Link between superconductivity and types of carriers in FeSe thin films

In iron-based superconductors, $\beta $-FeSe possesses the simplest tetragonal structure but attracts much attention due to its unusual properties. It exhibits a great boost of the superconducting transition temperature ($T_{\mathrm{c}})$ in the monolayer form, under high pressure, via ion/cluster intercalations and electric field gating. There is a common consensus that the enhancement of $T_{\mathrm{c}}$ is accompanied with the evolution of electronic structure of the Fermi surface, that is, associated with the types of charge carriers. Although qualitative ARPES results have shown that the electron-like carriers play a key role in promoting the $T_{\mathrm{c}}$, hitherto, a quantitative link between the carrier nature and the superconductivity has not been clarified. In this work, with our successful synthesis of a series of high quality $\beta $-FeSe thin films of tunable $T_{\mathrm{c}}^{\mathrm{0}}$\textbf{`}s from 2 K to 14 K, we find by systematic transport measurements that the holes and electrons coexist in all the samples. While the concentration of electron-type carriers increases monotonically by about 6 times, the hole carrier density roughly holds a constant value. It implies an intimate relation between the electron carriers and the superconductivity. Moreover, our analysis on the monolayer FeSe samples of $T_{\mathrm{c}}$ \textasciitilde 40 K points to a vanishing hole pocket. Our results thereby unveil that the $T_{\mathrm{c}}$ enhancement in FeSe is related to the increase in the electron density, which becomes more pronounced upon a sudden decrease in the hole density.