The thermodynamics of low-dimensional systems departs significantly from
phenomenologically deducted macroscopic laws. Particular examples, not yet
fully understood, are provided by the breakdown of Fourier's law and the
ballistic transport of heat. Low-dimensional trapped ion systems provide an
experimentally accessible and well-controlled platform for the study of these
problems. In our work, we study the transport of thermal energy in
low-dimensional trapped ion crystals, focusing in particular on the influence
of the Aubry-like transition that occurs when a topological defect is present
in the crystal. We show that the transition significantly hinders efficient
heat transport, being responsible for the rise of a marked temperature gradient
in the non-equilibrium steady state. Further analysis reveals the importance of
the motional eigenfrequencies of the crystal.Comment: 9 pages, 5 figure