Geometrical lattice engineering of complex oxide heterostructures: a designer approach to emergent quantum states

Epitaxial heterostructures composed of complex oxides have fascinated researchers for over a decade as they offer multiple degrees of freedom to unveil emergent many-body phenomena often unattainable in bulk. Recently, apart from stabilizing such artificial structures along the conventional [001]-direction, tuning the growth direction along unconventional crystallographic axes has been highlighted as a promising route to realize novel quantum many-body phases. Here we illustrate this rapidly developing field of geometrical lattice engineering with the emphasis on a few prototypical examples of the recent experimental efforts to design complex oxide heterostructures along the (111) orientation for quantum phase discovery and potential applications.