Quantum entanglement, Kondo effect, and electronic transport in quantum dots system Sahib Babaee Tooski Institute of Molecular Physics, Polish Academy of Sciences, Poznań, Poland Collaboration Slovenia

Outline Introduction (Entanglement, Kondo effect, NRG) Entanglement and Kondo effect in triple quantum dots Friedel-Luttinger sum rule and Kondo effect in triple quantum dots Effect of assisted-hopping on transport in a quantum dot Summary

Outline Introduction (Entanglement, Kondo effect, NRG) Entanglement and Kondo effect in triple quantum dots Friedel-Luttinger sum rule and Kondo effect in triple quantum dots Effect of assisted hopping on transport in a quantum dot Summary

Concurrence to quantify quantum entanglement B Concurrence to quantify quantum entanglement Fully enanglement Un-enanglement

Kondo effect in metal with magnetic impurities (uo kondo) Kondo effect: 1) Scattering of conduction electron on a magnetic imputity via a spin-flip process. 2) Formation of singlet state entanglament

Quantum dot quantum dot Gates on top of GaAs/AlGaAs heterostructure segregate a portion of 2D electron gas quantum dot

S=1/2 Kondo effect in quantum dot Signature of Kondo Physics, T<<TK : Increase of the conductance for odd number of electrons Abrikosov-Suhl peak in DOS Unitary transmission with T=1 Goldhaber-Gordon, et al. Nature 391 (1998) 156

Landauer approach for electron transport using NRG Ljubljana Conductance Thermopower In are the transport integrals Transmission coefficient Single-particle effects Correlation effects Wilson Numerical renormalization group (NRG) 1982 Nobel Prize

Introduction Entanglement and Kondo effect in triple quantum dots Underscreened Kondo effect in triple quantum dots Effect of assisted hopping on transport in quantum dots Summary

Experimental TQD system color is not the same bloch and states Qubit in doublet subscpace Pseudo-spin L. Gaudreau, et al. Nature Phys. 8, 54 (2012);

Pairwise entanglement in triple quantum dots (increase thikness notation of t2 larger) one notation for states (t1 <t2) (t1 >t2) t1 t2 A C B t1 t2 A C B Monogamy

One electron in each dot Triple quantum dots One electron in each dot

Triple QDs and Anderson model

quantum phase transition Entanglement and Kondo effect T=0 (t1 <t2) (t1 >t2) Screened S=1/2 Kondo effect One stage Kondo effect Underscreened S=1 Kondo effect Two stages Kondo effect Kondo singlet Γ t1 t2 A C B R L Γ t1 t2 A C B R L Kondo singlet quantum phase transition

Phase diagram between entangled and unentangled ground state(figure thiknes made scheme larger, larger fluctuation spin, plot be larger) Γ t1 t2 A C B R L Kondo singlet S=1/2 Kondo Kondo singlet Γ t1 t2 A C B R L S=1 Kondo First-order quantum phase transition Concurrencies independent from charge fluctuation

Introduction Entanglement and Kondo effect in triple quantum dots Friedel-Luttinger sum rule and Kondo effect in triple quantum dots Effect of assisted hopping on transport in a quantum dot Summary

Singular and Non-Fermi liquids in both Kondo peaks Friedel sum rule Singular and Non-Fermi liquids in both Kondo peaks The Friedel sum rule relates the total charge displaced in the field of an impurity to the phase shift of a free electron at the Fermi momentum scattered at the impurity where is the so-called Luttinger integral. Screened S=1/2 Kondo effect Normal Fermi Liquid Underscreened S=1 Kondo effect Singular Fermi Liquid Kondo peaks in both Fermi liquids L. I. Glazman and M. E. Raikh, JETP Lett. 47, 452 (1988); T. K. Ng and P. A. Lee, Phys. Rev. Lett. 61, 1768 (1988); D. E. Logan, A. P. Tucker, and Ma. R. Galpin, Phys. Rev. B 90, 075150 (2014).

Friedel sum rule (Conductance) Linear conductance related with the phase shift and this related with the dot occupancy Screened S=1/2 Kondo effect Normal Fermi-liquid Underscreened S=1 Kondo effect singular Fermi-liquid Knowing the dot occupancy and conductance, one can determine the phase of the system D. E. Logan, A. P. Tucker, and Ma. R. Galpin, Phys. Rev. B 90, 075150 (2014).

quantum phase transition t1 < t2 Γ t1 t2 A C B R L ntot=5 ntot=2 t1 t2 A C B n=3 n=5 quantum phase transition Screened S=1/2 Kondo effect Normal Fermi liquid t1 t2 A C B n=4 n=6 no Kondo effect ntot=4 Underscreened S=1 Kondo effect Singular Fermi liquid Nagaoka ferromagnetic n=2 t1 t2 A C B

quantum phase transition Γ t1 t2 A C B R L t1 > t2 ntot=5 ntot=2 t1 t2 A C B n=5 Screened S=1/2 Kondo effect Normal Fermi liquid t1 t2 A C B n=4 n=6 no Kondo effect t1 t2 A C B n=3 n=2 ntot=4 Underscreened S=1 Kondo effect Singular Fermi liquid quantum phase transition

Introduction Entanglement and Kondo effect in triple quantum dots Friedel-Luttinger sum rule and Kondo effect in triple quantum dots Effect of assisted hopping on transport in a quantum dot Summary

Anderson model with assisted-hopping describes the Coulomb-interaction-mediated transfer of electron from the state |k> in the lead to the QD, when the QD is already occupied by an electron with the opposite spin

Perturbative analysis (i) (i) Different level renormalisations Haldane scaling theory f is the Fermi-Dirac distribution.

Perturbative analysis (ii) (ii) modified Kondo exchange coupling constant Schrieffer-Wolff transformation Effective single impurity S=1/2 Kondo model Exchange constant Kondo temperature Exponential reduction of the Kondo temperature for x 1

Static properties S.B.Tooski, A.Ramšak, B.R.Bułka,R.Žitko, New J. Phys. 16 (2014) 055001.

reduced Kondo coupling JK Static properties consequence of reduced Kondo coupling JK it makes the local spin more decoupled from the leads. At x=1 the upper level becomes decoupled

Gate-voltage dependence thermopower S and conductance G at high temperature T>TK Increasing x, upper atomic peak starts to be decouple from the leads For x=1, we have a single resonant level

Gate-voltage dependence thermopower S and conductance G at high temperature T>TK hopping transport is dominated A quantum dot with x has large Kondo induced S S increases 5 times Reasons for enhanced S: large charge fluctuation Increasing x, upper atomic peak starts to be decouple from the leads For x=1, we have a single resonant level

Gate-voltage dependence thermopower S and conductance G at low temperature T<TK x induces deviations in G from universality x kills Kondo

Gate-voltage dependence thermopower S and conductance G at low temperature T<TK Large x results in: large S Asymmetry in S x induces deviations in G from universality Sharp peaks in transport

Introduction Entanglement and Kondo effect in triple quantum dots Friedel-Luttinger sum rule and Kondo effect in triple quantum dots Effect of assisted hopping on transport in a quantum dot Summary

Summary Kondo singlet formation in TQD can lead to switching between entangled and unentangled states. TQD system is sensitive to symmetry breaking which can induce a quantum phase transition between the S=1/2 and S=1 ground states. Friedel sum rule can be used to describe transport for regular as well as singular Fermi liquids. Assisted hopping exponentially reduces Kondo temperature, significantly modifies electronic transport.

Publication list Journals: S. B. Tooski, R. Zitko, B. R. Bułka, A. Ramšak Friedel sum rule for the Anderson impurity model In preparation. 3. S. B. Tooski, A. Ramšak, B. R. Bułka, R. Zitko Effect of assisted hopping on thermopower in an interacting quantum dot New Journal of Physics 16, 055001 (2014). 4. S. B. Tooski, A. Ramšak, R. Zitko, B. R. Bułka Entanglement switching via the Kondo effect in triple quantum dots The European Physical Journal B 87, 145 (2014) Selected Editorial Board as Highlight of the Year 2014. 5. M. Urbaniak, S. B. Tooski, A. Ramšak, B. R. Bułka Thermal entanglement in a triple quantum dot system The European Physical Journal B 86, 1 (2013) 6. S. B. Tooski, B. R . Bułka Dark States and Transport through Quantum Dots Acta Physica Polonica A 121, 1231 (2012)

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