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Thermal Enhancement of Interference Effects in Quantum Point Contacts

Thermal Enhancement of Interference Effects in Quantum Point Contacts. Adel Abbout, Gabriel Lemarié and Jean-Louis Pichard Phys. Rev. Lett. 106, 156810 (2011). IRAMIS/SPEC CEA Saclay Service de Physique de l’Etat Condensé, 91191 Gif Sur Yvette cedex, France.

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Thermal Enhancement of Interference Effects in Quantum Point Contacts

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  1. Thermal Enhancement of Interference Effects in Quantum Point Contacts Adel Abbout, Gabriel Lemarié and Jean-Louis Pichard Phys. Rev. Lett. 106, 156810 (2011) IRAMIS/SPEC CEA Saclay Service de Physique de l’Etat Condensé, 91191 Gif Sur Yvette cedex, France

  2. Electron Interferometer formed with a quantum point contact and another scatterer in a 2DEG

  3. Interferences in one dimension 1d model with 2 scatterers L Scatterers with a weakly energy dependent transmission

  4. Interferences with a resonance L

  5. 2d model:Resonant Level Model for a quantum point contact

  6. From the RLM model towards realistic contacts RLM model QPCs in a 2DEG

  7. SGM imaging Conductance of the QPC as a function of the tip position (Harvard, Stanford, Cambridge, Grenoble,…)Topinka et al., Physics Today (Dec. 2003) 2DEG , QPC AFM cantilever The charged tip creates a depletion region inside the 2deg which can be scanned around the nanostructure (qpc) Dg falls off with distance r from the QPC, exhibiting fringes spaced by lF/2

  8. QPC Model used in the numerical studyLong and smooth adiabatic contactSharp opening of the conduction channels + TIP (Square Lattice at low filling, t=1, EF=0.1)

  9. QPC biased at the beginning of thefirstplateau(Tip: V=1) T=0 T = 0.01 EF

  10. QPC biased at the beginning of thesecondplateau(Tip: V=-2) T=0 T =0.035 EF

  11. Resonant Level Model2 semi-infinite square lattices with a tip (potential v) on the right side coupled via a site of energy V0 and coupling terms -tc

  12. Self-energies describing the coupling to leadsexpressed in terms of surface elements of the lead GFsMethod of the mirror images for the lead GFs. Dyson equation for the tip • Transmission without tip ~ Lorentzian of width • Transmission with tip (Generalized Fisher-Lee formula) Narrow resonance:

  13. Expansion of the transmission T(E) when is small (Shot noise) Out of resonance: T0 < 1, 1/x Linear terms At resonance: T0=1; S0=0 1/x2 quadratic terms

  14. T=0 : Conductance • Out of resonance: • At resonance: Fringes spaced by (1/x decay) Almost no fringes (1/x2 decay)

  15. T > 0: Conductanceat resonance • 2 scales: • Temperature induced fringes: Thermal length: New scale:

  16. Rescaled Amplitude 1. Universal T-independent decay: 2. Maximum for Bottom to top: increasing temperature

  17. Numerical simulations and analytical resultsIncreasing temperature (top to bottom)

  18. The thermal enhancement can only be seen around the resonance

  19. RLM modelQPC ? • The expansion obtained in the RLM model can be extended to the QPC, if one takes the QPC staircase function instead of the RLM Lorentzian for T0(E). • The width of the energy interval where S0=T0(1-T0) is not negligible for the QPC plays the role of the of the RLM model for the QPC.

  20. Interference fringes obtained with a QPC and previous analytical results assuming the QPC transmission function Transmission ½ without tip, Redcurve: analyticalresults Black points: numerical simulations

  21. Peak to peak amplitude

  22. Similar scaling laws for the thermoelectric coefficients and the thermal conductance

  23. Summary

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