  A thermoelectric voltage is induced in a junction, constituted of two
dissimilar materials under a temperature gradient. Similarly, a thermosize
voltage is expected to be induced in a junction made by the same material but
having different sizes, so-called thermosize junction. This is a consequence of
dissimilarity in Seebeck coefficients due to differences in classical and/or
quantum size effects in the same materials with different sizes. The studies on
thermosize effects in literature are mainly based on semi-classical models
under relaxation time approximation or even simpler local equilibrium ones
where only very general ideas and results have been discussed without
considering quantum transport approaches and specific materials. To make more
realistic predictions for a possible experimental verification, here, we
consider ballistic thermosize junctions made by narrow and wide ($n$-$w$)
pristine graphene nanoribbons with perfect armchair edges and calculate the
electronic contribution to the thermosize voltage, at room temperature, by
using the Landauer formalism. The results show that the maximum thermosize
voltage can be achieved for semiconducting nanoribbons and it is about an order
of magnitude larger than that of metallic nanoribbons. In the semiconducting
case, the thermosize voltage forms a characteristic plateau for a finite range
of gating conditions. We demonstrate, through numerical calculations, that the
induced thermosize voltage per temperature difference can be in the scale of
mV/K, which is high enough for experimental measurements. Owing to their high
and persistent thermosize voltage values, graphene nanoribbons are expected to
be good candidate for device applications of thermosize effects.
