Since the first experimental observation of the phonon Hall effect (PHE) in 2005, its physical origin and theoretical explanation have been extensively investigated. While spin-orbit interactions are believed to play important roles under external magnetic fields, nonmagnetic effects are also possible. Here, we propose a mechanism of PHE which is induced by electric current in a nonequilibrium system through electron-phonon interactions. The influence of the drift electrons to the phonon degrees of freedom, as a correction to the Born-Oppenheimer approximation, is represented by an antisymmetric matrix which has the same form as in a typical phonon Hall model. We demonstrate the idea with a graphene-like hexagonal lattice having a finite phonon Hall conductivity under a driven electric current.
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