General Green’S Function Formalism for Layered Systems: Wave Function Approach
Update: 2018-02-24 10:11:09      Author: yangjuan@csrc.ac.cn

The single-particle Green’s function (GF) of mesoscopic structures plays a central role in mesoscopic quantum transport. The recursive GF technique based on the Dyson equation is a standard tool to compute this quantity numerically, but it still suffers from two limitations. First, it is limited to relatively small systems. Second, its connection to another widely used approaches – the wave function mode matching approach -- remains incomplete (see Fig. 1).

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Fig.1: Two widely-used approaches in mesoscopic quantum transport and their connection.

Recently, the research group of Prof. Wen Yang at CSRC together with Prof. Kai Chang at Institute of Semiconductors, CAS addressed both issues by developing a wave function approach to calculate the Green’s function of a general layered system. This new method enjoys two distinguishing features. First, only the interfaces between uniform regions need numerical treatment, so the time cost scales are determined by the number of interfaces [dashed boxes in Fig. 2(a)]. By contrast, the time cost of the recursive GF technique is determined by the length of the central region [dashed box in Fig. 2(b)]. Thus, it can speed up the calculation by 1-2 orders of magnitudes. Second, it establishes the reverse of the well-known Fisher-Lee relation (see Fig. 1) and hence connects the wave function mode-matching approach back to the GF approach, thus paving the way for extracting the scattering information of novel quasi-particles in the solid state by local transport measurements.

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Fig. 2: Two GF methods: (a) our wave-function approach; and (b) conventional recursive GF approach.

 

Reference:

[1]      Shu-Hui Zhang, Wen Yang, and Kai Chang, Phys. Rev. B 95, 075421 (2017).


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