Title: Quantum entanglement, Kondo effect, and electronic transport in quantum dots system (Sahib Babaee Tooski)
1Quantum entanglement, Kondo effect, and
electronic transport in quantum dots system
Sahib Babaee Tooski
Institute of Molecular Physics, Polish Academy of
Sciences, Poznan, Poland
Collaboration Slovenia
2Outline
- 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
3Outline
- 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
4Entanglement
Concurrence to quantify quantum entanglement
5Kondo effect 1) Scattering of conduction
electron on a magnetic imputity via a
spin-flip process. 2) Formation of singlet
state entanglament
Kondo effect in metal with magnetic impurities
(uo kondo)
6Quantum dot
Gates on top of GaAs/AlGaAs heterostructure
segregate a portion of 2D electron gas
quantum dot
7S1/2 Kondo effect in quantum dot
Signature of Kondo Physics, TltltTK Increase of
the conductance for odd number of electrons
Abrikosov-Suhl peak in DOS Unitary transmission
with T1
Goldhaber-Gordon, et al. Nature 391 (1998) 156
8Landauer 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
9- 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
10Experimental 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)
11Pairwise entanglement in triple quantum dots
(increase thikness notation of t2 larger) one
notation for states
(t1 ltt2)
(t1 gtt2)
Monogamy
12Triple quantum dots
One electron in each dot
13Triple QDs and Anderson model
14Entanglement and Kondo effect
T0
(t1 gtt2)
(t1 ltt2)
- Screened S1/2 Kondo effect
- One stage Kondo effect
- Underscreened S1 Kondo effect
- Two stages Kondo effect
quantum phase transition
15Phase diagram between entangled and unentangled
ground state(figure thiknes made scheme larger,
larger fluctuation spin, plot be larger)
S1/2 Kondo
S1 Kondo
First-order quantum phase transition
Concurrencies independent from charge fluctuation
16- 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
17Friedel 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
Screened S1/2 Kondo effect Normal Fermi Liquid
Underscreened S1 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).
18Friedel sum rule (Conductance)
Linear conductance related with the phase shift
and this related with the dot occupancy
Screened S1/2 Kondo effect Normal Fermi-liquid
Underscreened S1 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).
19t1 lt t2
ntot5
ntot2
quantum phase transition
Screened S1/2 Kondo effect Normal Fermi liquid
no Kondo effect
ntot4
Underscreened S1 Kondo effect Singular Fermi
liquid Nagaoka ferromagnetic
20t1 gt t2
ntot5
ntot2
Screened S1/2 Kondo effect Normal Fermi liquid
no Kondo effect
ntot4
Underscreened S1 Kondo effect Singular Fermi
liquid
quantum phase transition
21- 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
22Anderson model with assisted-hopping
describes the Coulomb-interaction-mediated
transfer of electron from the state kgt in the
lead to the QD, when the QD is already occupied
by an electron with the opposite spin
23Perturbative analysis (i)
(i) Different level renormalisations
Haldane scaling theory
f is the Fermi-Dirac distribution.
24Perturbative analysis (ii)
(ii) modified Kondo exchange coupling constant
Schrieffer-Wolff transformation
Effective single impurity S1/2 Kondo model
Exchange constant
Kondo temperature
Exponential reduction of the Kondo temperature
for x 1
25Static properties
S.B.Tooski, A.Ramšak, B.R.Bulka,R.Žitko, New J.
Phys. 16 (2014) 055001.
26Static properties
At x1 the upper level becomes decoupled
27Gate-voltage dependence thermopower S and
conductance G at high temperature TgtTK
- Increasing x, upper atomic peak starts to be
decouple from the leads
- For x1, we have a single resonant level
28Gate-voltage dependence thermopower S and
conductance G at high temperature TgtTK
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 x1, we have a single resonant level
29Gate-voltage dependence thermopower S and
conductance G at low temperature TltTK
- x induces deviations in G from universality
- x kills Kondo
30Gate-voltage dependence thermopower S and
conductance G at low temperature TltTK
- Large x results in
- large S
- Asymmetry in S
- x induces deviations in G from universality
- Sharp peaks in transport
31- 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
32Summary
- 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 S1/2 and S1 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.
33Publication list
- Journals
- S. B. Tooski, R. Zitko, B. R. Bulka, A. Ramšak
- Friedel sum rule for the Anderson impurity
model - In preparation.
- 3. S. B. Tooski, A. Ramšak, B. R. Bulka, 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. Bulka
- 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.
Bulka - Thermal entanglement in a triple quantum
dot system - The European Physical Journal B 86, 1
(2013) - 6. S. B. Tooski, B. R . Bulka
- Dark States and Transport through Quantum
Dots - Acta Physica Polonica A 121, 1231
(2012)
34Thank you for your attention