Design of a superlattice-based resonant-tunneling-device for phonons

我们从理论上研究了声子在超晶格中的传播。我们考虑了一种对声子起双势垒作用的SL结构。这种结构是通过夹在周期性SLS之间的块状材料来实现的。对于正常通过该系统的声子，我们推导出了共振频率和相应的衰变因子的解析公式。这些公式对于用于探测或产生准单色声学声子的声子隧穿器件的设计特别有用。其次，我们研究了声子通过SL探测器界面的共振传输。我们计算了声子透过率，并检测了由于位于SL-探测器界面的振动模而产生的特殊的共振峰。峰值取决于SL的周期数N，这种共振特征在大N和小N时消失，只有在适当的N范围内，我们才能看到共振。我们推导了N-依赖共振公式，即推广的Breit-Wigner公式，并讨论了其物理意义。此外，我们还数值研究了声子在SLS中的倾斜传播。周期受激拉曼散射中声子的显著特征主要与声子的布拉格反射产生的频隙有关。对于通过受激拉曼散射的声子，由于不同偏振模的耦合，除了普通的“模内”布拉格反射外，还可能发生“模间”布拉格反射，并根据布拉格反射的类型对相应的频隙进行了分类。另一方面，众所周知，嵌入在周期SL中的不均匀会导致频隙内的局域振动模。在本工作中，我们研究了双势垒系统，并从理论上考察了不同类型频隙中产生的局域模的差异。

We theoretically studied phonons propagating through superlattices (SLs). We considered a SL structure which acts as a double barrier for phonons. This structure is realized by a bulk material sandwiched between periodic SLs. For phonons normally propagating through this system, we derived analytical formulas for the resonant frequency and the corresponding decay factor. These formulas are especially useful for the design of phonon tunneling devices to be used for the detection or generation of quasi-monochromatic acoustic phonons.Next, we studied the resonant transmission of phonons propagating through a SL-detector interface. We calculated the phonon transmittance and examined the peculiar resonance peak due to the vibrational mode localized at SL-detector interface. The peak value depends on the number of periods N of SL, and this resonant feature disappears for large N and also small N. Only for an appropriate range of N, we can see the resonance. We derived the N-depandent resonant formula, i.e., generalized Breit-Wigner formula, and discussed the physical meaning.Furthermore, we numerically studied phonons obliquely propagating through SLs. The notable features of phonons in periodic SLs are mainly related to the appearance of frequency gaps originating from Bragg reflections of phonons. For phonons obliquely propagating through SLs, "intermode" Bragg reflections due to the coupling of different polarization modes can occur besides ordinary "intramode" Bragg reflections, and corresponding frequency gaps are classified according to types of Bragg reflection. On the other hand, it is well known that an inhomogeneity embedded in a periodic SL causes localized vibrational modes inside the frequency gaps. In the present work, we studied the double barrier system and examined the difference between localized modes generated in different types of frequency gap theoretically.