Entropy and Seebeck signals meet on the edges

We explore the electronic entropy per particle s and Seebeck coefficient S in zigzag graphene ribbons. Pristine and edge-doped ribbons are considered using tight-binding models to inspect the role of edge states in the observed thermal transport properties. As a bandgap opens when the ribbons are doped at one or both edges, due to asymmetric edge potentials, we find that s and S signals are closely related to each other: both develop sharp dip-peak lineshapes as the chemical potential lies in the gap, while the ratio s/S exhibits a nearly constant value equal to the elementary charge e at low temperatures. This constant ratio suggests that S can be seen as the transport differential entropy per charge, as suggested by some authors. Our calculations also indicate that measurement of s and S may be useful as a spectroscopic probe of different electronic energy scales involved in such quantities in gapped materials.