Magnetoelectronic states of carbon toroids

Toroidal and Coiled Carbon Nanotubes

“…In addition to the paramagnetic moments, existence of ferromagnetic moments at low temperatures in the toroidal CNTs without heteroatoms was also predicted by using a π-orbital nearest-neighbor TB Hamiltonian with the London approximation, which is attributed to the presence of pentagons and heptagons [59]. Another important phenomenon, i.e., the Aharonov-Bohm effect can be also observed in the toroidal CNTs [60][61][62][63][64]. Indeed, the magnetic properties of the toroidal CNTs are affected by many factors.…”

Effect of external fields on low-frequency optical properties of achiral carbon tori

“…The wavefunction could be conveniently expanded in real space according to all the 4 pm 2p z orbitals. Moreover, the hopping parameter could be further modified by the Peierls phase (G i j ) which is induced by the applied magnetic field [8,17]. The magnetic field is assumed to be…”

“…From the scanning force microscopy image, a CT is a thin system which has a height or width of 1.0-1.2 nm and diameter of 300-500 nm. The new zero-dimensional system has attracted many investigations, such as electronic properties [3][4][5][6][7][8][9][10], magnetic properties [11][12][13][14][15][16][17][18], optical properties [19][20][21] and transport properties [22][23][24]. In experiments, low-temperature magnetotransport measurements on CTs have been performed, manifesting negative magnetoresistance and weak electron-electron interaction.…”

“…According to calculated energy gaps [3,4], there are four types of carbon tori including the curvature effect: (I) E g ∝ 1/r , (II) E g ∼ 0 (ACTs), (III) E g ∝ 1/R (ACTs) and (IV) E g ∝ (1/r ) 2 . The electronic structures (state energy, energy gap and state degeneracy) could be further affected by electric fields [7,9,10], magnetic fields [7][8][9][10], defects [7] and structural deformations [27].…”

“…When carbon tori are threaded by a uniform magnetic field along the symmetric axis (B ), the longitudinal angular momentum changes from L to L + φ/φ 0 (φ is magnetic flux and φ 0 = hc/e). However, the perpendicular magnetic field B ⊥ leads to the coupling of different Ls [8,21]. According to theoretical studies, the effect of B ⊥ on the energy gap is weaker than that of B .…”