Lattice vibration and thermodynamical properties of a single-layer graphene in the presence of vacancy defects

The phonon density of states(PDOS) and the thermodynamical properties including the heat capacity, the free energy,and the entropy of a single-layer graphene with vacancy defects have been studied theoretically. We first analytically derive the general formula of the lattice vibration frequency, and then numerically discuss the effect of the defects on the PDOS. Our results suggest that the vacancy defects will induce the sawtooth-like oscillation of the PDOS and the specific oscillation patterns depend on the concentration and the spatial distribution of the vacancies. In addition, it is verified that the vacancy defects will cause the increase of the heat capacity because of the vacancy-induced low-frequency resonant peak. Moreover, the influences of the vacancies on the free energy and the entropy are investigated.     

指向物理核心素养的分解式实验探究——以“串联电路中的电压规律”实验教学为例

初中物理所涉及的探究问题中,有些比较复杂,如果试图仅靠一个实验得出结论,则容易导致学生在探究过程中思维混乱、逻辑不清,最终牵强地得出结论.为了关注学生探究能力的发展、学科核心素养的培养,此时有必要将复杂问题有逻辑、有条理地分解成多个逐层递进的简单问题,以保证在探究逐步深入的过程中,每一步都是有着严密的逻辑和充足的证据.基于这种认识,以人教版"串联电路中的电压规律"为例,提出相应的实验教学改进建议.     

Quantum Transport through a Rigidly Connected Double Quantum-Dot Shuttle

We design a double quantum-dot （QD） shuttle （DQDS） model including two rigidly connected QDs that are softly linked to two leads via deformable organic materiaJs. Based on the full quantum mechanical approaches we explore the influences on the electron transport induced by the electrical and mechanical degrees of freedom. First of a/l the modified rate equations of the DQDS are derived theoretically and then a numerical investigation on the quantum transport through the DQDS is performed. For the classical DQDS, the time-dependent evolutions of the electron- occupation probabilities and the currents flowing through the DQDS show the periodic oscillations with their periods determined by the oscillation period of the DQDS. Both the mechanical oscillation amplitude and the interdot coupling can play crucial roles in adjusting the peak shapes of the currents and the probabilities. For the quantum DQDS, the current and electron-occupation probabilities of the DQDS evolve into a stationary state as time goes on, with no periodical oscillations observed. As a consequence, the sharp differences of the time-dependent properties between the c/assica/ and quantum DQDS systems are clearly demonstrated, which should be greatly helpful in designing new nanoelectromechanical devices. Also, this work is of great significance to understanding the kind of rigidly connected QD shuttle systems that have more than two QDs.