Abstract

We introduce a numerical method for computing conductivity via the Kubo formula for incommensurate 2D bilayer heterostructures using a tight-binding framework. We begin by deriving the momentum space formulation and Kubo formula from the real space tight-binding model using the appropriate Bloch transformation operator. We further discuss the resulting algorithm along with its convergence rate and computational cost in terms of model parameters such as relaxation time and temperature. In particular, we show that for low frequencies, low temperature, and long relaxation times conductivity can be computed very efficiently using the momentum space algorithm for a wide class of materials. We then showcase our method by computing conductivity for twisted bilayer graphene (tBLG) for small twist angles.

Graphical abstract

中文翻译：

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二维异质结构的久保电导率的高效计算

摘要

我们引入了一种数值方法，用于通过紧密结合框架通过Kubo公式计算不相称的2D双层异质结构的电导率。我们首先使用适当的Bloch变换算子从实际空间紧密绑定模型中得出动量空间公式和久保公式。我们将根据模型参数（例如松弛时间和温度）进一步讨论所得算法及其收敛速度和计算成本。特别是，我们表明，对于低频，低温和长弛豫时间，可以使用动量空间算法针对多种材料非常有效地计算电导率。然后，我们通过计算较小扭曲角的扭曲双层石墨烯（tBLG）的电导率来展示我们的方法。

图形概要