Dynamical time-reversal and inversion symmetry breaking, dimensional crossover, and chiral anomaly in $\alpha$-(BEDT-TTF)$_2$I$_3$

In most Dirac semimetals, time-reversal and inversion symmetries are believed to play a crucial role in their stability. We demonstrate that these symmetries are broken in Dirac fermions in the organic conductor $\alpha$-(BEDT-TTF)$_2$I$_3$ due to the strong electronic correlation. The system is a three-dimensional type-II Dirac semimetal in the coherent inter-layer tunneling regime. A chiral anomaly is predicted to be observed in the magnetoresistance when the magnetic field is tuned to the inter-layer tunneling direction. Our result suggests that $\alpha$-(BEDT-TTF)$_2$I$_3$ is a useful platform to explore the interplay between the chiral anomaly and the strong correlation and/or dimensionality.