What Makes the T$_{\mathrm{c}} $of FeSe/SrTiO$_{\mathrm{3}}$ so High ?*

Raising the superconducting transition temperature to a point where applications are practical is one of the most important challenges in science. In the history of high \textit{Tc }superconductivity there are two landmark events: the discovery of copper-oxide superconductor in 1986, and the discovery of iron-based superconductor in 2006 For the Fe-based superconductors the record of T$_{\mathrm{c}}$ was 55$K$[1] until 2012. In the interface system composed of an one unit cell thick FeSe film grown on the TiO$_{\mathrm{2}}$ terminated (001) surface of SrTiO$_{\mathrm{3\thinspace }}$an anomalously large superconducting-like energy gap was seen by scan tunneling microscopy for [2]. Later ARPES works show the gap opening temperature can reach nearly the liquid nitrogen boiling temperature [3-7]. More recently several FeSe-related bulk and thin film high T$_{\mathrm{c}}$ systems have be discovered. This talk reviews some of the recent experimental [7] and theoretical [8] progresses in the study of the mechanism for high temperature superconductivity in this interface system. It offers the author's personal view of why T$_{\mathrm{c}} $is so high and how to further increase it [9£¬10]. References: \begin{enumerate} \item Z.A. Ren \textit{et al.}, Chin. Phys. Lett. \textbf{25}, 2215-2216 (2008). \item Q.Y. Wang \textit{et al.}, Chin. Phys. Lett. \textbf{29}, 037402 (2012). \item D.F. Liu \textit{al.}, Nature Commun. \textbf{3}, 931 (2012). \item S. He \textit{et al.}, Nature Materials \textbf{12}, 605-610 (2013). \item S. Tan \textit{et al.}, Nature Materials \textbf{12}, 634-640 (2013). \item R. Peng \textit{et al.}, Nature Commun. \textbf{5}, 5044 (2014). \item J.J. Lee \textit{et al,} Nature \textbf{515,} 245 (2014). \item Zixiang Li \textit{et al}, to be published. \item D.-H. Lee, Chin. Phys. B, 2015, 24 (\textbf{11}): 117405 \textbf{doi:} 10.1088/1674-1056/24/11/117405 \item Much of the contents of this talk are stimulated by the collaborative work with Z-X Shen and his ARPES group members and T. Deveraux and his group members. \end{enumerate}