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Gauss's Law: Planar Symmetry01:27

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A planar symmetry of charge density is obtained when charges are uniformly spread over a large flat surface. In planar symmetry, all points in a plane parallel to the plane of charge are identical with respect to the charges. Suppose the plane of the charge distribution is the xy-plane, and the electric field at a space point P with coordinates (x, y, z) is to be determined. Since the charge density is the same at all (x, y) - coordinates in the z = 0 plane, by symmetry, the electric field at P...
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Coordination compounds and complexes exhibit different colors, geometries, and magnetic behavior, depending on the metal atom/ion and ligands from which they are composed. In an attempt to explain the bonding and structure of coordination complexes, Linus Pauling proposed the valence bond theory, or VBT, using the concepts of hybridization and the overlapping of the atomic orbitals. According to VBT, the central metal atom or ion (Lewis acid) hybridizes to provide empty orbitals of suitable...
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A charge distribution has cylindrical symmetry if the charge density depends only upon the distance from the axis of the cylinder and does not vary along the axis or with the direction about the axis. In other words, if a system varies if it is rotated around the axis or shifted along the axis, it does not have cylindrical symmetry. In real systems, we do not have infinite cylinders; however, if the cylindrical object is considerably longer than the radius from it that we are interested in,...
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Metallic solids such as crystals of copper, aluminum, and iron are formed by metal atoms. The structure of metallic crystals is often described as a uniform distribution of atomic nuclei within a “sea” of delocalized electrons. The atoms within such a metallic solid are held together by a unique force known as metallic bonding that gives rise to many useful and varied bulk properties.
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An applied magnetic field causes loosely bound π-electrons in organic molecules to circulate, producing a local or induced diamagnetic field over a large spatial volume. As the molecules tumble in solution, the field generated by π-electrons in spherical substituents results in a zero net field. However, the net field generated by π-electrons in non-spherical substituents is not zero. The effect of this induced field depends on the orientation of the molecule with respect to B0,...
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Tetrahedral Complexes
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Highly-anisotropic plasmons in two-dimensional hyperbolic copper borides.

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    Two novel 2D copper borides, CuB6 and CuB3, exhibit broadband hyperbolic properties and anisotropic plasmonics. Their optical characteristics are tunable via doping, offering potential for advanced optoelectronics.

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    Area of Science:

    • Condensed Matter Physics
    • Materials Science
    • Nanophotonics

    Background:

    • Hyperbolic materials possess unique electromagnetic responses, enabling applications like negative refraction and sub-diffraction imaging.
    • Anisotropic two-dimensional (2D) materials are promising for optoelectronics due to their inherent in-plane anisotropy.
    • Natural hyperbolic materials offer advantages over artificial metamaterials.

    Purpose of the Study:

    • To investigate the electronic and optical properties of monolayer CuB6 and CuB3, two novel 2D hyperbolic materials.
    • To explore their potential for optoelectronic applications by analyzing their plasmonic behavior and hyperbolic characteristics.

    Main Methods:

    • First-principles calculations were employed to study the electronic and optical properties.
    • Analysis focused on identifying hyperbolic windows, plasmon excitation, and anisotropy.
    • The effect of electron (or hole) doping on material properties was simulated.

    Main Results:

    • Both CuB6 and CuB3 monolayers exhibit multiple broadband hyperbolic windows with low optical loss across infrared to ultraviolet regions.
    • Highly anisotropic plasmon excitation was predicted, with plasmon propagation nearly suppressed along the x-direction in CuB3.
    • Doping was shown to effectively regulate the hyperbolic windows and plasmonic properties.

    Conclusions:

    • Monolayer CuB6 and CuB3 are promising natural hyperbolic 2D materials with significant potential in nanophotonics and optoelectronics.
    • The tunability of their optical properties through doping provides a viable strategy for designing advanced optical devices.
    • These findings open new avenues for exploring 2D materials in advanced optical applications.