Abstract
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 ±ln2/(J − 1/2) with 2 ≤ J ≤ 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.
Highlights
Entropy is an important fundamental property of many-body systems
The quantization of entropy per electron was interpreted in ref. 2 as a signature of the Lifshitz electronic topological transition[3], which in the 2D case is characterised by a discontinuity in the electronic density of states (DOS)
We show that the entropy per electron in these systems acquires quantized universal values at low temperatures if the chemical potential passes through the edge of consequent gaps
Summary
Entropy is an important fundamental property of many-body systems. It governs their thermodynamics, heat transfer, thermoelectric and thermo-magnetic properties. Lifshitz transitions widely occur in multi-valley semimetals, doped semiconductor quantum wells, multi-band superconducting systems such as iron-pnictide compounds[5] and in 2D Dirac materials, as we discuss below In this Report, we analyze theoretically the behavior of the entropy per particle as a function of the chemical potential in a gapped graphene deposited on a substrate and other low-buckled Dirac materials, e.g. silicene and germanene. We show that the entropy per electron in these systems acquires quantized universal values at low temperatures if the chemical potential passes through the edge of consequent gaps. It is a universal property of electronic systems characterised by a step-like behaviour of the density of states. We believe that the measurements of the entropy per particle (e.g. following the technique of ref. 1) may reveal hidden peculiarities of the band structure of new materials
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