Electronic heat transport across a molecular wire: Power spectrum of heat fluctuations

With this study we analyze the fluctuations of an electronic heat current across a molecular wire. The wire is composed of a single energy level, which connects two leads that are held at different temperatures. By use of the Green function method we derive an explicit expression for the power spectral density of the emerging heat noise. This result assumes a form that is quite distinct from the power spectral density of the accompanying electric current noise. The complex expression simplifies considerably in the limit of zero frequency, yielding the heat noise intensity. The heat noise spectral density still depends on the frequency in the zero-temperature limit, assuming different asymptotic behaviors in the low- and high-frequency regions. These findings evidence that heat transport across molecular junctions can exhibit a rich structure beyond the common behavior that emerges in the linear response limit.

Figure 1

Setup of a molecular junction: two metal leads, filled with electron gas, are connected by a single-orbital ${\varepsilon }_0$. The coupling strengths are determined by the constants ${\Gamma }_{\text{L/R}}$. The left lead is prepared at a higher temperature as compared to the opposite right lead (i.e., $T_{\text{L}}>T_{\text{R}}$). The chemical potential, $\mu$, is the same for both leads so that no electric current due to a voltage bias is present.

Figure 2

Currents (top row) and zero-frequency components of PSDs of accompanying noises (bottom row) for charge (left column) and heat (right column) transport through the single-orbital wire as functions of orbital energy for $\Gamma =0.1$ meV. The remaining parameters are $T_L=5.2$ K, $T_R=3.2$ K (solid lines). For equal chemical potentials ${\mu }_L={\mu }_R=0$ the heat flow in panel (b) vanishes for equal temperatures $T_L=T_R$; its noise intensity in equilibrium at the temperature $T_L=T_R=4.2$ K is depicted versus orbital energy ${\varepsilon }_0$ by the dashed line in panel (d).

Figure 3

At zero-temperature $T_L=T_R=0$ the dependence of heat noise PSD versus frequency $\omega$ exhibits different power-law behaviors (dashed lines) for $\omega$ sampling intermediate values (proportional to ${\omega }^3$) as compared to the large frequency limit (proportional to ${\omega }^2$) when $\omega \to \infty$. The other parameters are ${\varepsilon }_0=0$ and $\Gamma =0.1\text{meV}$.