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Heavy fermion materials and physics

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

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Heavy fermion materials and physics

Xie Wu, Shen Bin, Zhang Yong-Jun, Guo Chun-Yu, Xu Jia-Cheng, Lu Xin, Yuan Hui-Qiu
Acta Phys. Sin., 2019, 68(17): 177101.
doi: 10.7498/aps.68.20190801
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  • 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.

    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.

    DownLoad: Full-Size Img PowerPoint

    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(Si1–xGex)2, suggesting two separate superconducting domes[8].

    DownLoad: Full-Size Img PowerPoint

    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]

    Figure 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].

    DownLoad: Full-Size Img PowerPoint

    图 4  (a) YbRh2Si2和YbRh2(Si0.95Ge0.05)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(Si0.95Ge0.05)2[43]; (b) B-T phase diagram of YbRh2Si2 at lower temperature, suggesting a superconducting region[47].

    DownLoad: Full-Size Img PowerPoint

    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].

    DownLoad: Full-Size Img PowerPoint

    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Ce/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 Ce/T[11](b) of CeCu2Si2, both showing a fully gapped behavior at the lowest temperature.

    DownLoad: Full-Size Img PowerPoint

    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]

    Figure 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].

    DownLoad: Full-Size Img PowerPoint

    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]

    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. 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].

    DownLoad: Full-Size Img PowerPoint

    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].

    DownLoad: Full-Size Img PowerPoint

    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].

    DownLoad: Full-Size Img PowerPoint

    图 11  YbPtBi在低温重费米子态的拓扑性质[133]　(a) 电子比热Cp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 Cp/T in different fields; (b) topological Hall effect at low temperatures.

    DownLoad: Full-Size Img PowerPoint

    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].

    DownLoad: Full-Size Img PowerPoint

    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/Kγ/mJ·mol–1·K–2Hc2 (0)/T
    CeT2X2CeCu2Si20.6410000.45//a
    CeCu2Ge20.64 (10 GPa)2//a
    CePd2Si20.5 (2.7 GPa)650.7//a　 1.3//c
    CeAu2Si22.5 (22.5 GPa)
    CeNi2Ge20.3350
    CeRh2Si20.35 (0.9 GPa)23
    CeTX3CeRhSi31.05 (2.6 GPa)1107
    CeIrSi31.59 (2.6 GPa)12030
    CeNiGe30.48 (6.8 GPa)342
    CeCoGe30.7 (5.5 GPa)3222
    CeIrGe31.6 (24 GPa)8017
    CemTnIn3m+2nCeIn30.25 (2.5 GPa)3700.45
    CeCoIn52.330011.6—11.9//a　 4.95//c
    CeRhIn51.9 (1.77 GPa)5010.2//c
    CeIrIn50.47000.53
    CePt2In72.3 (3.1 GPa)34015
    Ce2CoIn80.4460
    Ce2RhIn82.0 (2.3 GPa)4005.36
    Ce2PdIn80.68550
    Ce3PdIn110.422902.8
    其他铈基CePt3Si0.753905
    CePd5Al20.57 (10.8 GPa)560.25
    镨基PrOs4Sb121.855002.3
    PrTi2Al200.21000.006
    PrV2Al200.05900.014
    镱基YbRh2Si20.002
    β-YbAlB40.081300.03
    铀基UIr0.14 (2.6 GPa)48.50.026
    UGe20.7 (1.2 GPa)1001.4
    UBe130.910009
    UPt30.55, 0.484222.8//a
    UCoGe0.66555//a
    URhGe0.251602//a
    UNi2Al31.01201.6
    UPd2Al32.01500.8
    URu2Si21.565.510
    镎基NpPd5Al25.02003.7//a
    钚基PuCoGa518.07774
    PuCoIn52.520032//a, 10//c
    PuRhGa5980-15025//ab
    PuRhIn51.735023//ab
    DownLoad: CSV
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  • Received Date:  24 May 2019
  • Accepted Date:  19 June 2019
  • Available Online:  01 September 2019
  • Published Online:  05 September 2019

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