Counting the Zero Modes and Magnetic Moment by Topology of a Phenalenyl-Tessellation Molecule with Vacancies

摘要

The rule of phenalenyl unit tiling specifies a class of polyaromatic hydrocarbon molecules. These nanographene molecules, which we call phenalenyl-tessellation molecules (PTMs), show a particular electronic property owing to their topology. We derive a relationship between the number of vacancies n and the difference N-A - N-B between the numbers of atomic A-sites N-A and atomic B-sites N-B for a PTM as N-A - N-B = n - 1. In addition, because there is always one B-site zero mode, the number of A-site zero modes is given by n for a PTM. The resulting ground state with a total spin of vertical bar n - 1 vertical bar/2 becomes a non-trivial entangled state for n > 0.