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Ubiquitous stripe phase and enhanced electron pairing in interfacial high-Tc superconductor FeSe/BaTiO$_3$

Monolayer FeSe grown on SrTiO$_3$ provides a new playground for high-Tc superconductivity. A recent study shows the importance of stripy instability for superconductivity enhancement in FeSe/SrTiO3. However, it is still under debate whether such a stripe phase is ubiquitously bound to the interfacial superconductivity. Here, we report on molecular beam epitaxy growth and low-temperature scanning tunneling microscopy study of FeSe films on BaTiO$_3$(001). We find that the stripe phase is more prominent in FeSe/BaTiO$_3$. Long-range stripes exist in bilayer and triple-layer FeSe films at 4 K and even persist up to 77 K in the case of bilayer FeSe, with enlarged superconducting gaps upon alkali-metal deposition. The results point out an intimate correlation between the interfacial superconductivity and the stripe phase.