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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.
The energy spectra for the tight-binding models on the Lieb and kagome lattices both exhibit a flat band. We present a model which continuously interpolates between these two limits. The flat band located in the middle of the three-band spectrum for
We investigate a generalized two-dimensional Weyl Hamiltonian, which may describe the low-energy properties of mechanically deformed graphene and of the organic compound alpha-(BEDT-TTF)_2I_3 under pressure. The associated dispersion has generically
We study theoretically two-dimensional single-crystalline sheets of semiconductors that form a honeycomb lattice with a period below 10 nm. These systems could combine the usual semiconductor properties with Dirac bands. Using atomistic tight-binding
The enchanting Dirac fermions in graphene stimulated us to seek for other two-dimensional (2D) Dirac materials, and boron monolayers may be a good candidate. So far, a number of monolayer boron sheets have been theoretically predicted, and three have
Non-Hermitian systems, which contain gain or loss, commonly host exceptional point degeneracies rather than the diabolic points found in Hermitian systems. We present a class of non-Hermitian lattice models with symmetry-stabilized diabolic points, s