1. QUANTUM TRANSPORT IN THE TUNNELING AND COTUNNELING REGIMENS Javier F. Nossa M.

2. 25 Nov 2010 Quantum transport in the Tunneling and Cotunneling regimens J.F. Nossa Goal I want to show you an animation that I have been working with!!! Why? Because I like animations!!! Quantum transport.

3. Sequential Regimen sourcedraingate occupied energy levels unoccupied energy levels quantized energy levels Fermi Level of Source is lower than first unoccupied level of dot Energy spacing must be greater than thermal smearing System 25 Nov 2010 Quantum transport in the Tunneling and Cotunneling regimens J.F. Nossa

4. Sequential Regimen Applying a potential, the dot energy levels are shifted. Fermi energy of source is higher than first dot unoccupied energy level An electron can now occupy the dot sourcedraingate electrons Coulomb blockade prevents others. 25 Nov 2010 Quantum transport in the Tunneling and Cotunneling regimens J.F. Nossa

5. sourcedraingate Constant interaction model: Charging energy Sequential Regimen Ground state energy levels We fix and vary 25 Nov 2010 Quantum transport in the Tunneling and Cotunneling regimens J.F. Nossa tunneling in tunneling out This cycle is known as single electron tunneling

6. Sequential Regimen Current Current Step 25 Nov 2010 Quantum transport in the Tunneling and Cotunneling regimens J.F. Nossa

7. drain Constant interaction model: gate Charging energy Sequential Regimen Energy levels Source§ We fix and vary 25 Nov 2010 Quantum transport in the Tunneling and Cotunneling regimens J.F. Nossa

8. Sequential Regimen 25 Nov 2010 Quantum transport in the Tunneling and Cotunneling regimens J.F. Nossa

9. drain Constant interaction model: gate Charging energy Sequential Regimen Energy levels Source We change both and 25 Nov 2010 Quantum transport in the Tunneling and Cotunneling regimens J.F. Nossa

10. Sequential Regimen Coulomb diamonds, differential conductance Current Oscillations Current Steps 25 Nov 2010 Quantum transport in the Tunneling and Cotunneling regimens J.F. Nossa

11. Anderson Model 25 Nov 2010 Quantum transport in the Tunneling and Cotunneling regimens J.F. Nossa Two level system Coulomb diamond N=0N=1N=2

12. Sequential Regimen So far we have taken into account only ground states...... what if we included excited states? 25 Nov 2010 Quantum transport in the Tunneling and Cotunneling regimens J.F. Nossa

13. Sequential Regimen N N+1 25 Nov 2010 Quantum transport in the Tunneling and Cotunneling regimens J.F. Nossa If a line terminates at the N-electron Coulomb blockade region, the transition necessarily involves an N-electron excited state

14. Anderson Model 25 Nov 2010 Quantum transport in the Tunneling and Cotunneling regimens J.F. Nossa Two level system Coulomb diamond N=0N=1N=2

15. Cotunneling Regimen drain gate Source§ Cotunneling Two-particle processes. Higher order tunneling process Intermediated state Virtual processBecause So far, only single-particle processes have been considered. First order processes in the tunneling Hamiltonian. One electron occupies the dot while, at the same time, another electron leaves the dot 25 Nov 2010 Quantum transport in the Tunneling and Cotunneling regimens J.F. Nossa

16. Cotunneling Regimen Spin Effects in Single-Electron Transistors, Ghislain Granger, MIT 2005 Elastic Cotunneling Initial state Intermediate state Final state 25 Nov 2010 Quantum transport in the Tunneling and Cotunneling regimens J.F. Nossa

17. Cotunneling Regimen Inelastic Cotunneling Initial state Intermediate state Final state The dot is left in an excited state 25 Nov 2010 Quantum transport in the Tunneling and Cotunneling regimens J.F. Nossa

18. Cotunneling Regimen S. De Franceschi et.al., Phys. Rev. Lett. 86, 878 Cotunneling in the differential conductance Sequential tunneling: current inside the diamond is not allowed Two regimes: one consisting of elastic processes only, and one including both elastic and inelastic contributions 25 Nov 2010 Quantum transport in the Tunneling and Cotunneling regimens J.F. Nossa

19. Anderson Model 25 Nov 2010 Quantum transport in the Tunneling and Cotunneling regimens J.F. Nossa Two level system Coulomb diamond N=0N=1N=2

20. Anderson Model 25 Nov 2010 Quantum transport in the Tunneling and Cotunneling regimens J.F. Nossa Two level system Coulomb diamond N=0N=1N=2

21. Anderson Model 25 Nov 2010 Quantum transport in the Tunneling and Cotunneling regimens J.F. Nossa N=0N=1 N=2 Step instead of peak

22. TUNNELING AND COTUNNELING PHENOMENA IN SET Javier F. Nossa M. THANK YOU !!!