中文摘要：

与其他非常规超导系列相比,重费米子超导体往往具有丰富多样的竞争序,超导与各种竞争序相伴而生,电子配对与反铁磁涨落、铁磁涨落、价态涨落、电四极矩涨落等量子临界涨落密切相关,扩充了非常规超导的研究内容.重费米子材料中的f电子往往同时参与超导与各种竞争序的形成,表现出局域与巡游的二重性.重费米子二流体理论为理解重费米子超导与竞争序的关系提供了新的思路.

英文摘要：

One of the most salient features of heavy fermion superconductivity is its coexistence with various competing orders.Superconductivity often emerges near or at the border of these exotic orders and their interplay may give rise to many interesting quantum phenomena. In this paper, we give a brief review of the various heavy fermion superconductors discovered so far and show there may exist an intimate connection between their superconducting pairing and quantum critical spin/charge/orbital fluctuations. We classify these superconductors into three categories：（A） CeM2X2, CenMmIn3n＋2m, CePt3Si, CeMX3, CeNiGe3, Ce2Ni3Ge5 and CePd5Al2, in which superconductivity emerges at the border of antiferromagnetic phase; Yb Rh2Si2, in which superconductivity was very recently found inside the antiferromagnetic phase at 2 mK; UX2Al3 and UPt3, in which superconductivity occurs inside the antiferromagnetic phase; and UBe13 and U6Fe, in which the connection between magnetism and superconductivity is not yet clear. Among them, CePt3Si and CeMX3 are noncentrosymmetric, while UPt3 exhibits spin triplet pairing inside an antiferromagnetic phase.（B）UGe2, URhGe, UCoGe, UIr and U2PtC2, are spin triplet superconductors under the influence of ferromagnetic order or fluctuations.（C）URu2Si2, PrOs4Sb12, PrT2X20, Pu-115, NpPd5Al2 and β-YbAlB4, in which superconductivity may be related to other exotic quantum states or fluctuations such as hidden order, valence fluctuations and quadrupolar fluctuations.In these compounds, f-electrons may participate in both superconductivity and other competing orders and often behave simultaneously itinerant and localized. These could be described by a phenomenological two-fluid theory, in which two coexisting fluids—an itinerant heavy electron fluid（the Kondo liquid） and a spin liquid of unhybridized local f-moments—compete to give rise to the various low temperature orders as well as superconductivity. Combining the two-fluid picture and the idea of spin-fluctuation-induced supercond