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To gain insight into the unconventional superconductivity of Fe-pnictides with no electron pockets, we measure the thermal conductivity $kappa$ and penetration depth $lambda$ in the heavily hole-doped regime of Ba$_{1-x}$K$_x$Fe$_2$As$_2$. The residu al thermal conductivity $(kappa/T)_{T rightarrow 0,{rm K}}$ and $T$-dependence of $lambda$ consistently indicate the fully gapped superconductivity at $x=0.76$ and the (line) nodal superconductivity at higher hole concentrations. The magnitudes of $frac{kappa}{T}cdot T_c|_{T rightarrow 0,{rm K}}$ and $frac{dlambda}{d(T/T_c)}$ at low temperatures, both of which are determined by the properties of the low-energy excitations, exhibit a highly unusual non-monotonic x-dependence. These results indicate a dramatic change of the nodal characteristics in a narrow doping range, suggesting a doping crossover of the gap function between the s-wave states with and without sign reversal between $Gamma$-centered hole pockets.
In Mott insulators, the strong electron-electron Coulomb repulsion prevents metallicity and charge excitations are gapped. In dimensions greater than one, their spins are usually ordered antiferromagnetically at low temperatures. Geometrical frustrat ions can destroy this long-range order, leading to exotic quantum spin liquid (QSL) states. However, their magnetic ground states have been a long-standing mystery. Here we show that a QSL state in the organic Mott insulator EtMe$_3$Sb[Pd(dmit)$_2$]$_2$ with two-dimensional triangular lattice has Pauli-paramagnetic-like low-energy excitations, which are a hallmark of itinerant fermions. Our torque magnetometry down to low temperatures (30 mK) up to high fields (32 T) reveal distinct residual paramagnetic susceptibility comparable to that in a half-filled two-dimensional metal. This demonstrates that the system is in a magnetically gapless ground state, a critical state with infinite magnetic correlation length. Moreover, our results are robust against deuteration, pointing toward the emergence of an extended `quantum critical phase, in which low-energy spin excitations behave as in paramagnetic metals with Fermi surface, despite the frozen charge degree of freedom.
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