Theoretical study on phonons in nanowire superlattices

我们从理论上研究了由两个圆柱形层交替堆叠组成的纳米线超晶格中的振动模式。重点讨论了方向对称扭转模，并解析计算了声子色散关系。我们还推导了纳米线超晶格中产生的频率间隙的简单表达式。此外，我们还计算了声子在有限周期内通过纳米线超晶格的透射率。在计算结果的基础上，研究了超晶格纵向约束和径向约束的影响。接下来，我们研究了由缺陷层夹在两个周期NWSLs之间实现的双势垒结构中的声子传输。重点研究了可解析得到色散关系的扭转模，并计算了透射率。我们可以在由NWSL的周期性决定的频率间隙中看到共振峰。此峰源于与缺陷层局部振动模式的共振。我们还计算了这个局域模态的本征频率。特别地，我们研究了特征频率如何依赖于缺陷层的宽度。声子的径向约束产生一个临界频率，这是由NWSL的半径决定的。当声子的频率低于该临界频率时，缺陷层中定义的波数变为虚数。结果表明，只有在临界频率以上才能产生局域模态。

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.