Multiband transport and nonmetallic low-temperature state of K$_{0.50}$Na$_{0.24}$Fe$_{1.52}$Se$_{2}$

We report evidence for multiband transport and an insulating low-temperature normal state in superconducting K$_{0.50}$Na$_{0.24}$Fe$_{1.52}$Se$_{2}$ with T$_{\mathrm{c}} \approx $ 20 K. The temperature-dependent upper critical field H$_{\mathrm{c2}}$ is well described by a two-band model. After the superconductivity is suppressed by applying pulsed magnetic field at low temperature, the normal-state resistance is found to increase logarithmically as T $\to $ 0. This is similar as for high-T$_{\mathrm{c}}$ copper oxides and granular superconductors, suggesting that the superconductor-insulator transition is related to intrinsic nanoscale phase separation.\\[4pt] Work at Brookhaven is supported by the U.S. DOE under Contract No. DE-AC02-98CH10886 and in part by the Center for Emergent Superconductivity, an Energy Frontier Research Center funded by the U.S. DOE, Office for Basic Energy Science (C.P.). We acknowledge the support of the HLD at HZDR, member of the European Magnet Field Laboratory (EMFL). C.P. acknowledges support by the Alexander von Humboldt Foundation.