Strain-Driven Approach to Quantum Criticality in $A{\mathrm{Fe}}_2{\mathrm{As}}_2$ with $A=\mathrm{K}$, Rb, and Cs

The iron-based superconductors $A{\mathrm{Fe}}_2{\mathrm{As}}_2$ with $A=\mathrm{K}$, Rb, Cs exhibit large Sommerfeld coefficients approaching those of heavy-fermion systems. We have investigated the magnetostriction and thermal expansion of this series to shed light on this unusual behavior. Quantum oscillations of the magnetostriction allow identifying the band-specific quasiparticle masses which by far exceed the band-structure derived masses. The divergence of the Grüneisen ratio derived from thermal expansion indicates that with increasing volume along the series a quantum critical point is approached. The critical fluctuations responsible for the enhancement of the quasiparticle masses appear to weaken the superconducting state.

Figure 1

Normalized Fourier spectra of the oscillatory part of the magnetostriction coefficient ${\lambda }_i^{\text{osc}}$ (insets) along the $i=a$ (blue) and $c$ axis (red line) of $A122$, $A=\mathrm{K}$, Rb, and Cs, at $T=50\mathrm{mK}$ for $B\parallel c$ and $a$.

Figure 2

(a) Extremal cross-sectional areas of the Fermi surfaces of (K,Rb,Cs)122, expressed as fractions of the first Brillouin-zone volumes. (b) Effective quasiparticle masses $m^{*}$, plotted against the ionic radius of the alkaline atom $R_A$ [28, 29, 30]. The values presented by open symbols were obtained by assuming a constant total hole count and using the Sommerfeld coefficients [7, 8, 9]. Lines are guides to the eye.

Figure 3

(a) Comparison between chemical (black dots) and hydrostatic pressure dependences of the Sommerfeld coefficient $\gamma$ as a function of the unit-cell volume $V_{\mathrm{UC}}$ and that of a single FeAs layer $V_{\mathrm{FeAs}}$. The hydrostatic pressure dependences are extracted from the volume thermal expansion ${\alpha }_V$ for $V=V_{\mathrm{UC}}$ (blue lines) and $V_{\mathrm{FeAs}}$ (red lines). (b) The calculated $\gamma$ as a function of $U$ in a multiorbital Hubbard model for $A122$ ($A=\mathrm{K}$, Rb, Cs) (see text). (c) Evolution of the measured $\gamma$ with increasing $V_{\mathrm{FeAs}}$. Gray [35] and open dots [36] are estimated from high-pressure resistivity measurements. The red line is a fit to the data points. (d) The Grüneisen parameter $\mathrm{\Gamma }$, calculated from $\gamma$, $A_{\rho }$, and ${\alpha }_V$. The red line is determined with the fit shown in (d) under the assumption of a Fermi liquid. (e) Strain dependences of $\gamma$ and (f) the superconducting transition temperature $T_c$. Lines are guides to the eyes. The inset in (e) shows the Fe plane with the $3d_{xy}$ and $3d_{x^2-y^2}$ orbitals.

Figure 4

Evolution of $\gamma$ as a function of $V_{\mathrm{FeAs}}$ and hole doping expressed as filling $N$ of the Fe $3d$ states. In addition to the high-pressure data of ${\mathrm{KFe}}_2{\mathrm{As}}_2$ [33, 35, 36, 53], measurements of ${\mathrm{Ba}}_{1-x}{\mathrm{K}}_x{\mathrm{Fe}}_2{\mathrm{As}}_2$ [51, 54] and ${\mathrm{BaFe}}_2({\mathrm{As}}_{1-x}{\mathrm{P}}_x{)}_2$ [1, 52, 55, 56] have been included. The $\gamma$ values of ${\mathrm{BaFe}}_2({\mathrm{As}}_{1-x}{\mathrm{P}}_x{)}_2$ were estimated following Ref. [52]. The base plane shows a tentative phase diagram of a five-orbital Hubbard model with combined ($U$, $J$) interactions leading to a Mott-insulating state at $N=5$ [46].