Quantum Interference Supernodes, Thermoelectric Enhancement, and the Role of Dephasing

Abstract

Quantum interference (QI) can strongly enhance thermoelectric response, with higher-order "supernodes" predicted to yield scalable gains in thermopower and efficiency. A central question, however, is whether such features are intrinsically more fragile to dephasing. Using $Büttiker$ voltage-temperature probes, we establish an order-selection rule: the effective near-node order is set by the lowest among coherent and probe-assisted channels. Supernodes are therefore fragile in an absolute sense because their transmission is parametrically suppressed with order. However, once an incoherent floor dominates, the fractional suppression of thermopower, efficiency, and figure of merit becomes universal and order-independent. Illustrating these principles with benzene- and biphenyl-based junction calculations, we show that the geometry of environmental coupling -- through a single orbital or across many -- dictates whether coherence is lost by order reduction or by floor building. These results yield general scaling rules for the thermoelectric response of interference nodes under dephasing.

Figures (14)

• Figure S1: Transmission functions with a single probe. The $\pi$-system transmissions for benzene-dithiol (BDT, top) and biphenyl-dithiol (BPDT, bottom) junctions are shown. Solid, dashed, and dash-dotted curves correspond to the $LR$, $LP$, and $RP$ channels, respectively. Fits of the form ${\cal T}(E)\propto|E{-}E_{0}|^{2n}$ are overlaid, with the extracted exponents indicated in the legend. In the BDT junction, the nodal scaling is quadratic ($n=1$). In the BPDT junction, higher-order behavior emerges: quartic scaling ($n=2$), characteristic of a transmission supernode, together with nearly flat background contributions from probe-mediated incoherent transport. Because the thermopower is proportional to the energy derivative of the transmission, higher-order nodes (larger $n$) produce correspondingly sharper features and enhanced thermopower responses. Insets show the molecular junction geometries and probe coupling sites. Exponents were extracted over the range $|E{-}E_0|\leq0.3\,$eV. Calculations used the parameters discussed in Section \ref{['sec:hamiltonian']} and assume room temperature $T_0=300\,\mathrm{K}$.
• Figure : ( a) BDT Junction
• Figure : ( a) BDT Junction
• Figure S4: All-site dephasing renders fractional suppression order-agnostic. With one probe per site (each coupled with $\Gamma_{\rm P}/N$, so the total is $\Gamma_{\rm P}$), the normalized decays of $ZT_{\rm el}$, $\eta$, and $S$ versus $\Gamma_{\rm P}$ are nearly indistinguishable for BDT (quadratic node; left vertical axis) and BPDT (quartic supernode; right vertical axis) at $T=300$ K. This demonstrates that once a probe-induced floor is present, the fractional reduction of the response is governed primarily by $B(\Gamma_{\rm P})$ and is largely insensitive to the coherent order. Absolute values can still remain larger for supernodes, reflecting their higher coherent-limit enhancements, but the shape of the decay is universal. The modest residual curvature differences reflect geometry-dependent prefactors rather than a distinct order-selection mechanism.
• Figure : ( a) BDT Junction