Resonant Dephasing in the Electronic Mach-Zehnder Interferometer

We address the recently observed unexpected behavior of Aharonov-Bohm oscillations in the electronic Mach-Zehnder interferometer that was realized experimentally in a quantum Hall system [I. Neder et al., Phys. Rev. Lett. 96, 016804 (2006)]. We argue that the measured lobe structure in the visibility of oscillations and the phase rigidity result from a strong long-range interaction between two adjacent counterpropagating edge states, which leads to a resonant scattering of plasmons. The visibility and phase shift, which we express in terms of the transmission coefficient for plasmons, can be used for the tomography of edge states.

Figure 1

Schematic representation of the electronic Mach-Zehnder interferometer experimentally realized in Ref. 3. Two edge states (blue lines, ${\varphi }_1$ and ${\varphi }_2$), which propagate from left to right, are coupled via two quantum point contacts and form the Aharonov-Bohm loop. The bias $\Delta \mu$ applied to one of the source Ohmic contacts causes the current $I$ to flow around the loop, so that the differential conductance $G=dI/d\Delta \mu$ oscillates as a function of the phase ${\phi }_{\mathrm{AB}}$. The specific property of the setup in Ref. 3 is that the third counterpropagating edge state (red line, ${\varphi }_3$) closely approaches the upper branch of the MZ interferometer (inside the resonator shown by a dashed box) and strongly interacts with it.

Figure 2

In the case of a long-range interaction of counterpropagating edge states at the resonator of the length $L$ (see Fig. 1), the visibility of Aharonov-Bohm oscillations varies as a function of the normalized bias, $\Delta \mu L/2v_F$, in a lobelike manner. The phase of AB oscillations (not shown) stays constant at the lobes and changes abruptly by $\pi$ at zeros of the visibility. The visibility is plotted here for the simplified capacitive coupling model, Eq. (14), with $T_L=T_R$.

Figure 3

The visibility for the case of a short-range interaction inside the resonator (Luttinger constant $K=0.1$) is plotted versus bias normalized to the interaction dependent group velocity $v$ of plasmons.