Type-III and Tilted Dirac Cones Emerging from Flat Bands in Photonic Orbital Graphene

M Milićević,L Le Gratiet,G Montambaux,A Harouri,J Bloch,B Real,T Ozawa,A Amo,I Sagnes,A Lemaître,O Jamadi

doi:10.1103/physrevx.9.031010

Abstract

The extraordinary electronic properties of Dirac materials, the two-dimensional partners of Weyl semimetals, arise from the linear crossings in their band structure. When the dispersion around the Dirac points is tilted, the emergence of intricate transport phenomena has been predicted, such as modified Klein tunnelling, intrinsic anomalous Hall effects and ferrimagnetism. However, Dirac materials are rare, particularly with tilted Dirac cones. Recently, artificial materials whose building blocks present orbital degrees of freedom have appeared as promising candidates for the engineering of exotic Dirac dispersions. Here we take advantage of the orbital structure of photonic resonators arranged in a honeycomb lattice to implement photonic lattices with semi-Dirac, tilted and, most interestingly, type-III Dirac cones that combine flat and linear dispersions. The tilted cones emerge from the touching of a flat and a parabolic band with a non-trivial topological charge. These results open the way to the synthesis of orbital Dirac matter with unconventional transport properties and, in combination with polariton nonlinearities, to the study of topological and Dirac superfluids in photonic lattices.

Highlights

The extraordinary transport properties of Dirac materials arise from the spinor nature of their electronic wave functions and from the linear dispersion around Dirac and Weyl points
Type-III Dirac cones emerge from the touching of a flat and a parabolic band when synthetic photonic strain is introduced in the lattice, and they possess a nontrivial topological charge
The fact that they emerge from a flat band makes type-III Dirac cones robust to changes in the hopping, as we show below. The richness of this multiband system allows, in addition, the observation of semi-Dirac cones, which combine massless and massive dispersions. By analyzing their topological charge, i.e., the winding of the Hamiltonian around each Dirac point, we show that the semi-Dirac, tilted, and type-III Dirac cones emerge as a consequence of topological Lifshitz transitions induced by strain in the orbital bands

Summary

INTRODUCTION

The extraordinary transport properties of Dirac materials arise from the spinor nature of their electronic wave functions and from the linear dispersion around Dirac and Weyl points. Evidence of type-II Weyl points has recently been reported in microwave metamaterials [33,34] and via conical diffraction in laser-written waveguides with elaborate couplings [35] In most of these cases, the tilted Dirac cones appear as a consequence of band inversions [30,31], a situation in which the magnitude of the tilt cannot be controlled. The richness of this multiband system allows, in addition, the observation of semi-Dirac cones, which combine massless and massive dispersions By analyzing their topological charge, i.e., the winding of the Hamiltonian around each Dirac point, we show that the semi-Dirac, tilted, and type-III Dirac cones emerge as a consequence of topological Lifshitz transitions induced by strain in the orbital bands.

PHOTONIC ORBITAL LATTICE

TILTED AND SEMI-DIRAC CONES

TOPOLOGICAL INVARIANTS OF TILTED AND TYPE-III DIRAC CONES

CONCLUSION