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2LSU(2) regime: competition between Kondo and Intermediate Valence (a numerical collaboration)
George MartinsPhysics DepartmentOakland University
Carlos Busser (University of Wyoming)Enrique Anda (PUC – Rio – Brazil)
Adrian Feiguin (University of Wyoming)Edson Vernek (Uberlandia – Brazil)
Eugene Kim (Windsor – Canada)Pedro Orellana (PUC – Antofagasta – Chile)Gustavo Lara (PUC – Antofagasta – Chile)
Materials World
NetworkColaboracion
Interamericanade Materiales
Quantum Coherent Properties of Spins – III (UCF– December 2010)
arXiv:1010.1580to appear in PRB
DMRG – LDECALDECA – Slave Bosons
DMRGNRG
AnalyticalSlave BosonsSlave Bosons
LDECA - ED
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gV
Coulomb Blockade and Kondo effect in Quantum Dots
heG 22
gV
Coulomb Blockade
Kondo Regime
gV
U
gV
Below a certain characteristic
temperature (TK)
EF
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Model and Hamiltonian
, ; 2d gUH n n V n U n n
int 0, ; ;
h. c.ll L R
H t d c
Left and right leads have two channels which independently couple to either
α or β orbital
t t t
t t t
0t
0t0t
0t
U
U 4SU
2 2SU SU
tt
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‘Orbital’ Degeneracy: Orbital Kondo effect and SU(4) Kondo
Zarand, Brataas and G.-GordonSol. Stat. Comm. 126, 463 (2003)
U
U’ U=U’
P. J. Herrero et al. Nature 434, 484 (2005)
CNT
P. McEuen et al. Nature 428, 536 (2008)
Orbital KondoSU(2)
SU(4) Kondo
- -
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Observation of SU(4)
von Klitzing group PRL 101, 186804 (2008)
Sasaki et al. PRL 93, 017205 (2004) von Klitzing group
Physica E 9, 625 (2001)
Finkelstein groupPRL 99, 066801 (2007)
U ≠ U’
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Analyzing the finite t” regime (molecular orbitals)
0
0
cossin
t tt t
After symmetric – antisymmetric and bonding – antibonding transformations:
0
0
2 cos sin
2 cos sin
t t
t t
0
02
tt t
0
0
2
2
t t
t t
+
-U
U
t -
t +
U’0
SU(4)
4 2LSU(2)
t t
0t
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Busser and Martins, PRB 75, 045406 (2007)
Motivation
0.875tt
0.975tt
1.0tt
t t
SU(4) to 2LSU(2)
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gV U
N
,N
NRG results (φ = π/4, t”/t’=1.0)
+
_
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DMRG results (t”/t’ ~ 1.0)
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Conductance results using LDECA
gV U
+
-
LDECA E. V. Anda et al. PRB 78, 085308 (2008)
,n
fRG – Meden group (Aachen): NJP 9, 123 (2007)
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gV U
Variation with of the ‘critical’ gate potential
+
-N
,g cV ,g cV
The value of Vg for which the MO level is charged depends on
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gV
Effective gate potential
0
,
012
N
+
-U’
gV
gV
0
0
U
U
g gV V U N
U
Kondo
Competition between Kondo and
Intermediate Valence?
IntermediateValence
N
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Temperature dependence (NRG)
N
N
Gate-potential-dependent charge oscillations are associated to a low energy scale (of the order of TK)
units of U
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Definition of T0 for a single impurity.
00 0 0,g g gT V E V E V
00 gE V
0 , 0gT V
0 gE V
Energy gained by the formation of a many-body state (QD + reservoir)
DMRG
The idea behind the definition of T0 is to
be able to numerically compare the gain in
energy provided by each regime
Competition between Kondo and
Intermediate Valence?
Haldane’s TK
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Low energy scale physics
e-
+U’
e , ?g cV
e
e
T0(I V) > T0(K)
-U’+
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T0 crossing agrees for all cases
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Conclusions and future work
Subtle charge fluctuations are analyzed around a 2LSU(2) regime and characterized as a competition between Intermediate Valence and Kondo regimes
This competition can be quantified by the definition of an energy scale T0 which can be easily calculated numerically (DMRG).
Use of molecular orbitals is crucial. We believe that the definition of T0 can be
‘refined’ and used to explore the physics of many other systems.