Reciprocal Space and Brillouin Zones in Two and Three Dimensions
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In this expression, R is a lattice vector between a pair of unit cells: R = ua + vb + wc ; u, v, and w are integers and the dot product k R = kau + kbv + kcw . (In two dimensions, R = ua + vb and k R = kau + kbv .) At this point, we need to clarify the meaning of the vector k and find a way to define the twoand three-dimensional Brillouin zones. To do this, let’s consider the general, oblique, two dimensional lattice below. For this lattice,
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for “ Automated effective band structures for defective and mismatched supercells ”
where the transformation or supercell matrix M is nonsingular with integer components, which implies that the SC is commensurate to the pc. The determinant of M is the multiplicity N of the SC, i.e. the ratio of the respective volumes VSC/vpc. The hexagonal pc and orthorhombic SC of the two-dimensional honeycomb net is depicted in figure A.1a. In reciprocal space, there are consequently two dis...
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تاریخ انتشار 2005