Relativistic electric potential near a resting straight carbon nanotube of a finite-length with stationary current

Abstract

Based on the Lienard – Wiechert potentials for a uniformly and rectilinearly moving electron, a relativistic electric field is studied near a densely filled with potassium atoms single-walled carbon nanotube (K@CNT) with a stationary electric current inside it. The relativistic electric field in the laboratory coordinate system arises (due to the Lorentz transformations) only for a nanotube of a finite length. This field is a result of summation of the Coulomb fields of stationary positively charged ionic cores of potassium and an equal number of ballistically moving valence electrons of potassium that create a current. It is shown that the magnitude of the negative relativistic electric potential of K@CNT in the direction perpendicular to the nanotube does not depend on the direction of the current density. The relationship is obtained between the K@CNT radius and the number of open channels of ballistic electron transfer over potassium atoms. The Landauer formula is used, which relates the number of open quasi-one-dimensional channels and the direct current electrical conduction. For the first time, analytical formulas are obtained for the dependence of the relativistic potential near K@CNT on the electric voltage between the ends of the nanotube and on its radius in the limit of zero absolute temperature. The case is considered when the distance from the point of registration of the relativistic potential above the center of the nanotube is much less than its length. For nanotube with diameter of 2 nm and length of 100 µm, under an external electric field strength of 5 mV/µm, the magnitude of the potential of the relativistic electric field is of about 2 µV. Modern measurement techniques make it possible to register the predicted relativistic potential.