The quantum state of graphene

A stationary solution of quantum mechanical wave equation is the superposition of eigenfunctions. Each of them corresponds to a vector in the Hilbert space. In a graphene sample one can choose expansion coefficients to get the series convergent solely within the certain circle in the two-dimensional space. Outside this circle the analytic continuation is required in the form of a different series. The exact wave function is referred to as anomalous. It is not a superposition of conventional eigenfunctions and gets ouside the Hilbert space. Anomalous electron and antielectron are possible. The antielectron is not a vacancy in the conventional valence band. The anomalous electron-antielectron pair is created from the anomalous vacuum like the electron-positron pair is created from the electron-positron vacuum. Formation of the anomalous vacuum is not a single electron effect but the collective quantum phenomenon. In the film of graphene the anomalous states are located at the film edge and are expected to be of high conductivity.

Source: arXiv:2607.13057v1 - http://arxiv.org/abs/2607.13057v1 PDF: https://arxiv.org/pdf/2607.13057v1 Original Link: http://arxiv.org/abs/2607.13057v1