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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.
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Keywords:
- heavy fermion /
- unconventional superconductivity /
- strongly correlated topological states /
- quantum phase transition /
- quantum tuning
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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]
Fig. 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(Si1–xGex)2, suggesting two separate superconducting domes[8].
图 3 (a) CenMmIn3n+2m (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]
Fig. 3. (a) Schematic illustrations of crystalline structures in CenMmIn3n+2m (M = Co, Rh, Ir; n, m are integers) (M = Rh for example); (b) a schematic pressure-temperature phase diagram of CeIn3 and CeRhIn5[24].
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]
Fig. 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].
图 7 重费米子超导体超导相和量子相变 (a) CePd2Si2, 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) PrTi2Al20, 超导与多极矩序[89]; (d) β-YbAlB4, 超导远离反铁磁量子临界点[90]
Fig. 7. Heavy fermion superconductors and quantum phase diagrams: (a) CePd2Si2, superconductivity (SC) near an antiferromagnetic quantum critical point(QCP)[19]; (b) UCoGe, SC near a ferromagnetic QCP[87]; (c) PrTi2Al20, SC coexists with multipolar order and gets enhanced near its QCP[89]; (d) β-YbAlB4, SC far away from an antiferromagnetic QCP[90].
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; TN代表反铁磁转变温度, TFL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]Fig. 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. TN 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].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]
Fig. 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].
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]
Fig. 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].
表 1 重费米子超导材料(超导转变温度Tc, 比热系数γ, 上临界场Hc2(0))
Table 1. A summary of heavy fermion superconductors (Tc is superconducting transition temperature, γ is specific heat coefficient, Hc2(0) is the upper critical field).
类型 化合物 Tc/K γ/mJ·mol–1·K–2 Hc2 (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 CemTnIn3m+2n 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 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 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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