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

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.

Observation of Photonic Landau Levels in Strained Honeycomb Lattices

“…From the propagation length L r of the right edge state and the group velocity v g = 2.4 µm.s −1 measured in Fig. 4(b), we find a lifetime of τ ≈ 7 ps for polaritons in the propagating state, in agreement with previous experiments in polariton honeycomb lattices etched from the same wafer 33 .…”

Multi-orbital tight binding model for cavity-polariton lattices

“…We also point out some specific signatures of the spectrum related to the photon polarization that might be relevant for future experiments. Finally, we reproduce recently published experimental results on the emergence of tilted Dirac cones in polariton graphene lattices under strain [53], showing that we capture correctly the dependence of parameters with distance. This gives our model certain predictive capability that could be useful to engineer different effects on artificial microcavitypolariton lattices.…”

“…The extraordinary transport and topological properties of graphene have stimulated a number of experimental and theoretical studies of the polariton honeycomb lattice [4,10,35,41,42,45,[52][53][54][55][56][57][58][59][60]. Here we analyze the bulk band structure and the edge states spectrum based on the complete tightbinding model presented in the previous section, highlighting the role of its different physical ingredients.…”

“…To show this potentiality, we have analyze the case of a distorted honeycomb lattice as the one used in Ref. [53], where the length of the bond perpendicular to the zigzag edge was changed to be a ′ ≥ a. The left/right column corresponds to the emission linearly polarized parallel/perpendicular to the edge.…”

Dirac points emerging from flat bands in Lieb-kagome lattices

“…Typically, the systems are engineered to faithfully realize exotic tight-binding models with multiple orbitals or atoms per unit cell, as well as complex lattice geometries. In these artificial systems, direct imaging of localized states [4,7,8] or the study of tunable interaction-induced effects [9] are few examples which show approaches hitherto not easily realizable in conventional condensed matter systems.…”