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Abstract: Using a combination of the density functional theory and tight-binding calculations, we study electronic and optical properties of asymmetric chevron-type graphene nanoribbons recently synthesized with atomic precision. We demonstrate that the low-energy optical selection rules in such infinite chiral ribbons are more reminiscent of those for zigzag rather than for armchair ribbons. It is also shown that, starting from about 25 nm long ribbons, the low-energy absorption and therefore the selection rules of infinitely long ribbons are well reproduced in the finite cluster approach. Hence, ribbons longer than 25 nm (about 28 unit cells) can be treated as infinitely long ones. [ABSTRACT FROM AUTHOR]

Abstract: We review the behavior of the entropy per particle in various two-dimensional electronic systems. The entropy per particle is an important characteristic of any many-body system that tells how the entropy of the ensemble of electrons changes if one adds one more electron. Recently, it has been demonstrated how the entropy per particle of a two-dimensional electron gas can be extracted from the recharging current dynamics in a planar capacitor geometry. These experiments pave the way to the systematic studies of entropy in various crystal systems including novel two-dimensional crystals such as gapped graphene, germanene, and silicene. Theoretically, the entropy per particle is linked to the temperature derivative of the chemical potential of the electron gas by the Maxwell relation. Using this relation, we calculate the entropy per particle in the vicinity of topological transitions in various two-dimensional electronic systems. We show that the entropy experiences quantized steps at the points of Lifshitz transitions in a two-dimensional electron gas with a parabolic energy spectrum. In contrast, in doubled-gapped Dirac materials, the entropy per particle demonstrates characteristic spikes once the chemical potential passes through the band edges. The transition from a topological to trivial insulator phase in germanene is manifested by the disappearance of a strong zero-energy resonance in the entropy per particle dependence on the chemical potential. We conclude that studies of the entropy per particle shed light on multiple otherwise hidden peculiarities of the electronic band structure of novel two-dimensional crystals. [ABSTRACT FROM AUTHOR]