Unusual thermodynamics of low-energy phonons in the Dirac semimetal Cd_(3)As_(2)

By studying the thermal conductivity,specific heat,elastic modulus,and thermal expansion as a function of temperature for Cd_(3)As_(2),we have unveiled a couple of important thermodynamic features of the low-energy phonons strongly interacting with Dirac electrons.The existence of soft optical phonons,as inferred from the extremely low thermal conductivity,is unambiguously confirmed by low-temperature specific heat revealing significant deviation from Debye's description.The estimated Debye temperature is small in the range of 100-200 K and varies significantly depending upon the measurement used in its experimental determination.The thermodynamic Gr¨uneisen ratioγreveals a remarkable reduction below about 100 K,an energy scale that is highly relevant to the Dirac states,towards negative values below about 10 K that are indicative of lattice instability.