Nonadiabatic electron heat pump

We investigate a mechanism for extracting heat from metallic conductors based on the energy-selective transmission of electrons through a spatially asymmetric resonant structure subject to ac driving. This quantum refrigerator can operate at zero net electronic current as it replaces hot with cold electrons through two energetically symmetric inelastic channels. We present numerical results for a specific heterostructure and discuss general trends. We also explore the conditions under which the cooling rate may approach the ultimate limit given by the quantum of cooling power.

Figure 1

Asymmetric double-well heterostructure used for electron ac transport calculations. Energy levels are symmetrically placed around the common Fermi level. Dominant transmission processes contributing to cooling are shown: in lead R hot electrons are replaced with cold electrons, all within a range $\sim k_{B}T$ around $\mu$.

Figure 2

(Color online) (a) Heat production rate in lead R for the structure of Fig. 1 as a function of the driving amplitude $e{V}_{\mathrm{ac}}$ for various lead temperatures and $\hslash \Omega =1.94\mathrm{meV}$. See main text for details. (b) For $T=20\mathrm{K}$, heating contributions from inelastically reflected electrons (solid line) and total electric current (line) are shown.

Figure 3

(Color online) Cooling rate of the R electrode as a function of its temperature $T_{\mathrm{R}}$ for several values of $T_{\mathrm{L}}⩾T_{\mathrm{R}}$, with $\mu$ adjusted to yield zero electric current, for $\hslash \Omega =1.94\mathrm{meV}$ and $e{V}_{\mathrm{ac}}∕\hslash \Omega =0.2$.