Quanta of Ettingshausen and magnetothermoelectric coefficients

Background. In narrow electrically conductive nanoribbons, for example, in graphene nanoribbons (GNR), two types of quantization of electronic states take place: dimensional quantization and magnetic quantization (Landau quantization). The first is due to the fact that the width of the nanoribbon must fit, as in a rectangular potential pit, an integer number of de Broglie electron waves. The second is due to the fact that an integer number of wavelengths of such waves must fit into the cyclotron orbits of electrons. In this regard, the issue of the influence of these quantization types on the characteristics of transport phenomena in nanoscale conductors is relevant. The purpose of this study is to investigate the possibility of the Ettingshausen quantum effect existence and the accompanying magnetothermoelectric effect. Materials and methods. The objects of research are metallic graphene nanoribbons with a width of less than 100 nm and a length not exeeding the ballistic lengh of an electron in graphene, i. e. less than 1 $\mu$m. The work uses well-known methods of guantum physics, crystallophysics and the theory of two-dimensional electron gas. Results. Explicit expressions are obtained for the quanta of the Ettingshausen coefficient and the longitudinal magnetothermoelectric temperature difference. The results of the work can be used to create nanoscale magnetothermoelectric devices of a new generation. Conclusions. It is shown that the combined dimensional and magnetic quantization in narrow graphene nanoribbons leads to the appearance of the Ettingshausen quantum effect. At the same time, quanta of the linear value of the Ettingshausen coefficient and the absolute magnetothermoelectric temperature difference appear.