Electronic lifetimes in ballistic quantum dots electrostatically coupled to metallic environments

We calculate the lifetime of low-energy electronic excitations in a two-dimensional quantum dot near a metallic gate. We find different behaviors depending on the relative values of the dot size, the dot-gate distance, and the Thomas-Fermi screening length within the dot. The standard Fermi liquid behavior is obtained when the dot-gate distance is much shorter than the dot size or when it is so large that intrinsic effects dominate. Departures from the Fermi liquid behavior are found in the unscreened dipole case of small dots far away from the gate, for which a Caldeira-Leggett model is applicable. At intermediate distances, a marginal Fermi liquid is obtained if there is sufficient screening within the dot. In these last two nontrivial cases, the level width decays as a power law with the dot-gate distance.

Figure 1

(Color online). Sketch of system studied in the text.

Figure 2

(Color online). Diagram representing the calculation in Eq. (2). The filled bubble describes the time-dependent response of the environment (improper polarization). Labels $m$ and $n$ stand for electron states within the dot.

Figure 3

(Color online). Schematic behavior of the decay rate $\Gamma \left(E\right)$, of state of energy $E$, as a function of $E$, for the unscreened dipole case discussed in Sec. 3.