Nanotransformation and Current Fluctuations in Exciton Condensate Junctions

We analyze the nonlinear transport properties of a bilayer exciton condensate that is contacted by four metallic leads by calculating the full counting statistics of electron transport for arbitrary system parameters. Despite its formal similarity to a superconductor the transport properties of the exciton condensate turn out to be completely different. We recover the generic features of exciton condensates such as counterpropagating currents driven by excitonic Andreev reflections and make predictions for nonlinear transconductance between the layers as well as for the current (cross)correlations and generalized Johnson-Nyquist relationships. Finally, we explore the possibility of connecting another mesoscopic system (in our case a quantum point contact) to the bottom layer of the exciton condensate and show how the excitonic Andreev reflections can be used for transforming voltage at the nanoscale.

Figure 1

Sketch of the experimental setup. The double layer EC is contacted with four metallic electrodes.

Figure 2

(a) current in the top (red) and bottom (blue) layer as a function of $V_T$, for a fixed value $V_B=\Delta /2$. ${\Gamma }_{LT}={\Gamma }_{LB}=0.171$ corresponds to transmission of 0.5 for the uncoupled system, $T=0.01\Delta$. For $|V_T|$, $|V_B|<2\Delta$ the bilayer exhibits counterpropagating currents, exciton blockade occurs at $V_B=V_T$. (b) differential conductance $d{I}_T/d{V}_T$ (red) shows a resonance peak and tends to the typical value for a quantum point contact whereas the transconductance $d{I}_B/d{V}_T$ shows a resonance peak before vanishing at larger bias.

Figure 3

(a) The parallel bias configuration (exciton blockade). Noise and cross correlations are shown as a function of $V_T=V_B=V$, for the three values of transmission for the uncoupled system of 0.3 (black), 0.5 (blue), 0.7 (red), and $T=0.01\Delta$. (b) The antiparallel bias configuration (counterpropagating currents). Noise and cross correlations are shown as a function of $V_T=-V_B=V$, again for the three values of contact transparency.

Figure 4

Transformation of voltages using the EC. We show $V_B$ due to the current in the bottom layer coupled to a quantum point contact as a function of the applied voltage $V_T$ for different transparencies of the QPC, ${\Gamma }_{LT}=0.2={\Gamma }_{RT}={\Gamma }_{LB}={\Gamma }_{RB}$ and the QPC transparency is varied from $T_1=0.1$ (blue curve), $T_1=0.3$ (red) to $T_1=0.7$ (black). The inset shows the sketch of the experimental setup.