We present a hierarchical quantum master equation (HQME) approach, which allows the numerically exact evaluation of higher-order current cumulants in the framework of full counting statistics for nonequilibrium charge transport in nanosystems. The novel methodology is exemplarily applied to a model of vibrationally coupled electron transport in a molecular nanojunction. We investigate the influence of cotunneling on avalanche-like transport, in particular in the nonresonant transport regime, where we find that inelastic cotunneling acts as trigger process for resonant avalanches. In this regime, we also demonstrate that the correction to the elastic noise upon opening of the inelastic transport channel is strongly affected by the nonequilibrium excitation of the vibration as well as the polaron shift.
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