1. Division of Open Systems Dynamics Department of Quantum Mechanics Seminar 1 20 April 2004 CHARGE TRANSPORT THROUGH A DOUBLE QUANTUM DOT IN THE PRESENCE OF DYNAMICAL DISORDER Jan Iwaniszewski with prof. Włodzimierz Jaskólski, prof. Colin Lambert, Lancaster, UK Supported by The Royal Society, London

2. Division of Open Systems Dynamics20.042004 2 Outline  Charge transport in coupled semiconductor quantum dots applications description  Dynamical disorder sources (defects) two-level fluctuator  Charge transport in the presence of fluctuators description two-level system and fluctuator modification of the current  Perspectives

3. Division of Open Systems Dynamics20.042004 3 Description of the system Model:  single-level dots  Coulomb blockade  weak coupling to leads  leads in thermal equilibrium  L,T  R,T ERER VRVR VLVL L R  J ELEL evolution of the total system empty state

4. Division of Open Systems Dynamics20.042004 4 Reduction of the description reduced evolution  2 nd order perturbation  infinitely fast relaxations in leads Born-Markov approximation where - density of states - detuning Fermi distribution

5. Division of Open Systems Dynamics20.042004 5 Rate equations ILIL IRIR One electron only - Coulomb blockade

6. Division of Open Systems Dynamics20.042004 6 Matrix calculus stationary solution weak coupling to the leads simplification for T=0, α R =β L =0

7. Division of Open Systems Dynamics20.042004 7 Dynamical disorder  Sources of dynamical disorder phonon field fluctuations of impurities defects of the lattice  Model - two-level fluctuator (TLF) the defect switches randomly between two discrete states  D its dynamics is governed by dichotomous Markov noise with correlation time τ=1/2γ

8. Division of Open Systems Dynamics20.042004 8 Perturbed system surrounding  L,T  R,T ERER VRVR VLVL =  =   J ELEL  Assumption: Fluctuator varries slower than relaxation processes in the leads

9. Division of Open Systems Dynamics20.042004 9 Current in the presence of TLF slow fluctuator limit fast fluctuator limit stationary current(exact but cumbersome) further simplifications weak coupling to the leads T=0 two cases: 1.tuned  =0 2.detuned  ≠0

10. Division of Open Systems Dynamics20.042004 10 Stationary current for  =0  L =0.2  L =0.4  L =0.6  L =0.8 a L =0.01  L =0.2  L =0.4  L =0.6  L =0.8 a L =0.001 a L =0.005 a L =0.010 a L =0.015  1 =0.5 estimation of the position of minimum Resonant decreasing of the current

11. Division of Open Systems Dynamics20.042004 11 Stationary current for  ≠0  =0.00  =0.05  =0.10  =0.15  1 =0.5 a l. =0.01  =1.0  =0.8  =0.6  =0.4  =0.2  1 =0.5 a l. =0.01 Resonant increasing of the current estimation of the position of maximum

12. Division of Open Systems Dynamics20.042004 12 What next?  Characteristic of the current coherency of the process spectral properties of the current  Beyond the applied approximations detailed (quantum) description of the fluctuator detailed treatment of coupling to the leads two electrons transport – weak Coulomb repulsion  Related problems stochastic perturbation of energy levels multilevel quantum dots three- or multi- wells semiconductor structures The aim of research Optimal control of charge transport through semiconductor heterostructures

13. Division of Open Systems Dynamics Department of Quantum Mechanics Seminar 13 20 April 2004 The End