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

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

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

‘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

- -

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’

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

Busser and Martins, PRB 75, 045406 (2007)

Motivation

0.875tt

0.975tt

1.0tt

t t

SU(4) to 2LSU(2)

gV U

N

,N

NRG results (φ = π/4, t”/t’=1.0)

+

_

DMRG results (t”/t’ ~ 1.0)

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)

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

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

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

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

Low energy scale physics

e-

+U’

e , ?g cV

e

e

T0(I V) > T0(K)

-U’+

T0 crossing agrees for all cases

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.