Integrating multiple properties in a single system is crucial for the continuous developments in electronic devices. However, some physical properties are mutually exclusive in nature. Here, we report the coexistence of two seemingly mutually exclusive properties-polarity and two-dimensional conductivity-in ferroelectric Ba$_{0.2}$Sr$_{0.8}$TiO$_3$ thin films at the LaAlO$_3$/Ba$_{0.2}$Sr$_{0.8}$TiO$_3$ interface at room temperature. The polarity of a ~3.2 nm Ba$_{0.2}$Sr$_{0.8}$TiO$_3$ thin film is preserved with a two-dimensional mobile carrier density of ~0.05 electron per unit cell. We show that the electronic reconstruction resulting from the competition between the built-in electric field of LaAlO$_3$ and the polarization of Ba$_{0.2}$Sr$_{0.8}$TiO$_3$ is responsible for this unusual two-dimensional conducting polar phase. The general concept of exploiting mutually exclusive properties at oxide interfaces via electronic reconstruction may be applicable to other strongly-correlated oxide interfaces, thus opening windows to new functional nanoscale materials for applications in novel nanoelectronics.
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