Three dimensional (3D) topological materials have a linear energy dispersion and exhibit many electronic properties superior to conventional materials such as fast response times, high mobility, and chiral transport. In this work, we demonstrate that 3D Dirac materials also have advantages over conventional semiconductors and graphene in thermionic applications. The low emission current suffered in graphene due to the vanishing density of states is enhanced by an increased group velocity in 3D Dirac materials. Furthermore, the thermal energy carried by electrons in 3D Dirac materials is twice of that in conventional materials with a parabolic electron energy dispersion. As a result, 3D Dirac materials have the best thermal efficiency or coefficient of performance when compared to conventional semiconductors and graphene. The generalized Richardson-Dushman law in 3D Dirac materials is derived. The law exhibits the interplay of the reduced density of states and enhanced emission velocity.

中文翻译：

---

三维狄拉克材料中的高效率和非理查森热电子学

三维 (3D) 拓扑材料具有线性能量色散，并表现出许多优于传统材料的电子特性，例如快速响应时间、高迁移率和手性传输。在这项工作中，我们证明了 3D Dirac 材料在热离子应用中也比传统半导体和石墨烯具有优势。由于 3D Dirac 材料中的群速度增加，石墨烯中由于状态密度消失而遭受的低发射电流得到增强。此外，3D Dirac 材料中电子携带的热能是具有抛物线电子能量色散的传统材料的两倍。因此，与传统半导体和石墨烯相比，3D Dirac 材料具有最佳的热效率或性能系数。导出了 3D Dirac 材料中的广义理查森-杜什曼定律。该定律表现出降低的态密度和提高的发射速度之间的相互作用。