Photon-assisted electron-hole shot noise in multiterminal conductors

Motivated by a recent experiment by Reydellet et al. [Phys. Rev. Lett. 90, 176803 (2003)] we discuss an interpretation of photon-assisted shot noise in mesoscopic multiprobe conductors in terms of electron-hole pair excitations. ac voltages are applied to the contacts of the sample. Of interest are correlations resulting from the fact that electrons and holes are generated in pairs. We show that with two out-of-phase ac potentials of equal magnitude and frequency, applied to different contacts, it is possible to trace out the Hanbury Brown Twiss exchange interference correlations in a four probe conductor. We calculate the distribution of Hanbury Brown Twiss phases for a four-probe single channel chaotic dot.

Figure 1

(Color online) An ac-bias voltage $V_1\cos \omega t$ in lead 1 excites correlated $\left(e\right)$ electron-$\left(h\right)$ hole pairs. In the zero-temperature limit, the zero-frequency current cross-correlation between the second and third lead is generated only by pairs which are split, one carrier sent into lead 2 and one carrier into lead 3. The current-correlation is a direct measure of the coincident generation of electron and hole in a pair.

Figure 2

(Color online) Electron-hole pairs originating from the lead 1 or 2 contribute to cross-correlations measured in 3 and 4. Indistinguishability of the sources leads to the dependence of the shot noise $S_{34}$ on the relative phase $\Delta \varphi$ of the voltage sources.

Figure 3

Mesoscopic distribution $P_{\beta }\left(\chi \right)$ of HBT phase $\chi$ that maximizes the value of cross-correlations $S_{34}$ in quantum dots. Angle $\chi$ is normalized by $\pi$ and $P_{\beta }(-\chi )=P_{\beta }\left(\chi \right)$. The difference between the presence of TRS (solid) and absence of TRS (dashed) is due to different distributions $P_{\beta }\left(\mathcal{T}\right)$ in Eq. (23).

Figure 4

Distribution functions of $S^{+}$ and $S^{-}$ (inset) for quantum dots with (solid) and without (dashed) time-reversal symmetry. Mesoscopic averages are similar in both cases, but the fluctuations are large. At small arguments $S^{-}$, the distributions on the inset are divergent as $P\left(S^{-}\right)\propto 1∕\sqrt{S^{-}}$.