2025/04/17 by Kishigi, Keita, Hasegawa, Yasumasa
#FOS: Physical sciences #Materials Science (cond-mat.mtrl-sci) #Mesoscale and Nanoscale Physics (cond-mat.mes-hall)
paper · doi:10.48550/arxiv.2504.12779
Two-dimensional massless Dirac fermions exhibit Dirac cones, which are classified into three types: type-I, type-II, and type-III. In both type-I and type-II cones, the energy dispersion is linear in all momentum directions. Type-I cones are characterized by a non-overtilted structure, where the Dirac point serves as a local minimum (maximum) for the upper (lower) band. In contrast, type-II cones exhibit overtilted dispersions, leading to the coexistence of electron and hole pockets. At the critical tilt, the linear energy dispersion vanishes in one momentum direction, corresponding to a type-III Dirac cone. We further define a special case, termed the "narrow-sense" type-III cone, where not only the linear term but also quadratic and higher-order terms vanish, resulting in a completely flat dispersion along one direction. In this work, we numerically investigate the temperature (T) -dependence of the electronic specific heat (C), as the Dirac cone is continuously tilted from type-I to narrow-sense type-III. A model with particle-hole symmetry is employed to ensure that the chemical potential (μ) remains temperature independent. Our results reveal a notable crossover in C near narrow-sense type-III, where C changes from C ∝ T2 below the crossover temperature (T\rm co) to C ∝ T(1)/(2) above T\rm co. This crossover is attributed to the energy-dependent structure of the density of states. The present findings suggest a feasible approach for experimentally probing the degree of Dirac cone tilting near the narrow-sense type-III limit.