Magnetism in graphene flakes with edge disorder

On electron propagation in triangular graphene quantum dots

“…This type of energy degeneracy is similarly observed within the current description of the zigzag momentum bases (134) as well as for the root and weight A 2 lattice models with real-valued hopping functions [4,5]. Possible lifting of this degeneracy by incorporating complex-valued factors in the tight-binding Hamiltonians (110) and (132), which appear for instance in presence of an external magnetic field [14,21], merits further investigation. Existence and form of a general counting algorithm for the degrees of degeneracy of the armchair and zigzag energy levels pose open problems.…”

“…Single and multiparticle propagation characteristics [16,52], behaviours in electric and magnetic fields [17,18,39] together with optical properties [6,35,50] of these graphene structures have been researched. As fundaments for further theoretical and experimental analysis, single-electron properties of single-layer circular [22,57], hexagonal [14,52,61] and triangular [2,18,21,24,53,61] quantum dots have been extensively numerically and analytically investigated. The tight-binding model [8,21,53], along with the associated Fermi level energy Dirac-Weyl approximation [54,61], serves as a common cornerstone of theoretical approach to electron propagation in the graphene honeycomb lattice.…”

Recent advances in magnetism of graphene from 0D to 2D

“…It is notable that the magnetism of GNFs, which is generally attributed to the unpaired electrons, is extremely sensitive to their shapes, sizes, boundary types and edge defects. 30 The π-magnetism of nanographene has been extensively reported in recent years. Theoretical models have predicted that nanographene with specific shapes can develop π-magnetism closely correlated with Coulomb repulsion interaction of electrons.…”

Dynamic and fluctuation properties of a graphene disk levitated by a diamagnetic force in air

“…In practice, graphene materials often have many voids and defects, which affect the magnetic permeability. Recently, Deyo and Hershfield computed the magnetization of graphene flakes with edge defects [25].…”

“…Thus, the graphene disk falls at a nearly constant velocity. The second term in equation (25) represents the Brownian motion of the graphene disk with the diffusion constant D = k B T/γ ⊥ . If the combined gravitational and magnetic forces are absent, the standard deviation of the vertical position is given by √ 2Dt for large t. In figure 7, the shaded area is sandwiched between two functions − √ 2Dt and √ 2Dt.…”