Dirac Cones Of Accidental Degeneracy In 2D Without Symmetry

As an important physical concept,the linear dispersion relation behind the Dirac point plays an important role in both condensed matter physics and classical wave systems.Various subsequent characteristics have also aroused widespread attention of scientific researchers such as topology,Quantum Hall effect,pseudo-diffusive transmission,zitterbewegung,etc.which produce many applications and influence the development of scientific research and industry applications.For classical wave systems,due to the similarity between classical wave systems and electronic systems and the convenience of designing classical wave systems such as photonic crystals and phononic crystals,it is feasible and convenient to study the Dirac point in classical wave systems.As an important part of the classical wave system,photonic crystals is inevitably vital to the study of the Dirac point.In this paper,we introduce a new method of creating accidental degenerate Dirac points through energy band manipulation in a two-dimensional photonic crystal.By using this method,we can break the dependance of Dirac point on the spatial symmetry of photonic crystals structure,and creat accidental degenerate Dirac points at multiple locations in the Brillouin zone of different photonic crystal systems with almost no spatial symmetry.We also verified of the characteristic of pseudo-diffusive transmission near the artificial accidental degenerate Dirac points,which further prove the correctness and universality of the method in creating accidental degenerate Dirac points by manipulation of the band diagrams.The main work of this paper is as follows:1.Introduceing a method of energy band manipulation in a two-dimensional photonic crystal system.This method selectively inserts dielectric pillars into the structure of the photonic crystal.The manipulating details about the position and the permittivity of the inserted pillars are determined by the distribution of the absolute value of electric field intensity in the position of brillouin zone,and the manipulation can realize directional movement control of the energy band.In our work,we apply this method to reduce the size of the band gap and shrink the the distance between two adjacent energy bands to a degenerate Dirac point.And since the spatial symmetry of the photonic crystal structure after the energy band manipulation is almost zero,the constructed Dirac points are accidental degenerate Dirac points with no spatial symmetry protection2.Verification of the previously discussed method of creating accidental degenerate Dirac points through energy band manipulation.We successfully creat accidental degenerate Dirac points at different positions of the Brillouin zone in multiple photonic crystal systems.The Dirac points are created by our method at K point of a triangular lattice photonic crystal,K point of a triangular-like lattice photonic crystal with a 45° apex angle,Brillouin zone symmetry line of a square lattice photonic crystal and the inside of the Brillouin zone of a square lattice photonic crystal.At the same time,in each case the existence of accidental degenerate Dirac point and the characteristic of linear dispersion relationship are observed from the photonic crystal band diagram after band manipulation and the three-dimensional dispersion surface distribution diagram near the frequency of the Dirac point.3.Further verification of the characteristic of pseudo-diffusive transmission near the accidental degenerate Dirac points constructed by band manipulation,which is to prove that the constructed accidental degenerate Dirac points have the same properties as ordinary Dirac points and further prove the correctness of the construction method.We first verified the characteristic of pseudo-diffusive transmisssion in the past case of triangular lattice photonic crystals that possess Dirac points and the square lattice photonic crystals that possess Dirac-like cones,which aim to prove the correctness of the verification simulation model we used.Then we successfully verified the pseudo-diffusive transmisssion property of Dirac points in our photonic crystal system with artificial accidental degenerate Dirac point,including a Dirac point at K point of a triangular lattice photonic crystal and a Dirac point inside the Brilliouin zone of a square lattice photonic crystal.The two verification cases cover all situations including triangular lattice photonic crystal,square lattice photonic crystal,boundary and interior of the Brillouin zone,which are absolutely enough to prove that there are indeed pseudo-scattering properties near the accidental degenerate Dirac point created by manipulatin of the band diagram.