Conductance in Coulomb blockaded molecules—fingerprints of wave-particle duality?

Abstract

In molecular electronics it is common to use the so called “NEGF-DFT” prescription where the mean-field describing electron–electron interactions is identified with the “Kohn–Sham potential” from density functional theory (DFT). However, a large number of experimentally observed molecular current–voltage (I–V) characteristics belong to the Coulomb blocade (CB) limit, and exhibit evidence of a rich interplay between charge quantization and size quantization, i.e. between particle and wave aspects of an electron. Although, NEGF-DFT techniques take into account the wave nature of electrons, they are essentially one-electron potentials and are inadequate to describe Coulomb blockade regime, especially under non-equilibrium conditions. Here, we present simple examples to illustrate the fact that such mean-field theories that may describe equilibrium properties do not necessarily describe non-equilibrium properties (like current flow) as well. While weak coupling with contacts and the associated charge quantization produce a suppressed zero-bias conduction or Coulomb Blockade followed by a staircase, size quantization generates an extensive body of single-particle excitations that create a quasiohmic rise in current with gateable onset voltages and symmetry properties. We discuss the underlying physics of these conduction processes using minimal models, starting with Coulomb blockade in a single spin-degenerate quantum dot, and subsequently the emergence of excitations in a double dot with singlet–triplet levels. The results bear compelling parallels with experimental results, underscoring the inadequacy of orthodox Coulomb blockade theory for size quantization, as well as traditional mean-field quantum transport calculations that only capture a small subset of the corresponding excitations within the molecular many-body Fock space.