Thermal transfer enhancement by hydrodynamic plasmons in electron bilayers

We develop a theory of heat transfer induced by thermal charge fluctuations in two-dimensional electron double layers. We consider pristine systems comprised of identical layers, and focus on the regime of sufficiently high temperatures and interlayer distances $d$, where the relevant charge fluctuations may be described using the hydrodynamic approach. In this limit heat transfer is dominated by the plasmon resonances. For systems with Galilean-invariant electron dispersion the interlayer thermal conductance $\mathrm{\varkappa }$ is proportional to the kinematic viscosity of the electron liquid, and decreases as $1\mathrm{/}{d}^4$. In the absence of Galilean invariance $\mathrm{\varkappa }\propto \sigma \mathrm{/}{d}^3$, where $\sigma$ is the intrinsic conductivity of the liquid. This strong enhancement can be traced to a drastically different broadening of plasmon resonances in systems with and without Galilean invariance.