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CHARGE TRANSPORT THROUGH A DOUBLE QUANTUM DOT IN THE PRESENCE OF DYNAMICAL DISORDER

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. Outline. Charge transport in coupled semiconductor quantum dots applications

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CHARGE TRANSPORT THROUGH A DOUBLE QUANTUM DOT IN THE PRESENCE OF DYNAMICAL DISORDER

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  1. CHARGE TRANSPORTTHROUGHADOUBLE QUANTUM DOTIN THE PRESENCE OF DYNAMICAL DISORDER Jan Iwaniszewski with prof. Włodzimierz Jaskólski, prof. Colin Lambert, Lancaster, UK Supported by The Royal Society, London Department of Quantum Mechanics Seminar

  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. empty state evolution of the total system J L,T ER  EL VL R,T VR R L Description of the system Model: • single-level dots • Coulomb blockade • weak coupling to leads • leads in thermal equilibrium

  4. where - density of states - detuning Fermi distribution Reduction of the description reduced evolution • 2nd order perturbation • infinitely fast relaxations in leads Born-Markov approximation

  5. IL IR One electron only - Coulomb blockade Rate equations

  6. stationary solution simplification for T=0, αR=βL=0 weak coupling to the leads Matrix calculus

  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. Assumption: Fluctuator varries slower than relaxation processes in the leads J =D0D1 L,T ER EL VL R,T VR g surrounding Perturbed system

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

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

  11. estimation of the position of maximum =0.00 =0.05 =0.10 =0.15 1=0.5 al.=0.01 Resonant increasing of the current =1.0 =0.8 =0.6 =0.4 =0.2 1=0.5 al.=0.01 Stationary current for ≠0

  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. The End Department of Quantum Mechanics Seminar

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