}$ scale display fractional power-law behavior in the intermediate frequency range from ${\varepsilon }_0^{*}$ to ${\varepsilon }_1^{*}$ as indicated by arrows.

Figure 4

(a) The coherent temperature and (b) the spin and orbital susceptibility, as functions of $n_d$ for a three-band model with $J_H=2.0$ (solid lines) and $J_H=1.0$ (dashed lines).

Figure 5

Quasiparticle self energy for $J_H=2.0$. The imaginary part of the quasiparticle self-energy in the log${}_{10}$-log${}_{10}$ scale as a function of electron occupation $n_d$ for $U=6.0$ and $J_H=2.0$. Note the data are shifted along the $y$ axis for better illustration. The linear dispersion of the self-energy in the plot indicates that power-law behavior exists in the intermediate frequency region as indicated by the arrows.

Figure 6

Quasiparticle self-energy for $J_H=1.0$. The imaginary part of the quasiparticle self-energy in the log${}_{10}$-log${}_{10}$ scale as a function of electron occupation $n_d$ for $U=6.0$ and $J_H=1.0$. Note that the data are shifted along the $y$ axis for better illustration. The linear dispersion of the self-energy in the plot indicates that power-law behavior exists in the intermediate frequency region as indicated by the arrows.

Figure 7

Local spin, orbital, and charge susceptibilities at zero frequency as functions of temperature for $n_d=1.75$, 2.00, 2.26 and $U=6.0$, $J_H=2.0$. The spin susceptibility has large static values and takes the Curie-Weiss form while the orbital susceptibility is Pauli-like and enhanced at intermediate temperature and around $n_d=2.0$. Note that the charge susceptibility is two orders of magnitude smaller than the orbital susceptibility and thus does not play an important role.