Fully Overheated Single-Electron Transistor

We consider the fully overheated single-electron transistor, where the heat balance is determined entirely by electron transfers. We find three distinct transport regimes corresponding to cotunneling, single-electron tunneling, and a competition between the two. We find an anomalous sensitivity to temperature fluctuations at the crossover between the two latter regimes that manifests in an exceptionally large Fano factor of current noise.

Figure 1

(a) SET biased by a voltage $V_b$. The charge in the central island can be tuned with the gate voltage $V_G$. (b) Coulomb diamonds in a symmetric SET. Blue dashed lines show the threshold voltage $V_C$ for SE tunneling. (c) Average temperature of the island versus bias voltage along the red vertical line in (b) for various tunnel conductances $G$. This illustrates the three transport regimes: I cotunneling, II competition, III SE tunneling. Dashed lines are asymptotes to pure cotunneling and pure SE tunneling.

Figure 2

(a) Differential conductance as a function of $V_b$ for several values of $G$. The dashed line is an asymptote for pure SE tunneling. (b) Temperature sensitivity $d(\ln I)/d(\ln T)$ as a function of $V_b$ for the same values. Inset: Fraction of SE transfers in the current flow.

Figure 3

Fano factor of the temperature-fluctuation-induced current noise for different values of $G/G_Q$. The dashed line is an analytic approximation for $G/G_Q={10}^{-6}$, and agrees well with the numerical result. The inset shows the Fano factor for $G/G_Q={10}^{-6}$ in an absolute voltage scale for various values of $e{V}_G/E_C$. The peaks fall on top of each other once rescaled to common $V_C$.