Quantized conductance and superconductivity of twisted graphene and other 2D crystals explained with the Eyring’s rate process theory and free volume concept

Abstract

Theoretical treatment originally intended to address proton transporting through a 2D (two dimensional) crystal like graphene and hexagonal boron nitride has been borrowed to examine conductivity and superconductivity of single layer, bilayer, trilaye, even multilayer graphene or other 2D crystals. The theory was developed based on the Eyring’s rate process theory and free volume concept under an assumption that protons behave exactly same as electrons, thus obtained equations should hold for electron conduction through a 2D crystal, too. These equations show that at high temperature regions conductivity should be scaled as σ=ν1e2h, similar to fractional/integral quantum Hall effect; while at low temperature regions conductivity should be scaled as σ=ν22eh, similar to Josephson junction effect. At high temperature regions, the parameter α, related to electron packing structure and critical to superconductivity, is canceled out and not present in derived equations, indicating that no superconductivity occurs in high temperature regions. While in low temperature regions, superconductivity should appear at temperature about 5 K or even higher, depending on electron packing structures. The fractional parameter f that can vary from fully close status with f=0 or full open status with f=1 should be controlled by the twisted angles. Our equations predict that superconductivity and insulating states are closely adjacent to each other; ”on” and ”off” superconductivity can be observed periodically when twisted angles are precisely varied from one direction to another. The volume ratio of conduction electrons to the conductive area and thickness play a critical role in superconductivity, implying that varying the area and/or thickness could have similar impact as twisted angle does. Our findings shed new lights on conductivity of stacked graphene or other 2D crystals.