Anomalous Phase-Coherence Scaling in a Quantum-Critical Dirac Semimetal

We have investigated the weak antilocalization (WAL) in the pressurized Dirac semimetal $\alpha$-(BEDT-TTF)$_2$I$_3$ across a correlation-driven quantum phase transition to a charge-ordered insulating state and evaluated the phase coherence length $L_{\phi}$ and its temperature scaling under various pressures from the low-temperature magnetoconductivity. In the high-pressure regime, the system exhibits the conventional two-dimensional dephasing behavior ($L_{\phi} \propto T^{-p}$ with $p \approx 1/2$), characteristic of electron-electron scattering in diffusive conductors. As the pressure approaches the critical pressure ($P_c \sim 1.2$ GPa), the temperature exponent is suppressed to $p \sim 0.3$, while $L_{\phi}$ remains large ($700\text{-}800$ nm at 0.5 K). This anomalous scaling suggests nontrivial inelastic scattering associated with Dirac electrons near the quantum critical point. The persistence of WAL across the transition supports a gapless or nearly gapless quantum phase transition.