Strong and nonmonotonic temperature dependence of Hall coefficient in superconducting K$_x$Fe$_{2-y}$Se$_2$ single crystals

In-plane resistivity, magnetoresistance and Hall effect measurements have been conducted on quenched K$_x$Fe$_{2-y}$Se$_2$ single crystals in order to analysis the normal-state transport properties. It is found that the Kohler's rule is well obeyed below about 80 K, but clearly violated above 80 K. Measurements of the Hall coefficient reveal a strong but non-monotonic temperature dependence with a maximum at about 80 K, in contrast to any other FeAs-based superconductors. With the two-band model analysis on the Hall coefficient, we conclude that a gap may open below 65 K. The data above 65 K are interpreted as a temperature induced crossover from a metallic state at a low temperature to an orbital-selective Mott phase at a high temperature. This is consistent with the recent data of angle resolved photoemission spectroscopy. These results call for a refined theoretical understanding, especially when the hole pockets are absent or become trivial in K$_x$Fe$_{2-y}$Se$_2$ superconductors.