Unveiling two-dimensional electron systems on ultra-wide bandgap semiconductor $\mathrm{\beta}$-Ga$_2$O$_3$

Ultra-wide bandgap (UWBG) semiconductors promise to revolutionize power electronics, yet a fundamental understanding of their interfacial electronic structure has been hindered by the absence of direct experimental observation. Here, we report the first momentum-resolved observation of two-dimensional electron systems on a UWBG material, enabled by angle resolved photoemission spectroscopy (ARPES) on high-purity $\beta$-Ga$_2$O$_3$ single crystals. Alkaline-metal-induced electron doping forms an isotropic circular Fermi surface, achieving a sheet carrier density of up to $1.0\times10^{14}$ $\mathrm{cm}^{-2}$. Self-consistent Poisson-Schr\"odinger calculations show that the electrons are confined within 1.2 nm of the surface and reveal an internal electric field of $18$ MV cm$^{-1}$. Crucially, our measurements reveal a pronounced renormalization of the electronic band structure: a series of carrier-density-dependent ARPES measurements shows that as the carrier density increases from $2\times10^{13}$ to $1.0\times10^{14}$ $\mathrm{cm}^{-2}$, the effective mass anomalously increases, nearly doubling to a final value of 0.48 $\textit{m}_{\mathrm{e}}$. This trend is notably opposite to that reported for other oxide semiconductors, pointing towards a unique renormalization mechanism in $\beta$-Ga$_2$O$_3$. Our findings establish the interfacial electronic structure of $\beta$-Ga$_2$O$_3$ and demonstrate that UWBG materials provide fertile ground for exploring carrier-density-driven electronic phenomena, opening new avenues for future quantum and power devices.