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Kondo Physics, Heavy Fermion Materials and Kondo Insulators
Z. Fisk UC Irvine
Zhejiang University April 12, 2015
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Outline
•some superconductivity history•f-electron physics •heavy Fermion superconductivity•some phenomenology of the dense Kondo lattice•Kondo insulators
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where it all began
1908 Onnes in his cryogenics laboratory in Leyden wins race
to liquefy Helium (at 4.2K)
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1933 Zero resistance is not the signature effect of superconductivity:
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1950s: the Edisonian approach to discovering new superconductors
and the era of conventional superconductivity
Fermi: systematics of materials may give a clue
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CeIn3 CeMIn5 Ce2MIn8
Crystal Structures
M = Co, Rh, Ir (isovalent)
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0
1
2
3
4
?SC
SCSC
X
0.50.50.5 IrRh CoCo
AFM
T* (
K)
CeCoIn5 CeRhIn5 CeIrIn5 CeCoIn5
P. Pagliuso et al., PRB 64, 100503 (2001).
AF and Superconductivity in CeMIn5systems
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0.0 0.5 1.0 1.5 2.0 2.50
1
2
3
4
5
6
AFM
T(K
)
x% (x=Cd,Hg)
CeCo(In1-x
Hgx)
5
CeCo(In1-x
Cdx)
5
Tc
TN
SC
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dilution studies of CeCoIn5
Cross over from single ion Kondo to C/T ln(T/T*) near 2D percolation
threshold
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• Heavy Fermion Superconductor with Tc ≈ 2.3 K
(C. Petrovic et al. J. Phys.: Condensed Matter 13, L337 (2001).)
• Quasi 2D electronic structure(e.g. D. Hall et al., Phys. Rev. B 64, 212508 (2001).)
• Unconventional SC state Line nodes, most likely d(x2 - y2) symmetry(e.g. R. Movshovich et al., Phys. Rev. Lett. 86, 5152 (2001). Izawa et al., Phys. Rev. Lett. 87, 057002 (2001))
• Normal state Non-Fermi-liquid behavior )rTCm/T – logT probably due to strong AF fluctuations(e.g. V.A. Sidorov et al., cond-mat/0202251,Shishido et al., J. Phys. Soc. Jpn. 71, 162 (2002).)
Heavy Fermion Superconductor CeCoIn 5
M = Co
Theoretical expectations near 2D AF QCP,r (T / T sf
)Cm/T – log (T / T sf )
T sf: a characteristic energy of spin-fluctuations(e.g. T. Moriya and K. Ueda, Adv. Phys. 49, 555 (2000).,G. R. Stewart, Rev. Mod. Phys. 73, 797 (2001). )
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• Systematic increase of M/H with La dilution at low temperatures Possible origins:
1) Crystal field splitting 2) Kondo coupling TK
3) Intersite coupling
• Single impurity limit: x(La) > 0.95
Systematic change in low T susceptibility
• Constant high temp.TK
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6
148 K
197 K
7(2)
7(1)
1/2>-1/2>
Crystal field analyses for Ce1-xLaxCoIn5
T(K)
M/H
(B
//c)
M
/H (
B//
a,b)
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Basis of our analysis: TK << T* (intersite) << (crystal field)
1 K 50 K 200 K
Energy scale diagram of Ce1-xLaxCoIn5
4) Change in the ground state properties at around x = 0.5.
1) T*ab, T*c, T*s are essentially identical.
2) T* originates from the single- ion TK at x 1 limit.
3) The systematic increase should arise from intersite correlation.
Tcoh T* at x 0 limit.
Evolution of intersite AF fluctuationssimilar to RVB with energy scale of T* and correlation length of several a
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Entropy development in quantum critical regime
C/T α lnTTypically: C/T = (Rln2/T*)ln(T*/T) and S(T*) = Rln2T* sets the scale for heavy Fermion physicsFor heavy Fermion superconductors:
S(Tc) ~ 10-20% Rln2 ↔ Tc/T* ~ 1/20
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Source of coherence scale in dense Kondo lattice
Kondo coupling parameter (J) determines both TK and T*
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T
J
TN
TKondo
QCP
T*
Tc
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Kondo scale: TK = -1e-1/J
RKKY scale: T* = cJ2
J = -1/ln(TK ) = √(c-1T* )
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. Table I Experimental *T , TK and g for a variety of Kondo lattice compounds.
Compound T* (K) TK (K) g (mJ/mol K2) Jr c Reference
CeRhIn5 20 0.15 5.7 0.10 0.45 5,7,(H.L.)
CeCu6 35 3.5 8 0.15 0.49 8,9
U2Zn17 20 2.7 12.3 0.15 0.41 10,11,12
CeCu2Si2 75 10 4 0.15 0.47 5,13,14
CePb3 20 3 13 0.15 0.41 15,16
CeCoIn5 50 6.6 7.6 0.16 0.55 3,5,6
CePd2Si2 40 9 7.8 0.17 0.41 17,18
URu2Si2 55 12 6.5 0.17 0.45 5,19,20
CePd2Al3 40 10 9.7 0.18 0.45 21,22,23
CeRu2Si2 60 20 6.68 0.19 0.42 24,25
UBe13 55 20 8 0.19 0.43 26,27
YbRh2Si2 70 20 7.8 0.19 0.53 (Z.F.)
YbNi2B2C 50 20 11 0.21 0.47 28
UPd2Al3 60 25 9.7 0.21 0.48 23,29
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intrinsic Kondo impurities in pure CeCoIn5
low T properties consistent with
~ 10% free Kondo centers
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conclusions
• dense Kondo lattice scale set by Kondo single ion scale
• Kondo liquid state disrupted by percolative non-Kondo component
• similarity between doped dense Kondo and cuprate superconductors: Swiss cheese
• residual Kondo gas in stoichiometric systems
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Kondo Insulators Aeppli & Fisk: Comments Cond. Mat. Phys. 16, 155 (1992)
• FeSi S. Föex ,J. Phys. Rad. 9, 37 (1938); V. Jaccarino et al., Phys. Rev. 160, 476 (1967)
• SmB6 A. Menth et al., Phys. Rev. Lett. 22, 295 (1969)
• CeNiSn T. Takabatake et al., Jpn. J. Appl. Phys. Suppl. 26, 547 (1987)
• Ce3Bi4Pt3 M. F. Hundley et al., Phys. Rev. B 42, 6842
(1990)
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Remarks
• SmB6: robust surface conducting state• Surface conducting state only present when
gap becomes well formed• SmB6 unique so far• Aspects of Kondo insulator physics present in
many materials• Failed Kondo insulators: CePd3, CeNiSn• Other materials: Ce compounds, Yb
compounds, FeSi, half Heuslers, SmS
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