nanoelectronics - Institut d'Études Scientifiques de Cargèse (IESC)

Posters
Entanglement and the Kondo effect in triple quantum dots
S. B. Tooski 1, 2, 3 , B. Bulka 3 , R. Zitko 1,2 , and A. Ramsak 1, 2
1 Faculty of Mathematics and Physics, University of Ljubljana, Ljubljana, Slovenia
2 J. Stefan Institute, Ljubljana, Slovenia
3 Institute of Molecular Physics, Polish Academy of Sciences, ul. M. Smoluchowskiego 17,
Poznan, Poland
We analyze a system of triple quantum dots in a triangular geometry, in which one of the
quantum dots is connected to metallic leads, Fig. 1. We expect that the Kondo effect
between the leads and central dot C (with intra-dot Coulomb interactions) can induce perfect
spin entangled states between dots A and B (dots without intra-dot interactions). Using
Wilson’s numerical renormalization group technique [1], we investigate various spin-spin
correlation functions, probabilities for antiparallel and parallel spin alignment, and the
concurrence [2] to quantify quantum entanglement in the triple quantum dot system [3], in the
regime where each dot is essentially singly occupied by adjusting a global back-gate voltage.
As a consequence of quantum phase transition an abrupt switch between fully entangled and
separate states between A and B dots takes place. By tuning the interdot coupling t and the
dot-lead coupling Γ, one can switch abruptly ferromagnetic and antiferromagnetic interaction
between A and B dots. The effective Ruderman-Kittel-Kasuya-Yoshida (RKKY) interaction
between these dots is ferromagnetic in our simplified model. Here the spins order
ferromagnetically into a triplet state and undergo the S=1 Kondo screening at low
temperatures. This yields an uncompensated S=1/2 residual spin, and since half a unit of
spin is quenched by the conduction band via the Kondo effect, there clearly cannot be any
entanglement between the electrons on noninteracting dots. For t t , the antiferromagnetic
ordering wins and the electrons form an entangled singlet state on A and B dots. The
transition from the regime dominated by the RKKY interaction between A and B dots to the
Kondo singlet phase for C dot is in this case a true quantum phase transition and the
concurrence falls abruptly from C AB 1 to C AB 0.
c
A
t
B
t’ t’
L
C
R
Fig. 1. A triangle of quantum dots attached to the leads.
[1] R. Zitko, NRG_Ljubljana code; H. R. Krishna-murthy, J. W. Wilkins and K. G. Wilson,
Phys. Rev. B 21, 1003 (1980).
[2] A. Ramšak, J. Mravlje, R. Žitko, and J. Bonča, Phys. Rev. B 74, 241305(R) (2006); J.
Mravlje, A. Ramšak, and T. Rejec, Phys. Rev. B 73, 241305(R) (2006); T. Rejec and A.
Ramšak, Phys. Rev. B 68, 035342 (2003); A. Ramšak, I. Sega, and J. H. Jefferson, Phys.
Rev. A 74, 010304(R) (2006).
[3] W. Wang, Phys. Rev. B 78, 235316 (2008); A. K. Mitchell, T. F. Jarrold, and D. E. Logan
Phys. Rev. B 79, 085124 (2009).