Heavy fermion materials and physics

Xie Wu; Shen Bin; Zhang Yong-Jun; Guo Chun-Yu; Xu Jia-Cheng; Lu Xin; Yuan Hui-Qiu

doi:10.7498/aps.68.20190801

Abstract

As typical examples of strongly correlated electron systems, heavy fermion materials exhibit diverse quantum ground states such as antiferromagnetic order, ferromagnetic order, non-Fermi-liquid phases, unconventional superconductivity, quantum spin liquids, orbital order and topological order. In contrast to other strongly correlated electron systems, heavy fermion systems have relatively small characteristic energy scales, which allows different quantum states to be tuned continuously by using external parameters such as pressure, magnetic field and chemical doping. Heavy fermion materials thus serve as ideal systems for studying quantum phase transitions, superconductivity and their interplay. In this review, we briefly introduce the history of the field of heavy fermions and the current status both in China and in other countries. The properties of several representative heavy fermion systems are summarized, and some frontier scientific issues in this field are discussed, in particular, concerning heavy fermion superconductors, quantum phase transitions and exotic topological states in strongly correlated electron systems.

Keywords:

heavy fermion /
unconventional superconductivity /
strongly correlated topological states /
quantum phase transition /
quantum tuning

Authors and contacts

1.
Center for Correlated Matter, Zhejiang University, Hangzhou 310058, China
2.
Department of Physics, Zhejiang University, Hangzhou 310027, China

Corresponding author: Yuan Hui-Qiu, hqyuan@zju.edu.cn

Funds: Project supported by the National Key R&D Program of China (Grant Nos. 2017YFA0303100, 2016YFA0300202), the National Natural Science Foundation of China (Grant Nos. U1632275, 11674279), the Young Scientists Fund of the Natural Science Foundation of Zhejiang Province, China (Grant No. LR18A04001), and the Science Challenge Project of China (Grant No. TZ2016004)

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图 1 重费米子材料大多是含有镧系或锕系元素的金属间化合物

Figure 1. Intermetallic compounds with lanthanides or actinides form the majority of heavy fermion materials.

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图 2 (a) CeCu₂Si₂结构示意图; (b), (c)超导电性在电阻和比热上的体现^[3]; (d) 压力诱导的双超导相^[8]

Figure 2. (a) A schematic illustration of the crystal structure of CeCu₂Si₂; (b) and (c) evidences for superconductivity in CeCu₂Si₂ from resistivity and heat capacity, respectively^[3]; (d) temperature-pressure phase diagram of CeCu₂Si₂ and CeCu₂(Si_1–_xGe_x)₂, suggesting two separate superconducting domes^[8].

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图 3 (a) Ce_nM_mIn₃_n₊₂_m(M = Co, Rh, Ir; n, m为整数)体系的晶体结构 (以M = Rh为例); (b) CeIn₃和CeRhIn₅的压力-温度相图示意图^[24]

Figure 3. (a) Schematic illustrations of crystalline structures in Ce_nM_mIn₃_n₊₂_m(M = Co, Rh, Ir; n, m are integers) (M = Rh for example); (b) a schematic pressure-temperature phase diagram of CeIn₃ and CeRhIn₅^[24].

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图 4 (a) YbRh₂Si₂和YbRh₂(Si_0.95Ge_0.05)₂的B-T相图^[43]; (b) 极低温下的YbRh₂Si₂的B-T相图^[47]

Figure 4. (a) Magnetic field (B)-temperature (T) phase diagram of YbRh₂Si₂ and YbRh₂(Si_0.95Ge_0.05)₂^[43]; (b) B-T phase diagram of YbRh₂Si₂ at lower temperature, suggesting a superconducting region^[47].

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图 5 (a) UBe₁₃结构示意图; (b) UPt₃结构示意图; (c) Th掺杂的UBe₁₃相图^[53]; (d) UPt₃的超导相图^[58]

Figure 5. (a), (b) Schematic illustrations of the crystalline structure of UBe₁₃ and UPt₃, respectively; (c) superconducting phase diagram of UBe₁₃ as a function of Th-doping^[53]; (d) magnetic field–temperature superconducting phase diagram of UPt₃^[58].

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图 6 重费米子超导体CeCu₂Si₂的(a)磁场穿透深度Δλ^[10]和(b)低温比热系数C_e/T^[11], 两者在低温都呈指数衰减

Figure 6. Temperature dependence of the magnetic penetration depth Δλ^[10] (a) and specific heat C_e/T^[11](b) of CeCu₂Si₂, both showing a fully gapped behavior at the lowest temperature.

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图 7 重费米子超导体超导相和量子相变　(a) CePd₂Si_2, 超导出现在反铁磁量子临界点附近^[19]; (b) UCoGe, 超导出现在铁磁量子相变附近^[87]; (c) PrTi₂Al_20, 超导与多极矩序^[89]; (d) β-YbAlB_4, 超导远离反铁磁量子临界点^[90]

Figure 7. Heavy fermion superconductors and quantum phase diagrams: (a) CePd₂Si_2, superconductivity (SC) near an antiferromagnetic quantum critical point(QCP)^[19]; (b) UCoGe, SC near a ferromagnetic QCP^[87]; (c) PrTi₂Al_20, SC coexists with multipolar order and gets enhanced near its QCP^[89]; (d) β-YbAlB₄, SC far away from an antiferromagnetic QCP^[90].

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图 8 巡游量子临界点(a)和局域量子临界点(b)的理论相图　图中的横坐标是非热力的调控参量δ, 纵坐标表示温度T, 调控参量δ可以调节RKKY作用和Kondo作用的相对强度; 图(a)显示量子临界点伴随近藤效应的塌陷, 导致费米面在此发生跳变; 而在图(b)中, 近藤效应发生在反铁磁态内部, 费米面在量子临界点连续变化; T_N代表反铁磁转变温度, T_FL表示费米液体的温度上限, $ E_{\log }^* $标记小费米面到大费米面的转变, T₀代表近藤晶格形成的过渡区间^[99]

Figure 8. Schematic phase diagrams for itinerant quantum critical point (QCP) (a) and local QCP (b), respectively, proposed in one theoretical model. The x-axis denotes nonthermal tuning parameters δ, y-axis is the temperature T. T_N is the antiferromagnetic ordering temperature, $ E_{\log }^* $ denotes the volume change of Fermi surface and T₀ is the temperature regime where kondo lattice forms^[99].

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图 9 CeRhIn₅在(a)压力^[100]和(b) 磁场调制下的相图^[35]; (c) 可能的零温压力-磁场相图^[35]

Figure 9. Experimental phase diagram of CeRhIn₅ tuned by pressure^[100] (a) and magnetic field^[35] (b); (c) the proposed zero-temperature pressure-field global phase diagram^[35].

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图 10 (a) 拓扑近藤绝缘体SmB₆的电阻随温度变化测量结果^[116], 在低温, 电阻的上升趋势逐渐饱和, 形成一个平台; (b) 能带计算表明, SmB₆的能带结构中存在能带反转, 从而导致了表面狄拉克锥的出现^[128]

Figure 10. (a) Temperature dependence of resistivity for a possible topological Kondo insulator SmB₆, where a clear plateau is observed at low temperature^[116]; (b) band inversion and surface Dirac cone of SmB₆, from band-structure calculation^[128].

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图 11 YbPtBi在低温重费米子态的拓扑性质^[133]　(a) 电子比热C_p正比于温度T的三次方; (b) 拓扑霍尔效应

Figure 11. Topological properties of the low temperature heavy fermion state in YbPtBi^[133]: (a) T³-behavior of the low temperature specific heat C_p/T in different fields; (b) topological Hall effect at low temperatures.

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图 12 (a) URu₂Si₂材料在压力下的相图^[146], 隐藏序相逐渐被抑制, 转变为反铁磁序, 同时超导相消失; (b) CePdAl材料的磁场-温度相图^[150], 在某一磁场区间内, 比热测量结果表明其熵出现极大增加; (c) CeCoIn₅中子散射结果表明其超导上临界磁场附近存在一个特殊的Q相^[151]

Figure 12. (a) Pressure-temperature phase diagram of URu₂Si₂^[146]; (b) magnetic field- temperature phase diagram of CePdAl^[150]; (c) Q-phase of CeCoIn₅, by neutron scattering measurements^[151].

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表 1 重费米子超导材料(超导转变温度T_c, 比热系数γ, 上临界场H_c2(0))

Table 1. A summary of heavy fermion superconductors (T_c is superconducting transition temperature, γ is specific heat coefficient, H_c2(0) is the upper critical field).

类型	化合物	T_c/K	γ/mJ·mol^–1·K^–2	H_c2 (0)/T
CeT₂X₂	CeCu₂Si₂	0.64	1000	0.45//a
	CeCu₂Ge₂	0.64 (10 GPa)		2//a
	CePd₂Si₂	0.5 (2.7 GPa)	65	0.7//a　 1.3//c
	CeAu₂Si₂	2.5 (22.5 GPa)
	CeNi₂Ge₂	0.3	350
	CeRh₂Si₂	0.35 (0.9 GPa)	23
CeTX₃	CeRhSi₃	1.05 (2.6 GPa)	110	7
	CeIrSi₃	1.59 (2.6 GPa)	120	30
	CeNiGe₃	0.48 (6.8 GPa)	34	2
	CeCoGe₃	0.7 (5.5 GPa)	32	22
	CeIrGe₃	1.6 (24 GPa)	80	17
Ce_mT_nIn₃_m₊₂_n	CeIn₃	0.25 (2.5 GPa)	370	0.45
	CeCoIn₅	2.3	300	11.6—11.9//a　 4.95//c
	CeRhIn₅	1.9 (1.77 GPa)	50	10.2//c
	CeIrIn₅	0.4	700	0.53
	CePt₂In₇	2.3 (3.1 GPa)	340	15
	Ce₂CoIn₈	0.4	460
	Ce₂RhIn₈	2.0 (2.3 GPa)	400	5.36
	Ce₂PdIn₈	0.68	550
	Ce₃PdIn₁₁	0.42	290	2.8
其他铈基	CePt₃Si	0.75	390	5
其他铈基	CePd₅Al₂	0.57 (10.8 GPa)	56	0.25
镨基	PrOs₄Sb₁₂	1.85	500	2.3
	PrTi₂Al₂₀	0.2	100	0.006
	PrV₂Al₂₀	0.05	90	0.014
镱基	YbRh₂Si₂	0.002
镱基	β-YbAlB₄	0.08	130	0.03
铀基	UIr	0.14 (2.6 GPa)	48.5	0.026
	UGe₂	0.7 (1.2 GPa)	100	1.4
	UBe₁₃	0.9	1000	9
	UPt₃	0.55, 0.48	422	2.8//a
	UCoGe	0.66	55	5//a
	URhGe	0.25	160	2//a
	UNi₂Al₃	1.0	120	1.6
	UPd₂Al₃	2.0	150	0.8
	URu₂Si₂	1.5	65.5	10
镎基	NpPd₅Al₂	5.0	200	3.7//a
钚基	PuCoGa₅	18.0	77	74
	PuCoIn₅	2.5	200	32//a, 10//c
	PuRhGa₅	9	80-150	25//ab
	PuRhIn₅	1.7	350	23//ab

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