Seebeck, Peltier and Thomson coefficient quanta in nanoscale conductors

Background. Nanoscale conductors, in particular graphene nanoribbons and carbon nanotubes, are increasingly being used in nanoelectronics and related arears of the nanoindustry. In them, there are not only effects related to electrical conductivity, but also other transfer phenomena, primarily thermoelectric phenomena. Materials and methods. The objects of research are metal nanoribbons with edges of the “zigzag” type and carbon nanotubes of the “armchair” type with transverse dimensions not exсeeding 100 nm and a length less then the length of the ballistic transport of free charge carriers. The work uses well-known methods of quantum mechanics, solid state physics, crystal physics and the theory of transfer phenomena in a two-dimensional electron gas. Results. Thermoelectric phenomena in graphene-like 2D crystals are described, the influence of quantum-dimensional effects on thermoelectric coefficients is investigated, and explicit expressions for the quanta of the Seebeck, Peltier and Thomson coefficients are obtained. Conclusions. It is shown that in ultrathin conductors whose transverse dimensions are commensurable with the De Broglie wavelength of an electron, the thermoelectric coefficients are quantized and do not vanish even at temperature equal to absolute zero. The results of the work can be useful in the calculation and design of nanoelectronic devices operating in the presence of temperature gradients.