Distinguishing Tunneling from Hopping—Temperature, Length and Voltage Behavior

A key question of molecular electronics is how far the charge transport is coherent, which is often coded to ‘<i>tunneling</i>’ (coherent) vs. ‘<i>hopping</i>’ (incoherent). Although coherent transport is associated with rich quantum mechanical phenomena, coherent electrons are “too-fast” to interact with the molecular medium and therefore yield a rather featureless voltage response. In contrast, incoherent transport involves molecular deformation and environment polarization, which leads to far richer current-voltage characteristics. Traditionally, the lack or existence of <i>temperature </i>dependence is taken as a prime criterion for <i>tunneling </i>or <i>hopping</i>, respectively. However, there are opposite cases of <i>temperature</i>-independent <i>hopping </i>(as in inverted Marcus regime) or <i>temperature</i>-dependent <i>tunneling </i>(by temperature broadening of DOS of the contacts). Overall, it undermines the reliability of <i>temperature </i>response for <i>tunneling / hopping</i> distinction. It is less known, that also the <i>voltage</i>-response differs considerably between the two mechanisms: off-resonance <i>tunneling </i>is characterized by mild, polynomial <i>voltage </i>dependence in contrast to <i>hopping</i>, which is characterized by a strong, exponential dependence on <i>voltage</i>. The third control-parameter, <i>length</i>, has somewhat ‘opposite’ effect: <i>tunneling </i>decays exponentially (strongly) with <i>length</i>, and <i>hopping </i>is only weakly <i>length</i>-dependent. Therefore, it is often argued that <i>hopping </i>is typical of long transport distance, exceeding ∼4 nm. In contrast, we recently demonstrated transport by <i>hopping </i>across a minute distance of merely ∼1 nm. Moreover, observing the combined interplay of the three parameters: <i>temperature</i>, <i>voltage </i>and <i>length</i>, reveals behavior that exceed simplistic models, suggesting that the real transport model is yet beyond our conceptualization. My talk will bring various examples of experimental transport traces and suggest possible analytical protocols to elucidate the <i>tunneling - hopping</i> dilemma.