Towards high-temperature coherence-enhanced transport in few-atomic layers heterostructures.

The possibility to exploit quantum coherence to strongly enhance the efficiency of charge transport would open the way for novel technological application. Transition-metal-oxides (TMOs) heterostructures are emerging as a potential solid-state platform to access the coherence-enhanced transport regime. In this work we lay the fundaments of a theoretical description of coherent transport in these systems in relation with a possible realization in thin LaVO$_3$/SrVO$_3$ heterostructures. As a first step, we consider the most idealized description of the transport of a single-excitation in terms of an effective one-dimensional open quantum system and show that the non-equilibrium steady state current is coherently enhanced when the coupling to the external collectors is of the order of the hopping along the chain, a condition associated with the solid-state analogue of superradiance. We also discuss the role of dephasing, static disorder and recombination, and we derive analytical formulas to define the maximal length scale compatible with the observation of coherent transport phenomena. The second step towards the understanding of the basic mechanism of coherent transport is a model which includes short-range electron-electron interactions, which are central in many TMOs. We compute the conductance of a correlated finite-size chain modelled by a Hubbard model and show that the coherence-driven enhancement of the transport efficiency is robust against the presence of a Coulomb repulsion as long as the latter is not so large as to give rise to Mott localization. Interestingly, to some extent the effect of interactions appears to have an effect similar to dephasing. Finally, we discuss the experimental implementation of the above conditions to achieve coherence-enhanced transport of photo-excitations in few monolayers LaVO$_3$/SrVO$_3$ heterostructures.