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In the heavily hole-doped iron-based superconductors $A$Fe$_2$As$_2$ ($A=$ K,Rb, and Cs), the electron effective mass increases rapidly with alkali-ionradius. To study how the mass enhancement affects the superconducting state, wemeasure the London penetration depth $\lambda(T)$ in clean crystals of$A$Fe$_2$As$_2$ down to low temperature $T\sim0.1$ K. In all systems, thesuperfluid stiffness $\rho_s(T)=\lambda^2(0)/\lambda^2(T)$ can be approximatedby a power-law $T$ dependence at low temperatures, indicating the robustness ofstrong momentum anisotropy in the superconducting gap $\Delta(k)$. The power$\alpha$ increases from $\sim1$ with mass enhancement and approaches anunconventional exponent $\alpha\sim 1.5$ in the heaviest CsFe$_2$As$_2$. Thisappears to be a hallmark of superconductors near antiferromagnetic quantumcritical points, where the quasiparticles excited across the anisotropic$\Delta(k)$ are significantly influenced by the momentum dependence of quantumcritical fluctuations.

Evolution of quasiparticle excitations with critical mass enhancement in superconducting AFe2As2 (A = K, Rb, and Cs)