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Register a new userEntropy spikes as a signature of Lifshitz transitions in the Dirac materials
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We demonstrate theoretically that the characteristic feature of a 2D system undergoing $N$ consequent Lifshitz topological transitions is the occurrence of spikes of entropy per particle $s$ of a magnitude $pm ln 2/(J-1/2)$ with $2 leq J leq N$ at low temperatures. We derive a general expression for $s$ as a function of chemical potential, temperature and gap magnitude for the gapped Dirac materials. Inside the smallest gap, the dependence of $s$ on the chemical potential exhibits a dip-and-peak structure in the temperature vicinity of the Dirac point. The spikes of the entropy per particles can be considered as a signature of the Dirac materials. These distinctive characteristics of gapped Dirac materials can be detected in transport experiments where the temperature is modulated in gated structures.
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A topological Dirac semimetal is a novel state of quantum matter which has recently attracted much attention as an apparent 3D version of graphene. In this paper, we report critically important results on the electronic structure of the 3D Dirac semimetal Na3Bi at a surface that reveals its nontrivial groundstate. Our studies, for the first time, reveal that the two 3D Dirac cones go through a topological change in the constant energy contour as a function of the binding energy, featuring a Lifshitz point, which is missing in a strict 3D analog of graphene (in other words Na3Bi is not a true 3D analog of graphene). Our results identify the first example of a band saddle point singularity in 3D Dirac materials. This is in contrast to its 2D analogs such as graphene and the helical Dirac surface states of a topological insulator. The observation of multiple Dirac nodes in Na3Bi connecting via a Lifshitz point along its crystalline rotational axis away from the Kramers point serves as a decisive signature for the symmetry-protected nature of the Dirac semimetals topological groundstate.
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