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We study the tunneling phenomenon of a ladder system with a Peierlsdistortion in a magnetic flux, and the response of electrons the insulator isinvestigated when the tunneling current flows on one-dimensional gapped chainsalong the external electric field. Without the magnetic field, the laddersystem is insulated by the charge density wave order. Then, by the increase ofthe magnetic field, it becomes metallic with the disappearance of thedistortion of the lattice.  Finally, the gap appears, and it becomes a insulator.  At the metallic state, the topological transition also occurs. To show thisphenomenon, we consider the distortion by the phonon in the ladder model, andcalculate the distortion gap and the transition probability by using bothLandau-Zener formula and the instanton method. The transition to the metallicstates will be applied to the current control by the magnetic field.

Current control of systems with a Peierls distortion by magnetic field