二维电子散射的R-矩阵形式
R-matrix formalism for electron scattering in two dimensions
摘要：
研究了一般有限程不可分势在二维空间中的散射现象。这种情况可以出现在笛卡尔几何或圆柱对称的异质结构中。增加散射问题的维度，允许导电通道之间的散射以及从导电通道到消逝通道的散射等新过程。对于称为共振能量的能量的某些值，与一维问题相比，通过散射区域的透射发生显著变化。如果势具有吸引特性，则甚至倏逝通道也可以被看作总透射率的下降。多通道电流散射矩阵的确定使用其表示的R-矩阵。通过电流散射矩阵的极点定量地表征了共振透射峰。局部化概率密度的详细地图支持共振的物理解释。我们的形式主义适用于一个量子点在二维电子气和一个圆锥形的量子点点内嵌入一个圆柱形纳米线。
英文摘要：
We investigate the scattering phenomena in two dimensions produced by a general finite-range nonseparable potential. This situation can appear either in a Cartesian geometry or in a heterostructure with cylindrical symmetry. Increasing the dimensionality of the scattering problem new processes as the scattering between conducting channels and the scattering from conducting to evanescent channels are allowed. For certain values of the energy called resonance energy the transmission through the scattering region changes dramatically in comparison with an one-dimensional problem. If the potential has an attractive character even the evanescent channels can be seen as dips of the total transmission. The multi-channel current scattering matrix is determined using its representation in terms of the R-matrix. The resonant transmission peaks are characterized quantitatively through the poles of the current scattering matrix. Detailed maps of the localization probability density sustain the physical interpretation of the resonances. Our formalism is applied to a quantum dot in a two-dimensional electron gas and to a conical quantum dot dot embedded inside a cylindrical nanowire.
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