Kondo regime in triangular arrangements of quantum dots: Molecular orbitals, interference, and contact effects

Physical Review B - Condensed Matter and Materials Physics

Volumn 80, Issue 3, 2009, Pages

  Vernek, E ^a,b   Busser C A ^a,c   Martins, G B ^c   Anda, E V ^d   Sandler, N ^a   Ulloa, S E ^a  

^a OHIO UNIVERSITY   (United States)

^b FEDERAL UNIVERSITY OF UBERLÂNDIA   (Brazil)

^c OAKLAND UNIVERSITY   (United States)

^d PONTIFICAL CATHOLIC UNIVERSITY OF RIO DE JANEIRO   (Brazil)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 69549137816     PISSN: 10980121     EISSN: 1550235X     Source Type: Journal    
DOI: 10.1103/PhysRevB.80.035119     Document Type: Article

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49. Although some of the results presented in Sec. 3 are for parameter values such that t3 t1, we checked that the results are qualitatively similar to the ones obtained for t3 t1. Therefore, one can be confident that the parameters used in Sec. 3 reflect the molecular regime situation (see also Sec. 3).
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52. Note that the partial conductances G1 and G2 in Fig. 4 have maximum values larger than the conductance quantum (G0 =2 e2 /h). As alluded above, the partial conductances, when their associated molecular orbitals overlap with each other, cannot be independently measured, having therefore no physical significance by themselves, and therefore do not have to be ≤ G0. When the molecular orbital levels are well separated in energy [and therefore the partial conductances match the total (measured) conductance], then Gi ≤ G0 i. For all cases, moreover, the total conductance GT ≤ G0, as one expects on physical grounds.
53. The origin of the finite-size effect is an unfavorable geometry for small clusters for t3 t4, which tends to "freeze" a spin in QD B. This suppresses spin fluctuations, with a consequent suppression of the Kondo effect. For a comprehensive discussion of similar effects in different systems (using ECA and DMRG), see Ref..
54. When two electrons are each occupying orbitals | ψ1 and | ψ2, for Vg /U0.5 (see Fig. 5, Ref.), the hopping from one lead to the orbitals (and vice versa) is maximized when the spins of the electrons in the molecular orbitals | ψ1 and | ψ2 are parallel to each other, i.e., ferromagnetically correlated, generating an effective ferromagnetic interaction between the orbitals. See G. B. Martins, C. A. Büsser, K. A. Al-Hassanieh, A. Moreo, and E. Dagotto, Phys. Rev. Lett. 94, 026804 (2005) for a similar effect in a different system. 10.1103/PhysRevLett.94.026804
55. Note that results for ni in Fig. 5 have to be multiplied by 2 to account for different spin orientations.
56. Except, obviously, for the LDOS results, where LDECA was used with λ1.0.
57. Although there is good qualitative agreement between FUSBMF and ECA in Fig. 7, the ECA conductance peaks are narrower. This arises from the fact that the clusters used for these calculations had just six sites, and therefore the results are not fully size-converged. The next cluster size available for this geometry contains 12 sites. Although feasible, ECA calculations for this cluster size consume considerably more CPU time.
58. To confirm this, a test for a simplified system containing a single-level QD with three leads shows that the conductance through two of the leads is not directly proportional to the LDOS at the QD.