AI 中文总结
该研究针对转角双层石墨烯约瑟夫森结中临界电流与电导反向变化的异常现象，提出量子度量诱导的约瑟夫森电流机制，通过模型验证其与实验结果高度吻合，为该异常提供了理论解释。
AI 中文摘要
在成熟的约瑟夫森结理论中，超导临界电流\ni_\n{c}\n随正常态电导\ng\n的增大而增大。然而，在一项基于转角双层石墨烯（TBG）的约瑟夫森结最新实验中，却意外观测到临界电流增大的同时伴随正常态电导的减小，我们将该现象称为临界电流异常。本研究指出，在基于TBG的约瑟夫森结中，由于能带的平坦性抑制了常规约瑟夫森电流，而量子度量诱导的约瑟夫森电流（QMJC）得以显现，因此会出现临界电流异常。当量子度量长度可与结长相比拟或更长时，QMJC便会出现。我们证明\ng\n和\ni_\n{c}\n均包含常规贡献与量子度量贡献，且存在参数范围使得\ni_\n{c}\n在\ng\n减小时仍能增大。我们首先通过修正的简单Lieb晶格模型，从解析和数值两方面验证了临界电流异常；再采用转角双层石墨烯的真实六带模型，证明其与实验结果高度吻合。因此，我们认为实验中观测到的临界电流异常，为成熟约瑟夫森结理论中未考虑的QMJC提供了有力证据。
英文摘要
In well-established theories of Josephson junctions, the superconducting critical current \( I_\mathrm{c} \) increases as the normal state conductance \( \mathcal{G} \) increases. However, in a recent experiment in twisted bilayer graphene (TBG) based Josephson junctions, unexpectedly, it was observed that the increase of the critical current is accompanied by a decrease of the normal state conductance. We call this phenomenon the critical current anomaly. In this work, we point out that in the TBG-based Josephson junction, due to the suppression of the conventional Josephson current by the flatness of the band and the quantum metric enabled Josephson current (QMJC), the critical current anomaly can occur. The QMJC appears if the quantum metric length is comparable or longer than the junction length. We show that both \( \mathcal{G} \) and \( I_\mathrm{c} \) have the conventional and the quantum metric contributions, and there are parameter regimes in which \( I_\mathrm{c} \) increases even when \( \mathcal{G} \) decreases. We first demonstrate the critical current anomaly by a simple modified Lieb-lattice model both analytically and numerically. The incredible consistency with the experimental results is demonstrated using a realistic six-band model of twisted bilayer graphene. Therefore, we suggest that the critical current anomaly observed in the experiment provide strong evidence of QMJC which were ignored in well-established theories of Josephson junctions.
