1. Kondo Physics, Heavy Fermion Materials and Kondo Insulators
Z. Fisk UC Irvine
Zhejiang University April 12, 2015

2. Outline some superconductivity history f-electron physics
heavy Fermion superconductivity
some phenomenology of the dense Kondo lattice
Kondo insulators

3. where it all began
Onnes in his cryogenics laboratory in Leyden wins race to liquefy Helium (at 4.2K)

7. 1933 Zero resistance is not the signature effect of superconductivity:

8. Fermi: systematics of materials may give a clue
1950s: the Edisonian approach to discovering new superconductors and the era of conventional superconductivity
Fermi: systematics of materials may give a clue

48. Crystal Structures
CeIn3
CeMIn5
Ce2MIn8
M = Co, Rh, Ir (isovalent)

59. dilution studies of CeCoIn5
Cross over from single ion Kondo to C/T  ln(T/T*) near 2D percolation threshold

61. Heavy Fermion Superconductor CeCoIn５
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, (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, (2001))
Normal state
Non-Fermi-liquid behavior )
rTCm/T – logT
probably due to strong AF fluctuations
(e.g. V.A. Sidorov et al., cond-mat/ ,
Shishido et al., J. Phys. Soc. Jpn. 71, 162 (2002).)
This is 115 workshop, so the audience, I believe, do not want to hear these introduction any longer, but the point I would like to remind of is that CeCoIn5 have been reported to have non-Fermi-liquid behavior such as the T linear dependence of the transport and the logarithmic temperature dependence of the specific heat. This should be compared with the theoretical expectations for the system near the 2D AF QCP. The resistivity and the specific heat are expected to be T-linear and log T with the renormalized temperature with the T^sf, a characteristic energy of spin-fluctuation.
Therefore, by the La dilution study, we might be able to observe the prominent effect of the intersite coupling in this material.
CeCoIn5 is know as a heavy fermion superconductor with high Tc around 2.3 K.
This is the rare compound showing NFL and SC under ambient pressure.
It has a layered structure with CeIn3 layers stacked with CoIn2 layers,
and owing to this, the electronic structure has basically the quasi two dimensional character.
The superconducting and normal states of this material are both interesting:
The SC state is unconventional with SC gap with line nodes and the symmetry is most likely d(x2-y2)type;
Moreover, the normal state shows non-fermi-liquid behavior maybe because of a strong AＦ fluctuations, which suggests a strong intersite coupling in this system.
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). )
M = Co

64. Systematic change in low T susceptibility
Constant high temp.TK
Single impurity limit:
x(La) > 0.95
Systematic increase of
M/H with La dilution
at low temperatures
Possible origins:
1) Crystal field splitting
2) Kondo coupling TK
3) Intersite coupling
This is the c-axis susceptibility for various concentrations of La.
As in the resistivity, the high temperature parts collapse on the same curve,
suggesting that the high temperature T_K is constant for the entire alloying range.
On the other hand,
the low temperature part systematically increases as La is doped until it finally
hits the single impurity limit again around %.
Here, I would like to spend some time to talk about the origin of the low T change.
Taking account of the fact that this is due to the La doping,
this could be ascribed to the change in a single or combination of these three parameters.
Crystal field splitting, Kondo coupling, and the intersite coupling.

65. M/H (B//c) M/H (B//a,b) T(K) Crystal field analyses for Ce1-xLaxCoIn56
148 K
197 K
7(2)
7(1)
1/2>
-1/2>
Let me first briefly talk about the crystal field scheme of CeCoIn5 and its change due to the La doping.
In order to find out the crystal filed scheme, first we performed the fitting to the susceptibility of the single impurity limit where the crystal field should be the best defined. These are the fitting results to the c and ab components of the susceptibility.
Based on these analyses, we found the scheme has a doublet ground state with gamma seven (1), separated from the gamma 7(2) and gamma 6 with fairly large gaps of around 150 and 200 K.
This scheme can reproduce the results of independent measurements of anisotropic field dependence of the magnetization at the single impurity limit.
Taking account of the fact that all the susceptibility curves are the same at high temperatures in the whole range of the La dilution, it is quite suggestive that this scheme is relevant not only for the single impurity limit, but also for the entire alloying regime.
T(K)

68. Energy scale diagram of Ce1-xLaxCoIn5
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.
4) Change in the ground state
properties at around x = 0.5.
Combining the results obtained through all the scaling procedure,
I would like to summarize the energy scale diagram.
There are several important findings.
First, all these three parameters T^ab, T^c from the susceptibility, and T^* from the specific heat collapse on top of each other, showing that they are basically the same.
Second, all these originate from the Kondo temperature at the single impurity limit.
Third, the intersite correlation lead the systematic increase of the characteristic energy of the spin fluctuation.
The coherent temperature found in the resistivity becomes the same as the characteristic temperature at the lattice limit.
Fourth, we found the change in the ground state from the Fermi liquid behavior to non-Fermi-liquid behavior across the 50%.
These results strongly suggest that intersite coupling generates the local AF interaction with a correlation length of the several lattice constant a, very similar to the picture of RVB state .
Finally, I would like to point out the very basic relation that guided us to observe such systematic changes.
It is because all three parameters Tk, T* and crystal field splitting energy are well separated from each other.
Evolution of intersite AF fluctuations
similar to RVB with energy scale of T*
and correlation length of several a
Basis of our analysis: TK << T* (intersite) << (crystal field)
1 K K K

69. Entropy development in quantum critical regime
C/T α lnT
Typically: C/T = (Rln2/T*)ln(T*/T)
and S(T*) = Rln2
T* sets the scale for heavy Fermion physics
For heavy Fermion superconductors:
S(Tc) ~ 10-20% Rln2 ↔ Tc/T* ~ 1/20

70. Source of coherence scale in dense Kondo lattice
Kondo coupling parameter (J) determines both TK and T*

72. T J TN
TKondo
QCP T* Tc

73. Kondo scale: TK = -1e-1/J RKKY scale: T
Kondo scale: TK = -1e-1/J RKKY scale: T* = cJ2  J = -1/ln(TK ) = √(c-1T* )

74. Table I. Experimental T*, TK and g for a variety of Kondo lattice compounds.
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
0.49
8,9
U2Zn17
2.7
12.3
0.41
10,11,12
CeCu2Si2 75 10 4
0.47
5,13,14
CePb3 3 13
15,16
CeCoIn5 50
6.6
7.6
0.16
0.55
3,5,6
CePd2Si2 40 9
7.8
0.17
17,18
URu2Si2 55 12
6.5
5,19,20
CePd2Al3
9.7
0.18
21,22,23
CeRu2Si2 60
6.68
0.19
0.42
24,25
UBe13
0.43
26,27
YbRh2Si2 70
0.53
(Z.F.)
YbNi2B2C 11
0.21 28
UPd2Al3 25
0.48
23,29

76. intrinsic Kondo impurities in pure CeCoIn5
low T properties consistent with
~ 10% free Kondo centers

81. 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

82. SmB6 A. Menth et al., Phys. Rev. Lett. 22, 295 (1969)
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)

105. arXiv:

125. 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