Quanta of hall and magnetoresistance coefficients in electrically conductive nanoribbons

Background. The quantum nature of the dependence of the Hall resistance on the magnetic field induction in a two-dimensional electron gas is a well-known thing. It is caused by the spatial quantization in a magnetic field, causing their circular motion along orbits of only a certain radius. An equally important circumstance when observing galvanomagnetic effects in electrically conductive narrov (less 100 nm) nanoribbons is the effect of dimensional quantization. The purpose of this work is to study the influence of this effect on the occurrence of the quanta of Hall and magnetoresistance coefficients. Materials and methods. The objects of the study are metallic graphene nanoribbons with “zigzag” type edges and a width not exceeding 100 nm of a length less than the length of the ballistic transport of free charge carriers. The work uses well-known methods of quantum physics, solid state physics, crystal physics and quantum theory of transfer phenomena in a two-dimensional electron gas. Results. Antisymmetric and symmetric parts of the resistivity tensor of a 2D-conductor in a transverse magnetic field are investigated. Explicit expressions are obtained not only for the quantum of specific Hall resistance, but also for the quantum of the Hall coefficient, and for the quanta of relative longitudinal and transvers magnetoresistance, and for the quantum of absolute magnetoresistance. The results of the work can be used in calculation and design of nanoscale galvanomagnetic sensors and magnetoresistors.