Structural stability of electrical current in graphene-hexagonal boron nitride heterostructures: a quantum chaos approach

The graphene-hexagonal boron nitride (G-hBN) plays a role of quantum dynamical systems under the influence of external fields. Quantum chaos theory concerning level repulsion can provide a clear picture of the influence of the structural factors such as impurity, number of atoms, and distance between the layers and environmental factors such as the external electric fields on the current-voltage variation. The association schemes theory in the perspective of the cycle graph is introduced to establish a relationship between the atoms in graphene and the hBN lattice. By using Bose–Mesner algebra, we have obtained an analytical method to study the conductivity in the G-hBN. We have recognized the insulator-metal transition in G-hBN by synchronously changing the Brody distribution from Poisson to Wigner distribution. We have considered the lattice with NT(G/hBN)=50×100\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$N_T(G/hBN)=50 \times 100$$\end{document} atoms to study the impact of the impurity types on conductivity. Increasing the voltage in the G-hBN results in a negative differential resistance in the current-voltage diagram. We have observed that choosing the voltage from the NDR region results in the appearance of Wigner distribution in the level of energy spectrums. The Wigner distribution is essentially a measure for detecting the presence of quantum chaos. The study reports the threshold value of the transverse electric fields, and sufficiently (silicon/carbon) doping for generating the electrical current in the μA\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mu \; A$$\end{document} range. The obtained results indicate that carbon atoms, by low concentration, are acted better than silicon in this transition.