How to achieve extreme anisotropy and divergent density of states for vanishing wavenumbers in a highly-symmetric crystal?
Anisotropic properties of crystals are known for centuries since the discovery of fluorite and other birefringent optical crystals. However, it was widely believed that crystals of higher symmetry classes (such as cubic) can not have anisotropy in zeroth order by small wavenumber in the vicinity of a high symmetry point of the Brillouin zone. We predict theoretically and demonstrate in numerical simulations that this actually happens in a structure as simple as a square lattice of air holes buried in crystalline silicon (see Fig. 1). The clue to theoretical explanation is the denegeracy of the eigenmodes. Degenerate waves have less symmetry than the crystal itself, thus making it possible for them to interact non-isotropically with other eigenstates in the crystal. Anisotropy can be so strong that the effective mass tensor changes its sign upon rotation of the wavevector, right in the vicinity of the Gamma-point. This changes the topology of the isofrequency surface dramatically, leadi
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