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Abstract

Heavy fermion superconductors belong to a special class of strongly correlated systems and unconventional superconductors. The emergence of superconductivity in these materials is closely associated with the presence of quantum critical fluctuations. Heavy fermion superconductors of different structures often exhibit distinct competing orders and superconducting phase diagrams, implying sensitive dependence of their electronic structures and pairing mechanism on the crystal symmetry. Here we give a brief introduction on recent theoretical and experimental progress in several different material families. We develop a new phenomenological framework of superconductivity combining the Eliashberg theory, a phenomenological form of quantum critical fluctuations, and strongly correlated band structure calculations for real materials. Our theory provides a unified way for systematic understanding of various heavy fermion superconductors.

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Authors and contacts

Corresponding author:Yang Yi-Feng,yifeng@iphy.ac.cn

Funds:Project supported by the National Basic Research Program of China (Grant No. 2017YFA0303103), the National Natural Science Foundation of China (Grant Nos. 11774401, 11974397), the Strategic Priority Research Program of Chinese Academy of Sciences, China (Grant No. XDB33010100), and the China Postdoctoral Science Foundation (Grant No. 2020M670422)

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Cited By

DownLoad: Full-Size Img PowerPoint

类别	材料	晶系(空间群)	$ T_{\rm{c}} $/K	$ \gamma $/mJ·mol^–1·K²	节点	特殊性质
Ce基	CeCu₂Si₂	四方($ I4/mmm $)	0.7	1000	无	超导与SDW相分离; 加压诱导第二个超导
	CeCu₂Ge₂	四方($ I4/mmm $)	0.64 (10.1 GPa)	200	—	反铁磁竞争序; 加压诱导第二个超导
	CePd₂Si₂	四方($ I4/mmm $)	0.43 (3 GPa)	65	—	反铁磁竞争序
	CeRh₂Si₂	四方($ I4/mmm $)	0.42 (1.06 GPa)	23	—	反铁磁竞争序
	CeAg₂Si₂^[61]	四方($ I4/mmm $)	1.25 (16 GPa)	—	—	反铁磁竞争序
	CeAu₂Si₂	四方($ I4/mmm $)	2.5 (22.5 GPa)	—	—	反铁磁竞争序
	CeNi₂Ge₂	四方($ I4/mmm $)	0.3	350	—	非费米液体正常态
	CeIn₃	立方($ Pm3 m $)	0.23 (2.45 GPa)	140	线	反铁磁竞争序
	CeIrIn₅	四方($ P4/mmm $)	0.4	750	线	非费米液体正常态
	CeCoIn₅	四方($ P4/mmm $)	2.3	250	线	自旋单态配对; 强磁场诱导Q相
	CeRhIn₅	四方($ P4/mmm $)	2.4 (2.3 GPa)	430	—	压力和磁场诱导费米面突变; 强磁场诱导向列序
	CePt₂In₇	四方($ I4/mmm $)	2.3 (3.1 GPa)	340	—	反铁磁竞争序
	Ce₂RhIn₈	四方($ P4/mmm $)	2.0 (2.3 GPa)	400	—	反铁磁竞争序
	Ce₂PdIn₈	四方($ P4/mmm $)	0.68	550	线	非费米液体正常态
	Ce₂CoIn₈	四方($ P4/mmm $)	0.4	500	—	非费米液体正常态
	Ce₃PdIn₁₁	四方($ P4/mmm $)	0.42	290	—	两个反铁磁序
	CePt₃Si	四方($ P4 mm $)	0.75	390	线	反铁磁竞争序; 破缺中心反演; 混合宇称配对?
	CeIrSi₃	四方($ I4 mm $)	1.65 (2.5 GPa)	120	—	反铁磁竞争序; 破缺中心反演; 混合宇称配对?
	CeRhSi₃	四方($ I4 mm $)	1.0 (2.6 GPa)	120	—	反铁磁竞争序; 破缺中心反演; 混合宇称配对?
	CeCoGe₃	四方($ I4 mm $)	0.69 (6.5 GPa)	32	—	反铁磁竞争序; 破缺中心反演; 混合宇称配对?
	CeRhGe₃^[62]	四方($ I4 mm $)	1.3 (21.5 GPa)	—	—	反铁磁竞争序; 破缺中心反演; 混合宇称配对?
	CeIrGe₃	四方($ I4 mm $)	1.6 (24 GPa)	80	—	反铁磁竞争序; 破缺中心反演; 混合宇称配对?
	CeNiGe₃	正交($ Cmmm $)	0.43 (6.8 GPa)	45	—	反铁磁竞争序; 加压诱导第二个超导
	Ce₂Rh₃Ge₅	正交($ Ibam $)	0.26 (4.0 GPa)	90	—	反铁磁竞争序
	CePd₅Al₂	四方($ I4/mmm $)	0.57 (10.8 GPa)	56	—	反铁磁竞争序
Yb基	YbRh₂Si₂	四方($ I4/mmm $)	0.002	—	—	磁场诱导非常规量子临界点
Yb基	β-YbAlB₄	正交($ Cmmm $)	0.08	150	—	$ T/B $标度行为; 磁场诱导拓扑金属正常态?
U基	UGe₂	正交($ Cmmm $)	0.8 (1.2 GPa)	34	线	铁磁竞争序; 等自旋三重态配对; 超导态破缺时间反演对称性
	UTe₂^[63,64]	正交 ($ Immm $)	1.6	110	点	铁磁涨落; 自旋三重态配对; 磁场诱导多个超导相
	URhGe	正交 ($ Pnma $)	0.25	163	—	铁磁竞争序; 等自旋三重态配对; 磁场诱导两个超导相
	UCoGe	正交 ($ Pnma $)	0.8	57	点? 线?	等自旋三重态配对; 铁磁竞争序; 磁场诱导两个超导相
	UIr	单斜 ($ P2_1 $)	0.15 (2.6 GPa)	49	—	多个铁磁相; 破缺中心反演; 混合宇称配对?
	U₂PtC₂	四方($ I4/mmm $)	1.47	150	—	无磁有序; 自旋三重态配对; 铁磁涨落
	UPd₂Al₃	六方($ P6/mmm $)	2.0	200	线	反铁磁竞争序; 自旋单态配对; 磁场调制FFLO?
	UNi₂Al₃	六方($ P6/mmm $)	1.1	120	—	反铁磁竞争序; 自旋三重态配对; 超导与反铁磁共存
	UBe₁₃	立方($ Fm\bar{3}c $)	0.95	1000	无	非费米液体正常态; 自旋三重态配对; Th掺杂诱导多个超导相
	UPt₃	六方($ P6_3/mmc $)	0.530, 0.480	440	线+点	自旋三重态配对; 多个超导相; 低温超导破缺时间反演对称性
	U₆Fe	四方($ I4/mcm $)	3.8	157	—	电荷密度波竞争序; 磁场调制FFLO?
	URu₂Si₂	四方($ I4/mmm $)	1.53	70	线	隐藏序正常态; 自旋单态配对; 破缺时间反演对称性
Pr基	PrOs₄Sb₁₂	立方($ Im\bar3 $)	1.82, 1.74	500	点? 无?	磁场诱导反铁电四极矩序; 两个超导相; 低温超导破缺时间反演对称性
	PrIr₂Zn₂₀	立方($ Fd\bar3 m $)	0.05	—	—	反铁电四极矩竞争序
	PrRh₂Zn₂₀	立方($ Fd\bar3 m $)	0.06	—	—	反铁电四极矩竞争序
	PrV₂Al₂₀	立方($ Fd\bar3 m $)	0.05	900	—	反铁电四极矩竞争序
	PrTi₂Al₂₀	立方($ Fd\bar3 m $)	0.2	100	—	铁电四极矩竞争序
Pu基	PuCoGa₅	四方($ P4/mmm $)	18.5	77	线	混合价态; 价态涨落机制? 自旋涨落机制?
	PuCoIn₅	四方($ P4/mmm $)	2.5	200	线	混合价态; 自旋涨落机制
	PuRhGa₅	四方($ P4/mmm $)	8.7	70	线	混合价态; 自旋涨落机制
	PuRhIn₅	四方($ P4/mmm $)	1.6	350	线	混合价态; 价态涨落机制? 自旋涨落机制?
Np基	NpPd₅Al₂	四方($ I4/mmm $)	4.9	200	点	非费米液体正常态
*表格中$ T_{\rm{c}}$后有括号表明为压力下超导, “—”表示尚无相关实验, “?”表示还不确定或存在争议. 表中主要数据及特殊性质可参考文献[65-68].

DownLoad: CSV

对称性变换	自旋单态	自旋三重态
费米子交换$ P $	$ P\psi({{k}})=\psi(-{{k}})=\psi({{k}}) $	$ P{{d}}({{k}})={{d}}(-{{k}})=-{{d}}({{k}}) $
空间旋转$ g $	$ g\psi({{k}})=\psi(D(g){{k}}) $	$ g{{d}}({{k}})={{d}}(D(g){{k}}) $
自旋旋转$ g_s $	$ g_s\psi({{k}})=\psi({{k}}) $	$ g_s{{d}}({{k}})=\bar D(g_s){{d}}({{k}}) $¹
时间反演$ \theta $	$ \theta\psi({{k}})=\psi^*(-{{k}}) $	$ \theta{{d}}({{k}})=-{{d}}^*(-{{k}}) $
空间反演$ I $	$ I\psi({{k}})=\psi(-{{k}}) $	$ I{{d}}({{k}})={{d}}(-{{k}}) $
$ U(1) $规范$\varPhi$	$\varPhi\psi({{k} })={\rm e}^{{\rm i}\phi}\psi({{k} })$	$\varPhi{{d} }({{k} })={\rm e}^{{\rm i}\phi}{{d} }({{k} })$
^*其中$D(g)$为晶体点群G的表示矩阵, $\bar D(g_s)$为SU(2)群的表示矩阵. ¹存在自旋-轨道耦合时, 自旋的旋转与${{k}}$ 的旋转不再独立, 即$g_s{{d}}({{k}})=\bar D(g_s){{d}}(\bar D(g_s){{k}})$.

DownLoad: CSV

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