Diapositiva 1

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Transport suppression in heterostructures driven
by an ac gate voltage
Miguel Rey Universidad Autónoma de Madrid
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• Coworkers

Michael Strass Sigmund Kohler Peter Hänggi
Fernando Sols
Chemical Physics (in press), cond-mat/0412221. AIP
Conf. Proc. 780, 45 (2005).
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Outline

• Introduction
• Models techniques
• transfer matrix (TM)
• tight binding (TB) Floquet theory
• high frequency approximation (HFA)
• Results
• current suppression TM, TB and HFA
• convergence of TM to TBHFA (WKB)
• Conclusions outlook

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Introduction

• coherent control of current, useful for quantum
  information purposes
• not only tunneling, but transport, can be almost
  completely suppressed (coherent destruction of
  tunneling is just not enough)

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Techniques

• Landauer formalism for ac problems
• transfer matrix / tight-binding description for
  heterostructures
• Greens function for Floquet theory
• high frequency approximation

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Some references

• general time-dependent systems
• Kohler et al., Phys. Rep. 406, 379 (2005)
• transfer-matrix with ac
• Wagner, Phys. Rev. A 51, 798 (1995)
• some experiments in double QDs with ac
• van der Wiel et al., Rev. Mod. Phys. 75, 1 (2003)
• Blick et al., Phys. Rev. B 56, 7899 (1996)
• high frequency approximation
• Kohler et al., Chem. Phys. 296, 243 (2004)
• orthogonality of ac states
• Wagner Sols, Phys. Rev. Lett. 83, 4377 (1999)

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Scattering formalismfor mesoscopic transport

• calculate (coherent) current within a scattering
  formalism
• holds in general for
  driven systems.
• ac induces inelastic channels (sidebands)
• inelastic channels preserve orthogonality of
  initial dc states.

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Techniquesmodelling
double-well heterostructure model potential ?
transfer matrices.
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Techniquesmodelling
double-well heterostructure model potential ?
transfer matrices.
tight-binding approximation metastable tunnel
doublet ? tight binding
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Transfer matrix approach
most general solution of Schrödingers equation
for piecewise constant potential time-dependent
gate voltage
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Transfer matrix approach
matching of wave-function spatial derivative ?
transfer matrix
time-averaged transmission probabilities for each
of the sidebands
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Tight-binding model
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Floquet theoryfor quantum transport
general solution for time-periodic Hamiltonians
Floquet state complex quasi-energy

• Floquet eigenvalue equation

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Floquet theoryfor quantum transport
general solution for time-periodic Hamiltonians
Floquet state complex quasi-energy
? retarded Greens function
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High frequency limit
effects of driving most pronounced for large
frequency ? expansion in
apply unitary transformation

• time-scale separation fast of driving, slow of
  tunneling

effect of transformation is to map time-dependent
problem into a static one (for tunneling)
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High frequency limit
transformation affects the leads too effective
electron distribution
? current in the HF limit
will vanish for zeros of
, i.e.
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Results

• current suppression.
• comparison TB vs TM vs HFA.
• check TB assumptions.
• noise (in progress).

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Results 1a current suppresion
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Results 1acurrent suppresion

• dc current suppression effect of
  renormalisation of interwell tunnel coupling
  not caused by the new electron distribution.
• TBFloquetHFA accounts well for shape value
  of current.
• TM numerics slightly different positions of
  minima does not predict total current
  suppression.

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Results 1b HFAcurrent at first minimum

• higher order terms included in TM TB cause
  non-vanishing of current at minimum.
• current at minimum goes to zero as expected in
  expansion.

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Results 2 WKBchecking the TB approximation

• TB assumes infinite barriers, time-independent
  coupling.
• ? possible source of differences in calculations.

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Results 2 WKBchecking the TB approximation
? increase of barrier height improves agreement
with TB theory
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Outlook noise (in progress)
current fluctuations can be characterized by its
zero-frequency noise
Fano factor relative noise strength

• results available only for TB HFA
• (TM still under development!)
• zero driving double barrier
• at current suppression QPC-like
• crossover region noise even lower

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Conclusions

• dc current in a double-well heterostructure can
  be controlled by the purely coherent influence of
  an oscillating gate voltage (? current
  suppression).
• HFA succesfully accounts for the effects obtained
  in a numerically exact calculation the
  divergencies can be explained in terms of a
  perturbative scheme.
• TM reproduces the TB-limit of weak coupling for
  sufficiently high and wide barriers.