Abstract
We describe a variational theory of multiband two-dimensional electron gases that captures the interplay between electrostatic confining potentials, orbital-dependent interlayer electronic hopping, and electron-electron interactions and apply it to the $d$-band two-dimensional electron gases that form near perovskite oxide surfaces and heterojunctions. These multiband two-dimensional electron gases are prone to the formation of Coulomb-interaction-driven orbitally-ordered nematic ground states. We find that as the electron density is lowered and interaction effects strengthen, spontaneous orbital order occurs first, followed by spin order. We compare our results with known properties of single-component two-dimensional electron gas systems and comment on closely related physics in semiconductor quantum wells and van der Waals heterostructures.
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