We theoretically demonstrate that a type-II class of tilted Dirac cones can emerge in generalized two-dimensional anisotropic lattice arrangements. This is achieved by introducing a special set of graphynelike exchange bonds by means of which the complete spectrum of the underlying Weyl Hamiltonian can be realized. Our ab initio calculations demonstrate a unique class of eigensolutions corresponding to a type-II class of Dirac fermionic excitations. Based on our approach, one can systematically synthesize a wide range of strongly anisotropic band diagrams having tilted Dirac cones with variable location and orientation. Moreover, we show that asymmetric conical diffraction, as well as edge states, can arise in these configurations. Our results can provide a versatile platform to observe, for the first time, optical transport around type-II Dirac points in two-dimensional optical settings under linear, nonlinear, and non-Hermitian conditions.

中文翻译：

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石墨烯状光子晶格中II型狄拉克点的出现

我们从理论上证明，倾斜的Dirac锥的II类类别可以出现在广义的二维各向异性晶格排列中。这是通过引入一组特殊的石墨烯状交换键来实现的，通过这些键，可以实现基本的韦尔·哈密顿量的完整谱。我们的从头开始计算表明对应于Dirac铁离子激发的II型类别的本征溶液的独特类别。根据我们的方法，可以系统地合成具有倾斜的狄拉克锥且位置和方向可变的各种强各向异性带图。此外，我们表明在这些配置中会出现不对称圆锥形衍射以及边缘状态。我们的结果可以提供一个多功能的平台，用于首次观察在线性，非线性和非厄密条件下在二维光学设置中II型Dirac点周围的光学传输。