Theoretical study on phonons in nanowire superlattices

从理论上研究了由两层柱状层交替堆积而成的纳米线超晶格中的振动模。我们以方位对称扭转模为研究对象，对声子色散关系进行了解析计算。我们还推导出了纳米线超晶格中产生的频隙的简单表达式。此外，我们还计算了有限周期数的纳米线超晶格中声子的透过率。基于我们的计算结果，考察了超晶格纵向约束和径向约束的影响。其次，我们研究了由缺陷层夹在两个周期NWSL之间实现的双势垒结构中的声子传输。重点研究了其色散关系可以解析得到的扭转模并计算了其透过率。我们可以看到由NWSL的周期性决定的频隙中的共振峰。该峰源于缺陷层振动模局域的共振。我们还计算了这种局域模的本征频率。特别是，我们研究了本征频率如何依赖于缺陷层的宽度。声子的径向限制产生一个临界频率，该频率由NWSL的半径决定。当声子频率低于此临界频率时，缺陷层中定义的波数变为虚数。我们的结果表明，只有在临界频率以上才能产生局域模。

We study theoretically vibrational modes in a nanowire superlattice consisting of an alternate stacking of two cylindrical layers. We focus on azimuthally symmetric torsional modes and calculate the phonon dispersion relations analytically. We also derive simple expressions for the frequency gaps generated in the nanowire superlattice. Moreover, we calculate the transmittance of phonons propagating through a nanowire superlattice with the finite number of periods. Based on our calculated results, effects of the superlattice longitudinal confinement and the radial confinement are examined.Next, we studied the phonon transmission in a double-barrier structure realized by a defect layer sandwiched between two periodic NWSLs. We focused on the torsional modes whose dispersion relations can be obtained analytically and calculated the transmittance. We can see the resonant peak in the frequency gap determined by the periodicity of the NWSL. This peak originates from the resonance with the vibrational mode localized at the defect layer. We also calculated the eigenfrequency of this localized mode. In particular, we examined how the eigenfrequency depends on the width of the defect layer. The radial confinement of the phonons generates a critical frequency, which is determined by the radius of the NWSL. When the frequency of phonons is lower than this critical frequency, the wave number defined in the defect layer becomes an imaginary number. Our results show that the localized modes can be generated only above the critical frequency.