A wide range of materials, like d-wave superconductors, graphene, and topological insulators, share a fundamental similarity: their low-energy fermionic excitations behave as massless Dirac particles rather than fermions obeying the usual Schrödinger Hamiltonian. This emergent behavior of Dirac fermions in condensed matter systems defines the unifying framework for a class of materials we call “Dirac materials.” In order to establish this class of materials, we illustrate how Dirac fermions emerge in multiple entirely different condensed matter systems and we discuss how Dirac fermions have been identified experimentally using electron spectroscopy techniques (angle-resolved photoemission spectroscopy and scanning tunneling spectroscopy). As a consequence of their common low-energy excitations, this diverse set of materials shares a significant number of universal properties in the low-energy (infrared) limit. We review these common properties including nodal points in the excitation spectrum, density of states, specific heat, transport, thermodynamic properties, impurity resonances, and magnetic field responses, as well as discuss many-body interaction effects. We further review how the emergence of Dirac excitations is controlled by specific symmetries of the material, such as time-reversal, gauge, and spin–orbit symmetries, and how by breaking these symmetries a finite Dirac mass is generated. We give examples of how the interaction of Dirac fermions with their distinct real material background leads to rich novel physics with common fingerprints such as the suppression of back scattering and impurity-induced resonant states.

中文翻译：

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狄拉克材料

各种材料，如 d 波超导体、石墨烯和拓扑绝缘体，都有一个基本相似之处：它们的低能费米子激发表现为无质量狄拉克粒子，而不是遵循通常的薛定谔哈密顿量的费米子。狄拉克费米子在凝聚态系统中的这种突现行为定义了我们称为“狄拉克材料”的一类材料的统一框架。为了建立这类材料，我们说明了狄拉克费米子如何出现在多个完全不同的凝聚态系统中，并讨论了狄拉克费米子是如何使用电子光谱技术（角分辨光发射光谱和扫描隧道光谱）通过实验识别的。由于它们共同的低能激发，这种多样化的材料在低能量（红外）极限中具有大量的通用特性。我们回顾了这些常见特性，包括激发光谱中的节点、状态密度、比热、传输、热力学特性、杂质共振和磁场响应，并讨论了多体相互作用效应。我们进一步回顾了狄拉克激发的出现如何受材料的特定对称性（例如时间反转、规范和自旋轨道对称性）控制，以及如何通过打破这些对称性来生成有限的狄拉克质量。我们举例说明了狄拉克费米子与其独特的真实材料背景的相互作用如何导致具有共同指纹的丰富的新物理学，例如反向散射和杂质诱导的共振态的抑制。