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

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