  The resistance of the electron gas at the interface between the two band
insulators LaAlO3 (LAO) and SrTiO3 (STO) typically drops monotonically with
temperature and R/T curves during cooling and warm-up look identical for large
area structures. Here we show that if the LAO/STO is laterally restricted by
nanopatterning the resistance exhibits a temperature anomaly. Warming up
nanostructures from low temperatures leads to one or two pronounced resistance
peaks between 50 and 100 K not observed for larger dimensions. During cool-down
current filaments emerge at the domain walls that form during the well-known
structural phase transition of the STO substrate. During warm-up the reverse
phase transition can interrupt filaments before the sheet conductivity which
dominates at higher temperature is reestablished. Due to the limited number of
filaments in a nanostructure this process can result in a complete loss of
conductance. As a consequence of these findings the transport physics extracted
from experiments in small and large area LAO/STO structures may need to be
reconsidered.
