Heat flow in nonlinear molecular junctions: Master equation analysis

We investigate the heat conduction properties of molecular junctions comprising nonlinear interactions. We find that these interactions can lead to phenomena such as negative differential thermal conductance and heat rectification. Based on analytically solvable models we derive an expression for the heat current that clearly reflects the interplay between internal molecular anharmonic interactions, the strength of molecular coupling to the thermal reservoirs, and junction asymmetry. This expression indicates that negative differential thermal conductance shows up when the molecule is strongly coupled to the thermal baths, even in the absence of internal molecular nonlinearities. In contrast, diodelike behavior is expected for a highly anharmonic molecule with an inherent structural asymmetry.

Figure 1

Conduction properties of a TLS system in the weak coupling limit. ${\omega }_0=150\mathrm{meV}$ (full), $100\mathrm{meV}$ (dashed), $25\mathrm{meV}$ (dotted). $T_s=400\mathrm{K}$ (model A), ${\Gamma }_K=1.2\mathrm{meV}$. Inset: Rectifying behavior of this model, ${\omega }_0=25\mathrm{meV}$, $\chi =0.75$ and $T_L=400\mathrm{K}$, $T_R=T_L-\Delta T$ (full); $T_R=400\mathrm{K}$, $T_L=T_R-\Delta T$ (dashed).

Figure 2

Conduction properties of the TLS system in the strong coupling limit $T_R=T_L-\Delta T$ (model A), $E_M^K=300\mathrm{meV}$ $(K=L,R)$, $V=1\mathrm{meV}$, ${\omega }_0=10\mathrm{meV}$, $T_L=500\mathrm{K}$ (full), $T_L=400\mathrm{K}$ (dashed), $T_L=300\mathrm{K}$ (dotted).

Figure 3

Controlling NDTC by modifying system-baths interaction strengths for a TLS model in the strong coupling limit. $T_R=T_L-\Delta T$ (model A), $T_L=300\mathrm{K}$, $V=1\mathrm{meV}$, ${\omega }_0=10\mathrm{meV}$, $E_M^K=10$ (full), $E_M^K=100$ (dashed), $E_M^K=150$ (dotted).

Figure 4

Rectification in the strong coupling limit for a TLS system. $E_M=300\mathrm{meV}$, $V=1\mathrm{meV}$, ${\omega }_0=10\mathrm{meV}$, $T_L=300\mathrm{K}$, $T_R=T_L-\Delta T$ (full); $T_R=300\mathrm{K}$, $T_L=T_R-\Delta T$ (dashed).

Figure 5

An overview of the parameter ranges providing negative differential thermal conductance (NDTC) and diodelike behavior. The $x$ axis (weak and strong coupling) relates to the system-bath interaction model. In order to obtain rectification the system should be asymmetric with respect to the $L$ and $R$ ends.