Dirac degeneracies are essential ingredients to control topological charge exchanges between bands and trigger the unique edge transport properties of topological materials. In addition, when Dirac cones are tilted, exotic phenomena can emerge such as anomalous Hall effect or unconventional Klein tunneling. However, the unique topological transport properties arising from the opening of tilted Dirac cone degeneracies have been left completely uncharted. Here, we demonstrate a new form of Dirac degeneracy that occurs in mechanical granular graphene (MGG): a tilted double Dirac cone, composed of two counter-tilted type-I Dirac cones. Different from the reported C6 systems, we show that the tilted double Dirac cone is present in a C2 granular graphene. Remarkably, a pair of anisotropic helical edge waves appears when the degeneracy is lifted. This leads to an anisotropic quantum spin-Hall topological insulator that possesses unique wave propagation properties, including anisotropic edge dispersion and direction-dependent edge-bulk mode conversion.

中文翻译：

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机械颗粒石墨烯中倾斜的双狄拉克锥和各向异性量子自旋霍尔拓扑绝缘体

狄拉克简并是控制带之间拓扑电荷交换和触发拓扑材料独特边缘传输特性的重要成分。此外，当狄拉克锥体倾斜时，会出现奇异现象，例如异常霍尔效应或非常规克莱因隧道。然而，由倾斜狄拉克锥简并的开放引起的独特拓扑输运性质完全未知。在这里，我们展示了机械颗粒石墨烯 (MGG) 中出现的一种新形式的狄拉克简并形式：倾斜的双狄拉克锥，由两个反向倾斜的 I 型狄拉克锥组成。与报道的 C6 系统不同，我们表明倾斜的双狄拉克锥存在于 C2 颗粒石墨烯中。值得注意的是，当简并性解除时，会出现一对各向异性的螺旋边缘波。