Quantum interference in off-resonant transport through single molecules

Abstract

We provide a simple set of rules for predicting interference effects in off-resonant transport through single molecule junctions. These effects fall into two classes, showing, respectively, an odd or an even number of nodes in the linear conductance within a given molecular charge state, and we demonstrate how to decide the interference class directly from the contacting geometry. For neutral alternant hydrocarbons, we employ the Coulson-Rushbrooke-McLachlan pairing theorem to show that the interference class is decided simply by tunneling on and off the molecule from same or different sublattices. More generally, we investigate a range of smaller molecules by means of exact diagonalization combined with a perturbative treatment of the molecule-lead tunnel coupling. While these results generally agree well with GW calculations, they are shown to be at odds with simpler mean-field treatments. For molecules with spin-degenerate ground states, we show that for most junctions interference causes no transmission nodes, but we argue that it may lead to a nonstandard gate dependence of the zero-bias Kondo resonance.

Destructive quantum interference in electron transport: A reconciliation of the molecular orbital and the atomic orbital perspective

“…where one contact atom is starred and the other one unstarred or for non-alternant hydrocarbons or for conjugated π systems containing hetero atoms, the pairing theorem can neither predict nor rule out DQI. In the literature these two cases are sometimes distinguished in terms of "easy zeros" (the same subset contacted) and "hard zeros" (different subsets contacted) 53 or linked to the occurence of an odd or even number of zeroes in T (E) 51,52 . But for the purpose of our article the important distinction is that for even-membered alternant hydrocarbons contacted at sites of the same subset DQI will always occur, while for all other cases DQI cannot be predicted without numerical calculations from a MO perspective.…”

“…5 cancel exactly at E F for this case and DQI occurs as a result as has also been observed in Refs. 51,52 . If on the other hand the contact AOs l and r belong to carbon atoms from different subsets, then (L+k) .…”

Interference enhanced thermoelectricity in quinoid type structures

“…This has the advantage that in the weak molecule lead coupling limit this analysis can be generalised for the correlated electron case by considering so-called Dyson orbitals and energies. 44 We argue that the central quinoid core structure is responsible for the two transmission nodes. This can be seen either based on graphical rules developed to predict QI in Hückel models 11 or by systematically reducing the Kohn-Sham Hamiltonian atom by atom as will be discussed below.…”

“…The use of quasi-particle energies instead of Hückel molecular yields split interference features. 44 The two central DQI features of the quinoid structure, see Figures 1(a) and 1(c), can be accounted for by considering the four molecular orbitals closest to the Fermi level (HOMO-1, HOMO, LUMO, LUMO+1). This may be seen by first considering the condition for the transmission going to zero, T(ε) ∝ |G l r (ε)| 2 = 0.…”

“…12,44 In terms of the analysis presented here, which was based on Eq. (1), the doubly degenerate transmission node can be interpreted graphically as in Figure 4(a).…”