Local density of states in clean two-dimensional superconductor–normal metal–superconductor heterostructures

Motivated by recent advances in the fabrication of Josephson junctions in which the weak link is made of a low-dimensional nonsuperconducting material, we present here a systematic theoretical study of the local density of states (LDOS) in a clean two-dimensional normal metal (N) coupled to two s-wave superconductors (S). To be precise, we employ the quasiclassical theory of superconductivity in the clean limit, based on Eilenberger’s equations, to investigate the phase-dependent LDOS as a function of factors such as the length or the width of the junction, a finite reflectivity, and a weak magnetic field. We show how the spectrum of Andreev bound states that appear inside the gap shape the phase-dependent LDOS in short and long junctions. We discuss the circumstances when a gap appears in the LDOS and when the continuum displays a significant phase dependence. The presence of a magnetic flux leads to a complex interference behavior, which is also reflected in the supercurrent-phase relation. Our results agree qualitatively with recent experiments on graphene SNS junctions. Finally, we show how the LDOS is connected to the supercurrent that can flow in these superconducting heterostructures and present an analytical relation between these two basic quantities.

受近期约瑟夫森结（Josephson junctions）制备技术进展的启发——这类结的弱连接部分采用低维非超导材料制备——我们对洁净二维正常金属（N）与两个s波超导体（S）耦合体系中的局域态密度（local density of states, LDOS）开展了系统性理论研究。具体而言，我们基于艾林伯格方程（Eilenberger’s equations），采用洁净极限下的超导准经典理论，探究了结的长度、宽度、有限反射率以及弱磁场等因素对相位依赖型局域态密度的影响。我们阐明了间隙内出现的安德列夫束缚态（Andreev bound states）能谱如何调控长短结中的相位依赖型局域态分布。我们讨论了局域态密度出现能隙以及连续谱呈现显著相位依赖性的具体情形。磁通量的存在会引发复杂的干涉行为，这一特征同样体现在超流-相位关系之中。我们的研究结果与近期石墨烯SNS结的相关实验定性吻合。最后，我们揭示了局域态密度与这类超导异质结中可传输超流之间的关联，并给出了这两个基本物理量之间的解析关系式。