  Electronic phase separation (EPS) originates from an incomplete
transformation between electronic phases, causing the inhomogeneous spatial
distribution of electronic properties. In the system of two-dimensional
electron gas (2DEG), the EPS is usually identified based on a percolative
metal-to-superconductor transition. Here, we report a metal-insulator
transition (MIT) in KTaO3-based 2DEG with the width of conductive channel
decreasing into micrometer scale. Hysteretic resistance-temperature relations
are observed due to the competition between metallic and insulating phases,
which is tunable by magnetic field. Such a size-dependent MIT effect is
attributed to the coexistence and separation of metallic and insulating phases.
Combining density functional theory calculation, we propose a theoretical model
to simulate the dynamic process of the EPS using the percolation theory,
demonstrating the mechanism of size-dependent MIT. Our work suggests a clear
and simple 2DEG platform to achieve the spatial coexistence of metallic and
insulating phases.
