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Electronic Band Structure

    How do we know whether a material is an insulator,semiconductor or conductor? The answer is electronic band structure. First things first. Let me give some necessary information which will bring
us to the band theory.

     Electric current is response of charged particles inside a material under influence of electric field. One of the charged particle that convey electricity inside a material is electron. Electrons are fermiyons. According to quantum mechanics only 2 electrons can share an energy state and Pauli Exclusion Principle states that they should have opposite spin. It means every short line that you see below contains only 2 electrons. Considering an isolated atom, energy levels are discrete and between these levels it is not possible to find an electron.
     energy levels ile ilgili görsel sonucu
     Things are getting more complex when we start to talk about atoms which lives inside a material. It is better to consider a crystal when we say material. A crystal contains infinitely (for all practical purposes) repeated units. These units are called unit cell.

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3D Plot of Electronic Band Structure  This is graphene's band structure. Hexagon that is seen in the middle of plot is reciprocal lattice of the graphene. Shape of the direct lattice and reciprocal lattice are same. Reciprocal lattice contains some high symmetry points and sharp peaks that is seen above are the point "K". Band structure at that point has a special name, Dirac Cone where electrons can move in relativistic speed like photon. They are called massless Dirac fermiyons.  Whenever we see a band structure plot we always confonr with 2D plot. Vertical axis is energy and horizontal axis is k-points. Bands are plotted for different paths between high stymmery points.          2D version is only a projection of  3D plot. 
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This blog is intended to provide better comprehension for some scientific topics. D.
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