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Dirac points in two-dimensional massless Dirac fermions are topologicallyprotected. Although single Dirac point cannot disappear solely, a pair of twoDirac points annihilates after merging at a time-reversal invariant momentum(TRIM). This process triggers a topological phase transition. In this paper, wenumerically calculate the electronic specific heat ($C$) of the systems with ahoneycomb lattice and $\alpha$-(BEDT-TTF)$_2$I$_3$ in the case that two Diracpoints are moving and merging by changing the ratio of the magnitude betweenthe transfer integrals, which can be controlled by uniaxial pressure forexample. When two Dirac points are close to but not at TRIM, the temperaturedependence exhibits a crossover from $C\propto T^{2.0}$ (expected for separatedDirac points) at low temperatures ($T\leq T_{\rm co}$) to $C\propto T^{1.5}$(expected in the case of the merged Dirac points) at high temperatures ($T\geqT_{\rm co}$). Here, $T_{\rm co}$ denotes the crossover temperature, which isdetermined by the potential barrier magnitude between two Dirac points. Ourfindings demonstrate that the precursor of the topological phase transition isobserved through the temperature-dependence of the electronic specific heat.

Observable precursor of topological phase transition: temperature-dependent electronic specific heat in two-dimensional Dirac fermions