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5$d$ transition metal oxides host a variety of exotic phases due to thecomparable strength of Coulomb repulsion and spin-orbit coupling. Herein, bypursuing density-functional studies on a delta-doped quasi-two-dimensionaliridate Sr$_3$Ir$_2$O$_7$, where a single SrO layer is replaced by LaO layer,we predict the formation of a spin-orbital entangled two-dimensional electrongas (2DEG) which is sharply confined on two IrO$_2$ layers close to the LaOlayer. In this bilayer crystal structure, an existing potential well is furtheraugmented with the inclusion of positively charged LaO layer which results inconfining the extra valence electron made available by the La$^{3+}$ ion. Theconfined electron is bound along crystal $a$ direction and is highly mobile inthe $bc$ plane. From the band structure point of view, now the existinghalf-filled $J_{eff}$ = 1/2 states are further electron doped to destroy theantiferromagnetic Mott insulating state of IrO$_2$ layers near to thedelta-doped layer. This leads to partially occupied Ir upper-Hubbard subbandswhich host the spin-orbital entangled 2DEG. The IrO$_2$ layers far away fromthe interface remain insulating and preserve the collinear G-type magneticordering of pristine Sr$_3$Ir$_2$O$_7$. The conductivity tensors calculatedusing semi-classical Boltzmann theory at room temperature reveal that the 2DEGexhibits large electrical conductivity of the order of 10$^{19}$.

Formation of spin-orbital entangled 2D electron gas in layer delta-doped bilayer iridate La$_{\delta}$Sr$_3$Ir$_2$O$_7$