Giant quantum freezing of nanojunctions mediated by the environment

We investigate the quantum heat exchange between a nanojunction and a many-body or electromagnetic environment far from equilibrium. It is shown that the two-temperature energy emission-absorption mechanism gives rise to a giant heat flow between the junction and the environment. We obtain analytical results for the heat flow in an idealized high-impedance environment, perform numerical calculations for the general case of interacting electrons, and discuss giant freezing and heating effects in the junction under typical experimental conditions.

Figure 1

Illustration of the nonequilibrium heating effects in a nanojunction. Electrons traversing the junction absorb external photons (incident wavy lines) and emit them, leading to heating of the contact. Plots show the giant heating effect, $\dot{Q}$, as a function of the difference of electron and environment temperatures ($V=0$) compared to the “quasiequilibrium” approximation, where the radiation density matrix is equilibrium, ${\dot{Q}}_0$. The full nonequilibrium analysis gives a heating effect that is at least 1 order of magnitude more pronounced than for the latter case: $\max (\dot{Q}/{\dot{Q}}_0)\sim \mathcal{N}>10$.

Figure 2

(a) Illustration of electron-hole pair generation in the tunnel junction, resulting in the distribution function $n_{\varepsilon }$ [Eq. (1)] of these pairs (environment). (b) Comparison of the distribution functions for $T=0$ in the leads and $T=V/2$.

Figure 3

Typical heat exchange $\dot{Q}$ in Eq. (1) of the ohmic environment with the tunnel junction between two normal leads. $\dot{Q}(T_{\mathrm{eff}},T,V)$ vs $T/T_0$ and voltages $\mathrm{eV}/T_0$ (scaling factor $T_0=30{\omega }_{\max }$.). We used ${\omega }_{\max }/{\omega }_{\min }=100$, $T_{\mathrm{env}}/T_0=1$, and $\rho \left(0\right)=10$. $\dot{Q}$ is measured in units of ${10}^3{\omega }_{\max }^2/\left(e^2{R}_T\right)$.

Figure 4

(a) Schematic presentation of the system: single contact junction, with contacts consisting of two thin plates, which are distance $d$ apart. Their thickness $a$ is much less than the extension in the $x$ and $y$ directions, such that they can be treated as two-dimensional contacts. The temperature of the contacts $T$ is kept constant, while the environment temperature $T_{\mathrm{env}}$ can be different, which results in heat production or removal in the junction. (b) Heating of a tunnel junction taking into account dynamic Coulomb interactions for the zero bias case ($V=0$) (red lines, lower $x$ axis) and the voltage dependence for $T=T_e$ (green lines, upper $x$ axis). The solid curves represent the quasiequilibrium curves and the dashed curves assume an equilibrium distribution for $N_{\omega }$ (temperature in units of $T_0=0.1E_{\mathrm{th}}$).