Photon heat transport in low-dimensional nanostructures

At low temperatures when the phonon modes are effectively frozen, photon transport is the dominating mechanism of thermal relaxation in metallic systems. Starting from a microscopic many-body Hamiltonian, we develop a nonequilibrium Green’s function method to study energy transport by photons in nanostructures. A formally exact expression for the energy current between a metallic island and a one-dimensional electromagnetic field is obtained. From this expression, we derive the quantized thermal conductance as well as show how the results can be generalized to nonequilibrium situations. Generally, the frequency-dependent current noise of the island electrons determines the energy transfer rate.

Figure 1

(Color online) Metallic island (blue) coupled to the electromagnetic field of a transmission line (lines around the yellow region). The voltage between the strips is ${\widehat{V}}_{\mathrm{TL}}$.

Figure 2

(Color online) (a) Circuit picture corresponding to the studied system. Transmission line acts as a series resistor to the island. In (b), the parallel transmission lines couple to vertical current noise, and in (c), the lines couple to vertical and horizontal noise. The maximum heat conductance in (b) is $G_Q$ and in (c) is $2G_Q$. The number of parallel transmission lines is irrelevant for the maximum heat conductance. In (d), the island contains a short conductor and is externally biased.

Figure 3

(Color online) Energy flow from a symmetric chaotic cavity $(N_L=N_R=1)$ as a function of voltage. We assumed that the cavity conductance at zero frequency $G_e\left(0\right)$ is matched to $Z_0^{-1}$. The different curves correspond to different cavity charge relaxation times $\tau$: $\tau =0$ (solid), $\tau =0.1\hslash \beta$ (dashed), $\tau =\hslash \beta$ (dotted), and $\tau =10\hslash \beta$ (dash dotted). The inset shows the $\tau ∕\hslash \beta$ dependence of the heat flow from the cavity $(V=0)$; the horizontal dashed line corresponds to the heat flow from an ideally matched Ohmic resistor without frequency dependence. When $\tau ∕\hslash \beta ⪡1$, the heat flow is close to the theoretical maximum and settles to a lower value as the fraction increases.