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2LSU(2 ) regime: competition between Kondo and Intermediate Valence (a numerical collaboration)

2LSU(2 ) regime: competition between Kondo and Intermediate Valence (a numerical collaboration). arXiv:1010.1580 to appear in PRB. George Martins Physics Department Oakland University. Colaboracion Interamericana de Materiales. Materials World Network. LDECA - ED.

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2LSU(2 ) regime: competition between Kondo and Intermediate Valence (a numerical collaboration)

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

  2. Coulomb Blockade and Kondo effect in Quantum Dots Below a certain characteristic temperature (TK) EF Coulomb Blockade Kondo Regime

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

  4. Zarand, Brataas and G.-Gordon Sol. Stat. Comm. 126, 463 (2003) ‘Orbital’ Degeneracy: Orbital Kondo effect and SU(4) Kondo SU(4) Kondo - - Orbital Kondo SU(2) P. McEuen et al. Nature 428, 536 (2008) U CNT U=U’ U’ P. J. Herreroet al. Nature 434, 484 (2005)

  5. Observation of SU(4) Sasaki et al. PRL 93, 017205 (2004) von Klitzing group Physica E 9, 625 (2001) U ≠ U’ von Klitzing group PRL 101, 186804 (2008) Finkelstein group PRL 99, 066801 (2007)

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

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

  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 Vg for which the MO level is charged depends on +

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

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

  14. Definition of T0 for a single impurity. Competition between Kondo and Intermediate Valence? The idea behind the definition of T0 is to be able to numerically compare the gain in energy provided by each regime DMRG Haldane’s TK Energy gained by the formation of a many-body state (QD + reservoir)

  15. Low energy scale physics - T0(I V)> T0(K) U’ + - U’ +

  16. T0 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 T0which 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.

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