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Recent experiments have explored two-dimensional electron gases (2DEGs) atoxide (111) surfaces and interfaces, finding evidence for hexagonal symmetrybreaking in SrTiO$_3$ at low temperature. We discuss many-body instabilities ofsuch (111) 2DEGs, incorporating multiorbital interactions in the $t_{2g}$manifold which can induce diverse magnetic and orbital orders. Such brokensymmetries may partly account for the observed nematicity, cooperating orcompeting with phonon mechanisms. We present an effective field theory for theinterplay of magnetism and nematic charge order, and discuss implications ofthe nematicity for transport and superconductivity in (111) 2DEGs.

Magnetic and nematic orders of the 2DEG at oxide (111) surfaces and interfaces