Semi-Dirac dispersion relation in photonic crystals

Abstract

A semi-Dirac cone refers to a peculiar type of dispersion relation that is linear along the symmetry line but quadratic in the perpendicular direction. Here, I demonstrate that a photonic crystal consisting of a square array of elliptical dielectric cylinders is able to produce this particular dispersion relation in the Brillouin zone center. A perturbation method is used to evaluate the linear slope and to affirm that the dispersion relation is a semi-Dirac type. Effective medium parameters calculated from a boundary effective medium theory not only explain the unexpected topological transition in the iso-frequency surfaces occurring at the semi-Dirac point, they also offer a perspective on the property at that point, where the photonic crystal behaves as a zero-refractive-index material along the symmetry axis but functions like at a photonic band edge in the perpendicular direction.

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• Floquet dynamics in two-dimensional semi-Dirac semimetals and three-dimensional Dirac semimetals
• Semi-Dirac Semimetal in Silicene Oxide
• Interplay between topology and disorder in a two-dimensional semi-Dirac material
• Direction dependent giant optical conductivity in 2D \textit{semi}-Dirac materials
• Semi-Dirac and Weyl Fermions in Transition Metal Oxides
• Non-linear transport without spin-orbit coupling or warping in two-dimensional Dirac semimetals
• Quantum thermoelectrics based on 2-D Semi-Dirac materials
• Signatures of merging Dirac points in optics and transport
• Role of four-fermion interaction and impurity in the states of two-dimensional semi-Dirac materials
• Berry curvature and Hall viscosities in an anisotropic Dirac semi-metal
• Effective medium theory for photonic pseudospin-1/2 system
• Valley-Selective Landau-Zener Oscillations in Semi-Dirac p-n Junctions
• The topological magnon bands in the Flux state in Sashtry-Sutherland lattice
• Highly anisotropic optical conductivities in two-dimensional tilted semi-Dirac bands
• Fermion-fermion interaction driven instability and criticality of quadratic band crossing systems with the breaking of time-reversal symmetry
• Nonlinear magnetotransport in a two-dimensional system with merging Dirac points
• Cooper instability generated by attractive fermion-fermion interaction in the two-dimensional semi-Dirac semimetals
• Non-Hermitian semi-Dirac semi-metals
• Off-resonant light-induced topological phase transition and thermoelectric transport in semi-Dirac materials
• An effective medium theory for predicting the existence of surface states
• Quantum Hall effective action for anisotropic Dirac semi-metal
• Fermion-fermion interaction driven phase transitions in rhombohedral trilayer graphene
• Electromagnetic Duality Symmetry-Protected Dirac-Like Cones
• Topological excitations in quasi two-dimensional quantum magnets with weak interlayer interactions