Z Fisk UC Irvine Zhejiang University April 12 2015 Outline some superconductivity history felectron physics heavy Fermion superconductivity some phenomenology of the dense Kondo lattice Kondo insulators ID: 280437
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Slide1
Kondo Physics, Heavy Fermion Materials and Kondo Insulators
Z. Fisk UC Irvine
Zhejiang University April 12, 2015Slide2
Outline
some superconductivity history
f-electron physics
heavy Fermion superconductivity
some phenomenology of the dense Kondo lattice
Kondo insulatorsSlide3
where it all began
Onnes in his cryogenics laboratory in Leyden wins race to liquefy Helium (at 4.2K)Slide4Slide5Slide6Slide7
1933 Zero resistance is not the signature effect of superconductivity:Slide8
1950s: the Edisonian approach to discovering new superconductors
and the era of conventional superconductivity
Fermi: systematics of materials may give a clueSlide9Slide10Slide11Slide12Slide13Slide14Slide15Slide16Slide17Slide18Slide19Slide20Slide21Slide22Slide23Slide24Slide25Slide26Slide27Slide28Slide29Slide30Slide31Slide32Slide33Slide34Slide35Slide36Slide37Slide38Slide39Slide40Slide41Slide42Slide43Slide44Slide45Slide46Slide47Slide48
CeIn
3
CeMIn
5
Ce
2
MIn
8
Crystal Structures
M = Co, Rh, Ir (isovalent)Slide49Slide50Slide51Slide52Slide53Slide54Slide55Slide56Slide57Slide58Slide59
dilution studies of CeCoIn5
Cross over from single ion Kondo to C/T
ln(T/T*) near 2D percolation thresholdSlide60Slide61
Heavy Fermion Superconductor with
T
c
≈ 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
(
x
2
-
y
2
) 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 CeCoIn５
M = Co
Theoretical expectations near 2D AF QCP,
r
(
T / T
sf
)
C
m
/
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). )Slide62Slide63Slide64
Systematic increase of
M/H
with La dilution
at low temperatures
Possible origins:
1) Crystal field splitting
2) Kondo coupling
T
K
3) Intersite coupling
Single impurity limit:
x
(La) > 0.95
Systematic change in low
T
susceptibility
Constant high temp.
T
KSlide65
6
148 K
197 K
7
(2)
7
(1)
1/2>
-1/2>
Crystal field analyses for Ce
1-
x
La
x
CoIn
5
T(K)
M/H (B//c)
M/H (B//a,b)Slide66Slide67Slide68
Basis of our analysis:
T
K
<<
T
*
(intersite) <<
(crystal field)
1 K 50 K 200 K
Energy scale diagram of Ce
1-
x
La
x
CoIn
5
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 T
K
at
x
1 limit.
3) The systematic increase should
arise from intersite correlation
.
T
coh
T
*
at
x
0 limit.
Evolution of intersite AF fluctuations
similar to RVB with energy scale of
T
*
and correlation length of several
aSlide69
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(T
c
) ~ 10-20% Rln2 ↔ T
c
/T* ~ 1/20Slide70
Source of coherence scale in dense Kondo lattice
Kondo coupling parameter (
J) determines both T
K
and T*Slide71Slide72
T
J
T
N
T
Kondo
QCP
T*
T
cSlide73
Kondo scale: TK
=
-1
e
-1/J
RKKY scale: T* = cJ
2
J = -1/ln(T
K
) = √(c
-1
T* )Slide74
Table I. Experimental
T*
,
T
K
and g
for a variety of Kondo lattice compounds.
Compound
T*
(K)
T
K
(K)
g
(mJ/mol K
2
)
J
r
c
Reference
CeRhIn
5
20
0.15
5.7
0.10
0.45
5,7,(H.L.)
CeCu
6
35
3.5
8
0.15
0.49
8,9
U
2
Zn
17
20
2.7
12.3
0.15
0.41
10,11,12
CeCu
2
Si
2
75
10
4
0.15
0.47
5,13,14
CePb
3
20
3
13
0.15
0.41
15,16
CeCoIn
5
50
6.6
7.6
0.16
0.55
3,5,6
CePd
2
Si
2
40
9
7.8
0.17
0.41
17,18
URu
2
Si
2
55
12
6.5
0.17
0.45
5,19,20
CePd
2
Al
3
40
10
9.7
0.18
0.45
21,22,23
CeRu
2
Si
2
60
20
6.68
0.19
0.42
24,25
UBe
13
55
20
8
0.19
0.43
26,27
YbRh
2
Si
2
70
20
7.8
0.19
0.53
(Z.F.)
YbNi
2
B
2
C
50
20
11
0.21
0.47
28
UPd
2
Al
3
60
25
9.7
0.21
0.48
23,29Slide75Slide76
intrinsic Kondo impurities in pure CeCoIn5
low T properties consistent with
~ 10% free Kondo centers Slide77Slide78Slide79Slide80Slide81
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 systemsSlide82
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)
SmB
6
A. Menth et al., Phys. Rev. Lett.
22
, 295 (1969)
CeNiSn
T. Takabatake et al., Jpn. J. Appl. Phys. Suppl.
26
, 547 (1987)
Ce
3
Bi4Pt3 M. F. Hundley et al., Phys. Rev. B 42, 6842 (1990)Slide83Slide84Slide85Slide86Slide87Slide88Slide89Slide90Slide91Slide92Slide93Slide94Slide95Slide96Slide97Slide98Slide99Slide100Slide101Slide102Slide103Slide104Slide105
arXiv:1211.6769Slide106Slide107Slide108Slide109Slide110Slide111Slide112Slide113Slide114Slide115Slide116Slide117Slide118Slide119Slide120Slide121Slide122Slide123Slide124Slide125
Remarks
SmB
6
: robust surface conducting state
Surface conducting state only present when gap becomes well formed
SmB
6
unique so far
Aspects of Kondo insulator physics present in many materials
Failed Kondo insulators: CePd
3,
CeNiSn
Other materials: Ce compounds, Yb compounds, FeSi, half Heuslers, SmSSlide126Slide127