Design Method for a Phenalenyl-Tessellation Molecule Based Nano-Graphene Network with Coexisting Localized Zero Modes and Dirac Zero Modes

For designing quantum devices using graphene nano-structures, there is importance in finding a general rule which controls the appearance of localized zero modes (LZMs) coexisting with the Dirac zero modes (DZMs).
Recently, we have discovered a class of graphene nano-molecular structures which we call Phenalenyl-Tessellation Molecule (PTM) with vacncies[1]. When a PTM contains atomic defects, there appear two types of special non-bonding molecular orbitals at the zero-energy level. One is LZM and the other is DZM. Considering a Vacancy-centered hexagonal Armchair Nano-Graphene (VANG) as a typical example of a PTM, one LZM and one DZM appear non-trivially, and they form a singlet[2,3].
In this presentaton, we report a general rule for the appearance of the LZMs and DZMs in a class of PTM-based poly-aromatic hydro carbon. Our rule is indispensable for designing quantum information devices using zero modes in decorated defective graphene with vacancies.
[1] N. Morishita and K. Kusakabe, J. Phys. Soc. Jpn. 88, 124707 (2019).
[2] N. Morishita, G. K. Sunnardianto, S. Miyao, andK. Kusakabe, J. Phys. Soc. Jpn. 85, 084703 (2016).
[3] S. Miyao, N. Morishita, G. K. Sunnardianto, andK. Kusakabe, J. Phys. Soc. Jpn. 86, 034802 (2017).