Abstract
To guide the potential applications of topological insulator, we provide a theoretical investigation for a finite temperature and an arbitrary length scale Josephson junction in the Furusaki–Tsukada formula. We have shown theoretically that a large degree of control over the generated critical supercurrent can be obtained by changing directions of the magnetizations in ferromagnet. The special importance for experimental measurements is the asymmetric character, oscillatory feature arising in the Fermi energy window, and energy shift phenomenon unveiled by a top gate voltage, which are independent of magnetization amplitude.
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