Near-field heat transfer and drag resistance in bilayers of composite fermions

Heat transfer is studied in the system of electron double layers of correlated composite fermion quantum liquids. In the near-field regime, the primary mechanism governing interlayer energy transfer is mediated by the Coulomb interaction of thermally-driven charge density fluctuations. The corresponding interlayer thermal conductance is computed across various limiting cases of the composite fermion Chern-Simons gauge theory, encompassing ballistic, diffusive, and hydrodynamic regimes. Plasmon enhancement of the heat transfer is discussed. The relationship between the heat transfer conductance and the drag resistance is presented for electron states formed in the fractional quantum Hall effect of even denominator filling fractions.

Figure 1

Schematic representation of the interactively coupled two-dimensional composite fermion liquids formed in an electron double layer system with interlayer spacing $d$. The composite fermion quasiparticles are depicted as circles with attached fluxes $\varphi$ labeled by arrows. The interlayer coupling is denoted by the Coulomb potential $U_{12}$. The underlying background of each layer represents disorder potential. Each layer is kept at different temperatures $T_{1,2}$ and wavy dashed lines pointing up or down represent vertical heat fluxes $J_{1,2}$ between the layers generated in the near-field regime.

Figure 2

Plots of the dimensionless function $\mathcal{F}$ defined by Eq. (16) that show its dependence on the interlayer separation $d$ at different temperatures as described by the dimensionless parameter ${\alpha }_T$ (top) and vise versa, the dependence on ${\alpha }_T$ at several values of $k_{\text{TF}}d$ (bottom).

Figure 3

Temperature dependence of the dimensionless thermal transfer conductance $\mathcal{K}=\varkappa /{\varkappa }_0$ [from Eq. (6)] plotted in the units of ${\varkappa }_0=r_s^2\nu v_{\text{F}}/8\pi {\varphi }^2{k}_{\text{F}}{d}^3$. The bottom panel shows the same data as the top panel but zoomed into the low-temperature domain of parameters.

Figure 4

Numerically evaluated dimensionless functions that describe the plasmon enhancement of thermal conductance $\varkappa$. Plasmon resonances are most pronounced for ${\mathrm{\Omega }}_p\tau >1$ therefore we constrain the plot only to the values of $\beta <1$.

Figure 5

Temperature dependence of the drag resistance presented in the dimensionless units. Based on Eq. (35) $\mathcal{R}$ is defined by ${\rho }_D$ in units of ${(1/4\pi e)}^2{(1/n{d}^2)}^2$ whereas ${\alpha }_T\propto T$. The domain of validity of Eq. (37), when $\mathcal{R}\propto T^{4/3}$, is limited to the lowest temperatures $T\ll E_{\text{F}}/{\left(k_{\text{F}}d\right)}^2$. Above this scale drag resistance is nearly linear in temperature $\mathcal{R}\propto TlnT$, see Eq. (40).