1. 2LSU(2) regime: competition between Kondo and Intermediate Valence (a numerical collaboration) George Martins Physics Department Oakland 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 Network Colaboracion Interamericana de Materiales Quantum Coherent Properties of Spins – III (UCF– December 2010) arXiv:1010.1580 to appear in PRB DMRG – LDECA LDECA – Slave Bosons DMRG NRG Analytical Slave Bosons LDECA - ED

2. Coulomb Blockade and Kondo effect in Quantum Dots Coulomb Blockade Kondo Regime Below a certain characteristic temperature (T K ) EFEF

3. Model and Hamiltonian Left and right leads have two channels which independently couple to either α or β orbital

4. ‘Orbital’ Degeneracy: Orbital Kondo effect and SU(4) Kondo Zarand, Brataas and G.-Gordon Sol. 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 Kondo SU(2) SU(4) Kondo - -

5. 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 group PRL 99, 066801 (2007) U ≠ U’

6. Analyzing the finite t” regime (molecular orbitals) After symmetric – antisymmetric and bonding – antibonding transformations: + - U U t - t + U’ SU(4) 2LSU(2)

7. Busser and Martins, PRB 75, 045406 (2007) Motivation SU(4) to 2LSU(2)

8. NRG results (φ = π/4, t”/t’=1.0) + _

9. DMRG results (t”/t’ ~ 1.0)

10. Conductance results using LDECA + - LDECA  E. V. Anda et al. PRB 78, 085308 (2008) fRG – Meden group (Aachen): NJP 9, 123 (2007)

11. Variation with of the ‘critical’ gate potential + - The value of V g for which the MO level is charged depends on

12. Effective gate potential + - U’ Kondo Competition between Kondo and Intermediate Valence? Intermediate Valence

13. Temperature dependence (NRG) Gate-potential-dependent charge oscillations are associated to a low energy scale (of the order of T K ) units of U

14. Definition of T 0 for a single impurity. Energy gained by the formation of a many-body state (QD + reservoir) DMRG The idea behind the definition of T 0 is to be able to numerically compare the gain in energy provided by each regime Competition between Kondo and Intermediate Valence? Haldane’s T K

15. Low energy scale physics - + U’ T 0 (I V) > T 0 (K) - U’ +

16. T 0 crossing agrees for all cases

17. 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 T 0 which can be easily calculated numerically (DMRG).  Use of molecular orbitals is crucial.  We believe that the definition of T 0 can be ‘refined’ and used to explore the physics of many other systems.