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We show that when the electron and hole densities are unbalanced, observablenonlinear anomalous Hall effect and current-induced orbital magnetizationappear at zero magnetic field in the weak charge ordering (CO) state of anorganic two-dimensional Dirac fermion system, a-(BEDT-TTF)2I3. Thesecurrent-induced phenomena are caused by a finite Berry curvature dipoleresulting from inversion symmetry breaking and Dirac cone tilting. In theactual system, however, these effects are canceled out between different typesof inversion asymmetric CO domains. To avoid the cancellation, we propose a newexperimental method to realize the selective formation of a single type ofdomain using the current-induced magnetization.

Possible Current-Induced Phenomena and Domain Control in an Organic Dirac Fermion System with Weak Charge Ordering