基于格林函数方法，理论研究纯净极限下铁磁/铁磁/s波超导异质结（F1F2S）中的关联函数与局域态密度（DOS）。满足Gor’kov方程的格林函数采用数值求解且无需准经典近似。发现当两铁磁交换场的夹角α为有限值（约0.5π）且F1为半金属时只有等自旋三重态能在F1中产生。此时反常等自旋Andreev反射占主导地位，在F2中产生零能Andreev束缚态。该束缚态使得F1中的态密度表现出较尖锐的零能峰（ZEP）。解析推导产生零能Andreev束缚态的条件并验证其与数值结果完美吻合。ZEP能够深入F1更体现出等自旋三重态关联的长程本质。F1F2S系统中长程ZEP的探测或许能为超导近邻效应产生长程三重态提供一个准确证据。
Based on the Green's function method, we study theoretically the pair correlations and the local density of states (DOS) in a ferromagnet/ferromagnet/s-wave superconductor (F1F2S) heterostructure in the clean limit. The Green's functions which satisfy the Gor'kov equations are calculated numerically without taking the quasiclassical approximation. We find that, when the angle α between the exchange fields in F1 and F2 is finite (α≈0.5π) and further F1 is a half-metal, only the equal-spin triplet correlation can be induced within the F1 layer. In this circumstance, the Andreev reflection is governed by the anomalous equal-spin-band Andreev reflection which can lead to a zero-energy Andreev bound state in the F2 layer. In the presence of the zero-energy Andreev bound state, the induced DOS in the F1 layer exhibits a rather sharp zero-energy peak (ZEP). We derive the condition for the occurrence of the zero-energy Andreev bound state analytically and verify that it can predict the numerical results excellently. In particular, we find that the ZEP structure of DOS can penetrate deep into the F1 layer reflecting the long-range nature of the equal-spin triplet correlation. Experimental detection of the long-range ZEP in our F1F2S system (by using STM, for instance) may provide unambiguous evidence for the presence of the long-range triplet pair correlation induced by the superconducting proximity effect.
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