The Problem of Scale in Electric Metrology of Nanostructures in the Context of the New SI Redefinition of the Base Electric Unit

Abstract

The classical, electrodynamic denition of the ampere is incoherent with quantum electrodynamics. The problem, although insignicant at the macroscopic scale, manifests clearly at the nanostructure level, where the consistently quantum approach is necessary. In this paper, we consider the Casimir eect to quantify inconsistencies that could have resulted if electric metrology of microstructures and nanostructures (including graphene) had been based on classical electrodynamics and the current SI denition of the ampere. The issue is discussed in the context of the New SI program, where the base electric unit is to be redened by xing the numerical value of the elementary charge. The conclusion supports the case for a prompt redenition of the base electric unit, which will make the electric metrology in general, and the electric metrology of nanostructures in particular, coherent with the international system of units.