Temperature-driven Topological Phase Transition and Intermediate Dirac Semimetal Phase in ZrTe$_5$

We present an infrared spectroscopy study of ZrTe$_5$, which confirms a recent theoretical proposal that this material exhibits a temperature-driven topological quantum phase transition from a weak to a strong topological insulating state with an intermediate Dirac semimetal state around $T_p \simeq$ 138K. Our study details the temperature evolution of the energy gap in the bulk electronic structure. We found that the energy gap closes around $T_p$ where the optical response exhibits characteristic signatures of a Dirac semimetal state, i.e. a linear frequency-dependent optical conductivity extrapolating to the origin (after subtracting a weak Drude response). This finding allows us to reconcile previous diverging reports about the topological nature of ZrTe$_5$ in terms of a variation of $T_p$ that depends on the crystal growth condition.