Title: Boltzmann Transport in Nanostructures as a Friction Effect,
Abstract: Surface scattering is the key limiting factor to thermal transport in
dielectric crystals as the length scales are reduced or when temperature is
lowered. To explain this phenomenon, it is commonly assumed that the mean free
paths of heat carriers are bound by the crystal size and that thermal
conductivity is reduced in a manner proportional to such mean free paths. We
show here that these conclusions rely on simplifying assumptions and
approximated transport models. Instead, starting from the linearized Boltzmann
transport equation in the relaxon basis, we show how the problem can be reduced
to a set of decoupled linear differential equations. Then, the heat flow can be
interpreted as a hydrodynamic phenomenon, with the relaxon gas being slowed
down in proximity of a surface by friction effects, similar to the flux of a
viscous fluid in a pipe. As an example, we study a ribbon and a trench of
monolayer molybdenum disulphide, describing the procedure to reconstruct the
temperature and thermal conductivity profile in the sample interior and showing
how to estimate the effect of nanostructuring. The approach is general and
could be extended to other transport carriers, such as electrons, or extended
to materials of higher dimensionality and to different geometries, such as thin
films.