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Tunneling and nonhyperbolicity in quantum dots.

Alessandro P S De Moura1, Ying-Cheng Lai, Richard Akis

  • 1Department of Mathematics and SSERC, Arizona State University, Tempe, Arizona 85287, USA.

Physical Review Letters
|June 13, 2002
PubMed
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Quantum mechanical tunneling, not semiclassical models, explains electronic transport in quantum dots. This quantum tunneling leads to conductance oscillations and wave function concentration, matching experimental data.

Area of Science:

  • Condensed Matter Physics
  • Quantum Mechanics
  • Nanotechnology

Background:

  • Standard semiclassical models fail to explain key electronic transport features in realistic quantum dots.
  • Quantum mechanical tunneling through Kolmogorov-Arnol'd-Moser islands is a significant, yet often overlooked, factor.

Purpose of the Study:

  • To investigate the role of quantum mechanical tunneling in electronic transport within quantum dots.
  • To provide a theoretical framework explaining observed transport phenomena beyond semiclassical approximations.

Main Methods:

  • Theoretical modeling of electron transport incorporating quantum mechanical tunneling.
  • Analysis of dynamical tunneling and its effect on electron wave functions.
  • Comparison of theoretical predictions with experimental results.

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Main Results:

  • Dynamical tunneling generates resonances identified by two quantum numbers.
  • These resonances result in observable conductance oscillations.
  • Wave functions concentrate near stable and unstable periodic orbits due to tunneling.

Conclusions:

  • Quantum mechanical tunneling is essential for understanding electronic transport in generic nanostructures, including quantum dots.
  • The proposed model, accounting for tunneling, accurately predicts experimental observations.
  • Semiclassical approaches are insufficient for a complete description of transport phenomena in these systems.