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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

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



Interferences in one dimension
Interferences in one dimension and another scatterer in a 2DEG

1d model with 2 scatterers

L

Scatterers with a weakly energy dependent transmission


Interferences with a resonance
Interferences with a resonance and another scatterer in a 2DEG

L


2d model resonant level model for a quantum point contact
2d model and another scatterer in a 2DEG:Resonant Level Model for a quantum point contact


From the rlm model towards realistic contacts
From the RLM model towards realistic contacts and another scatterer in a 2DEG

RLM model

QPCs in a 2DEG


SGM imaging and another scatterer in a 2DEGConductance 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


QPC Model used in the numerical study and another scatterer in a 2DEGLong and smooth adiabatic contactSharp opening of the conduction channels

+ TIP

(Square Lattice at low filling, t=1, EF=0.1)


Qpc biased at the beginning of the first plateau tip v 1
QPC biased at the beginning of the and another scatterer in a 2DEGfirstplateau(Tip: V=1)

T=0

T = 0.01 EF


Qpc biased at the beginning of the second plateau tip v 2
QPC biased at the beginning of the and another scatterer in a 2DEGsecondplateau(Tip: V=-2)

T=0

T =0.035 EF


Resonant Level Model and another scatterer in a 2DEG2 semi-infinite square lattices with a tip (potential v) on the right side coupled via a site of energy V0 and coupling terms -tc


Self-energies describing the coupling to leads and another scatterer in a 2DEGexpressed 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:


Expansion of the transmission t e when is small
Expansion of the transmission and another scatterer in a 2DEGT(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


T 0 conductance
T=0 : Conductance and another scatterer in a 2DEG

  • Out of resonance:

  • At resonance:

Fringes spaced by

(1/x decay)

Almost no fringes

(1/x2 decay)


T 0 conductance at resonance
T > 0: and another scatterer in a 2DEGConductanceat resonance

  • 2 scales:

  • Temperature induced fringes:

Thermal length:

New scale:


Rescaled amplitude
Rescaled Amplitude and another scatterer in a 2DEG

1. Universal T-independent decay:

2. Maximum for

Bottom to top: increasing temperature


Numerical simulations and analytical results increasing temperature top to bottom
Numerical simulations and another scatterer in a 2DEG and analytical resultsIncreasing temperature (top to bottom)



Rlm model qpc
RLM model resonanceQPC ?

  • 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.


Interference fringes obtained with a QPC resonanceand previous analytical results assuming the QPC transmission function

Transmission ½ without tip,

Redcurve: analyticalresults

Black points: numerical simulations




Summary
Summary the thermal conductance


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