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Heterointerfaces of SrTiO$_{3}$ with other transition metal oxides make up anintriguing family of systems with a bounty of coexisting and competing physicalorders. Some examples, such as LaAlO$_{3}$/SrTiO$_{3}$, support a high carrierdensity electron gas at the interface whose electronic properties aredetermined by a combination of lattice distortions, spin-orbit coupling,defects, and various regimes of magnetic and charge ordering. Here, we studyelectronic transport in mesoscale devices made with heterostructures ofSrTiO$_{3}$ sandwiched between layers of SmTiO$_{3}$, in which the transportproperties can be tuned from a regime of Fermi-liquid like resistivity ($\rho\sim T^{2}$) to a non-Fermi liquid ($\rho \sim T^{5/3}$) by controlling theSrTiO$_{3}$ thickness. In mesoscale devices at low temperatures, we findunexpected voltage fluctuations that grow in magnitude as $T$ is decreasedbelow 20 K, are suppressed with increasing contact electrode size, and areindependent of the drive current and contact spacing distance.Magnetoresistance fluctuations are also observed, which are reminiscent ofuniversal conductance fluctuations but not entirely consistent with theirconventional properties. Candidate explanations are considered, and a mechanismis suggested based on mesoscopic temporal fluctuations of the Seebeckcoefficient. An improved understanding of charge transport in these modelsystems, especially their quantum coherent properties, may lead to insightsinto the nature of transport in strongly correlated materials that deviate fromFermi liquid theory.

Potential Fluctuations at Low Temperatures in Mesoscopic-Scale SmTiO$_{3}$/SrTiO$_{3}$/SmTiO$_{3}$ Quantum Well Structures