Thermopower of molecular junctions: Tunneling to hopping crossover in DNA

We study the electrical conductance G and the thermopower S of single-molecule junctions and reveal signatures of different transport mechanisms: off-resonant tunneling, on-resonant coherent (ballistic) motion, and multi-step hopping. These mechanisms are identified by studying the behavior of G and S while varying molecular length and temperature. Based on a simple one-dimensional model for molecular junctions, we derive approximate expressions for the thermopower in these different regimes. Analytical results are compared to numerical simulations, performed using a variant of Büttiker's probe technique, the so-called voltage-temperature probe, which allows us to phenomenologically introduce environmentally induced elastic and inelastic electron scattering effects, while applying both voltage and temperature biases across the junction. We further simulate the thermopower of GC-rich DNA sequences with mediating A:T blocks and manifest the tunneling-to-hopping crossover in both the electrical conductance and the thermopower, in accord with measurements by Li et al. [Nat. Commun. 7, 11294 (2016)].