On Brillouin Zones
نویسندگان
چکیده
1 Mathematics Department, Pennsylvania State University, University Park, Pennsylvania, USA. E-mail: [email protected] 2 Instituto de Matemática Pura e Aplicada, Rio de Janeiro, Brazil. E-mail: [email protected] 3 Departamento de Matemática, Universidade Federal de Pernambuco, Recife, Brazil. 4 Institute for Mathematical Sciences and Mathematics Department, State University of New York, Stony Brook, New York, USA. E-mail: [email protected]
منابع مشابه
Reciprocal Space and Brillouin Zones in Two and Three Dimensions
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, ...
متن کاملMinimally Separating Sets, Mediatrices, and Brillouin Spaces
Brillouin zones and their boundaries were studied in [16] because they play an important role in focal decomposition as first defined by Peixoto in [9] and in physics ([1] and [3]). In so-called Brillouin spaces, the boundaries of the Brillouin zones have certain regularity properties which imply that they consist of pieces of mediatrices (or equidistant sets). The purpose of this note is two-f...
متن کاملfor “ 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...
متن کاملAllowed symmetries of soft-modes in cubic crystals
2014 On the basis of the Landau and Lifshitz criteria, the allowed symmetries of soft-modes in the cubic crystals having space-groups Oih (i = 1, 2, ...,10) are presented explicitly. All single valued representations for high-symmetry points in the three different Brillouin zones of the cubic system (P, F, I) have been investigated. Our results are compared with those of other authors. J. Physi...
متن کاملThe aliasing problem in lattice field theory
The intrinsically nonlinear nature of quantum field theory provides a fundamental complication for lattice calculations, when the physical implications of the subtleties of Fourier theory are taken into account. Even though the fundamental fields are constrained to the first Brillouin zone, Fourier theory tells us that the high-momentum components of products of these fields “bleed into” neighb...
متن کامل