Quanta of nernst coefficients and thermomagnetic emf

Background. The well-known quantum Hall effect observed in two-dimensional current conductors placed in a transvers magnetic field is due to the magnetic quantization of cyclotron orbits of charge carriers, leading to the appearance of Landau levels in theiz energy spectrum. This, in turn, causes quantization of the Hall resistance. Previously, we showed that in narrow nanowires (for example, in graphene nanoribbons), the effect of magnetic quantization is superimposed on the effect dimensional quantization, which also leads to quantization of the Hall and magnetoresistance coefficients. In this regard, it is of interest to study the influence of dimensional and magnetic quantization on the nature of the flow and other transfer phenomena that occur in two-dimensional conductors placed in a transverse magnetic field. The purpose of this work is to study galvanothermomagnetic phenomena on this subject: Nernst effects and thermomagnetic EMF. Materials and methods. The objects of research are graphene nanoribbons with metallic properties with zigzag-type edges less than 100 nm wide and a length not exceeding 1 $\mu$m (the ballistic path length of electrons in graphene). Well-known theoretical methods of quantum physics, crystallography and quantum theory of transport phenomena in two-dimensional electron gas were used. Results. Explicit expressions for the quanta of the Nernst coefficients and thermomagnetic EMF have been obtained, which allows us to take a fresh look at well-known galvanothermomagnetic phenomena and use the results obtained in the creation of nanoscale technical devices whose operation is based on these phenomena. Conclusions. It is shown that combined size and magnetic quantization of electronic states localized in narrow graphene nanoribbons leads to the emergence of the quantum Nernst effect and the appearance of quanta of the linear value of the Nernst coefficient, the strength of the transverse Nernst current, and the coefficient of the longitudinal absolute thermomagnetic EMF.