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Tunneling Through Quantum Dots with Discrete Symmetries

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Encyclopedia of Complexity and Systems Science

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Definition of the Subject

Electrons may be confined within a nano-size quantum box by various methods. Thefirst example of such confinement was demonstrated in the studies of optical properties ofsemiconductor precipitates in glasses [10]. Later on such confinement was realized in planarquantum dots. These dots are fabricated in semiconductor heterostructures, where the electronsalready confined in a two‐dimensional layer between two semiconductors (usuallyGaAs/GaAlAs) are locked in a nano-size puddle by electrostatic potential created byelectrodes superimposed on the heterostructure (see [25,51]for a description of the early stage of the physics of quantum dots). QDs may be alsoprepared by means of colloidal synthesis [4], grown as self‐assembledstructures of semiconductor droplets on a strained surface ofanother semiconductor [36], etc. Inparticular, quantum dots may be fabricated in a form of vertical structures possessingcylindrical symmetry [32].

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Abbreviations

Quantum dot:

Quantum dot (QD) is an element of artificial nanostructures. It arises in a situation when a finite number of electrons is confined in a puddle of \( { 10^{0} } \)–\( { 10^{2} } \) nanometer size either by means of external electrical potential imposed on semiconductor heterostructure or in a process of formation of non‐equilibrium self‐assembled structures. The electron wavelength in a QD is comparable with its size. As a result all energy levels are spatially quantized like in atoms or molecules. Quantum systems with fully quantized energy levels are defined as zero‐dimensional nano‐objects. Complex quantum dots consist of several QDs organized in linear or ring structures.

Discrete symmetry:

Group theory classifies all physical objects in accordance with their symmetry properties relative to symmetry transformations (rotations and translations) in space and time. These operations may be continuous or discrete. In the latter case one speaks about discrete rotational or translational symmetry.

Dynamical symmetry:

Dynamical symmetry characterizes not only the eigenstates of a Hamiltonian, but also the symmetry of transition between the states belonging to different irreducible representation of the symmetry group of the Hamiltonian under external dynamical perturbation. Dynamical symmetry may be continuous and discrete or combine both types of symmetry operations.

Kondo effect:

Kondo effect is the many particle phenomenon which arises in magnetically doped metals due to exchange scattering of metallic electrons on localized magnetic moments of impurities. Multiple electron scattering processes result in dynamical screening of impurity magnetic moment. As a result, impurity‐related electrical resistivity has a minimum at some temperature, and reaches the unitarity limit at \( { T\to 0 } \). This limit corresponds to maximum backward electron scattering. Kondo effect exists also in tunneling through small QDs. In this case the unitarity limit corresponds to maximum tunnel transparency of QD.

Quantum tunneling:

Quantum tunneling of electrons through potential barriers arises at low temperatures, where all overbarrier activation processes are frozen. In nanostructures this type of transport is realized on the interfaces between different materials forming nanostructure or in especially designed tunneling channels.

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Author information

Authors and Affiliations

  1. Physics Department and Ilse Katz Institute for Nanotechnology, Ben-Gurion University of the Negev, Beer-Sheva, Israel

    Yshai Avishai

  2. RTRA-Triangle de la Physique, LPS (Orsay) and CEA-SPHT (Saclay), Gif sur Yvette, France

    Yshai Avishai

  3. Department of Physics, Tel-Aviv University, Tel-Aviv, Israel

    Konstantin Kikoin

Authors
  1. Yshai Avishai
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Editors and Affiliations

  1. RAMTECH LIMITED, 122 Escalle Lane, Larkspur, CA, 94939, USA

    Robert A. Meyers Ph. D. (Editor-in-Chief) (Editor-in-Chief)

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Avishai, Y., Kikoin, K. (2009). Tunneling Through Quantum Dots with Discrete Symmetries. In: Meyers, R. (eds) Encyclopedia of Complexity and Systems Science. Springer, New York, NY. https://doi.org/10.1007/978-0-387-30440-3_571

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