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The interface between the two insulating oxides SrTiO$_3$ and LaAlO$_3$ givesrise to a two-dimensional electron system with intriguing transport phenomena,including superconductivity, which are controllable by a gate. Previousmeasurements on the (001) interface have shown that the superconductingcritical temperature, the Hall density, and the frequency of quantumoscillations, vary nonmonotonically and in a correlated fashion with the gatevoltage. In this paper we experimentally demonstrate that the (111) interfacefeatures a qualitatively distinct behavior, in which the frequency ofShubnikov-de Haas oscillations changes monotonically, while the variation ofother properties is nonmonotonic albeit uncorrelated. We develop a theoreticalmodel, incorporating the different symmetries of these interfaces as well aselectronic-correlation-induced band competition. We show that the latterdominates at (001), leading to similar nonmonotonicity in all observables,while the former is more important at (111), giving rise to highly curved Fermicontours, and accounting for all its anomalous transport measurements.

Symmetry and correlation effects on band structure explain the anomalous transport properties of (111) LaAlO$_3$/SrTiO$_3$