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 Scatterers with a weakly energy dependent transmission L

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)  g falls off with distance r from the QPC, exhibiting fringes spaced by F /2 2DEG, QPC AFM cantilever The charged tip creates a depletion region inside the 2deg which can be scanned around the nanostructure (qpc)

8. QPC Model used in the numerical study Long and smooth adiabatic contact Sharp opening of the conduction channels + TIP (Square Lattice at low filling, t=1, E F =0.1)

9. QPC biased at the beginning of the first plateau (Tip: V=1) T=0T = 0.01 E F

10. QPC biased at the beginning of the second plateau (Tip: V=-2) T=0T =0.035 E F

11. Resonant Level Model 2 semi-infinite square lattices with a tip (potential v) on the right side coupled via a site of energy V 0 and coupling terms -t c

12. Self-energies describing the coupling to leads expressed in terms of surface elements of the lead GFs Method 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 Out of resonance: T 0 < 1, 1/x Linear terms At resonance: T 0 =1; S 0 =0 1/x 2 quadratic terms (Shot noise)

14. T=0 : Conductance Out of resonance: At resonance: Fringes spaced by (1/x decay) Almost no fringes (1/x 2 decay)

15. T > 0: Conductance at 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 results Increasing temperature (top to bottom)

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

19. RLM model QPC ? 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 T 0 (E). The width of the energy interval where S 0 =T 0 (1-T 0 ) 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, Red curve: analytical results Black points: numerical simulations

21. Peak to peak amplitude

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

24. Summary