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Quantum Ballistic Conduction in Quasi-One-Dimensional Systems

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Abstract:

Phase-coherent electron transport through quasi-one-dimensional systems has developed into a very active and fascinating subfield of mesoscopic physics. We present a review of this development focusing on ballistic conduction through quantum wires (or constrictions). In quantum wires the electron conductance versus Fermi energy is quantized as a consequence of the reduced dimensionality and the subsequent quantization of transverse momentum. The presence of scatterers in otherwise “clean” wires can strongly suppress the quantum conductance, and can generate sharp resonances (which are due to quasibound states) if the scattering potential is attractive. These resonances can be of the Fano or Breit-Wigner type, depending on the size or/and strength of the scattering potential. Depending on the resonance width, the resonance structure is smeared out at finite temperature. The scattering approach is briefly discussed in order to derive the Landauer formula, which is the basic tool for calculating the conductance of a mesoscopic sample. Scattering theory in ballistic quantum wires is formulated in terms of the Lippmann-Schwinger equation. The Feshbach coupled-channel theory is employed in the last part of this review in order to treat Fano resonances.

Keywords: BALLISTIC TRANSPORT; CONDUCTANCE QUANTIZATION; CONSTRICTION; FANO RESONANCES; SCATTERING; TRANSMISSION

Document Type: Review Article

DOI: http://dx.doi.org/10.1166/jctn.2010.1379

Publication date: February 1, 2010

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  • Journal of Computational and Theoretical Nanoscience is an international peer-reviewed journal with a wide-ranging coverage, consolidates research activities in all aspects of computational and theoretical nanoscience into a single reference source. This journal offers scientists and engineers peer-reviewed research papers in all aspects of computational and theoretical nanoscience and nanotechnology in chemistry, physics, materials science, engineering and biology to publish original full papers and timely state-of-the-art reviews and short communications encompassing the fundamental and applied research.
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