Magic numbers of nanoholes in graphene: Tunable magnetism and semiconductivity

Patterned vacancy clusters (or nanoholes) can modify the electronic structure of graphene, and thereby generate entirely new functionalities. Knowledge of the relative stability of various nanoholes and associated properties is essential for the rational design and fabrication of practical devices. Extensive first-principles results reveal remarkable stability in certain ring configurations, as well as modified triangular and hexagonal vacancy configurations. The identified magic numbers of vacancies are 2, 4, 6, 28, 39, 42, 52, and 60. A large number of the nanoholes exhibit magnetic states with diverse energy band-gap values. Some large nanoholes possess nonzero net moments in all possible magnetic solutions, showing that the corresponding magnetization is robust against thermal fluctuation. Room-temperature ferromagnetism in graphene (and graphite) can be attributed to the local ferri- or ferromagnetism in large nanoholes, which can be created under irradiation and chemical treatment. Nanohole-induced, stable magnetic-semiconducting graphene is expected to be useful in graphene-based spintronics.

Figure 1

Atomic and magnetic structures for some selected (stable and all those that are discussed in the text) nanoholes. The predicted magic configurations with high degrees of stability are (a) 2A, (b) 4A, (c) 6A, (d) 28A, (e) 39A, (f) 42A, (g) 52A, and (h) 60A. Structures 2A, 4A, 6A, 12A, 19A, 48A, and 60A are nonmagnetic. Red (blue) isosurfaces denote positive (negative) spin polarization. The isosurface value is 0.015 electrons/${\AA }^3$.

Figure 2

Formation energy per vacancy as a function of the nanohole size. The size is measured as the number $n$ of vacancies that constitute the nanoholes. The line is used to guide the eyes.

Figure 3

Dissociation energies (a) $D_1$$\left(n\right)$ and (b) $D_2$$\left(n\right)$ as a function of the nanohole size. Only the configurations with large dissociation values or those discussed in the text are labeled. The magic nanoholes are highlighted in bold.

Figure 4

Diversity of net magnetic moment and band gap: (a) net moment and (b) calculated band-gap values as a function of nanohole size for selected configurations. The magic nanoholes are highlighted in bold.

Figure 5

Possible intrinsic origin of the high transition temperature in nanohole-induced magnetism exemplified by configurations 22A (upper panel) and 37A (lower panel). The energy differences relative to the nonmagnetic state and the net magnetic moments are shown. Red (blue) isosurfaces denote positive (negative) spin polarization. The isosurface value is 0.015 electrons/${\AA }^3$.