Edge-channel interference controlled by Landau level filling

We study the visibility of Aharonov-Bohm interference in an electronic Mach-Zehnder interferometer in the integer quantum Hall regime. The visibility is controlled by the filling factor $\nu$ and is observed only between $\nu \approx 2.0$ and 1.0, with an unexpected maximum near $\nu =1.5$. Three energy scales extracted from the temperature and voltage dependences of the visibility change in a very similar way with the filling factor, indicating that the different aspects of the interference depend sensitively on the local structure of the compressible and incompressible strips forming the quantum Hall edge channels.

Figure 1

SEM image of smaller Mach-Zehnder interferometer with the scheme of edge states for filling factor 2. The transmissions of QPC1 and QPC2 are set to 0.5. QPC0 reflects the inner edge channel (dashed line) and transmits the outer one (solid line). MG shifts the phase.

Figure 2

(Color online) (a) Two terminal magnetoconductance of the large interferometer with all QPCs opened. Inset shows an example of interference pattern at $B=4.7\text{T}$. (b) Visibility versus magnetic field for both interferometers. Full and open squares correspond to data acquired with at least 4 h waiting time, full circles with 1 h.

Figure 3

(Color online) (a) Visibility versus magnetic field for two back gate voltages, i.e., electron densities. (b) Determination of the $\nu =1.5$ point. Current recorded at detector D2, when QPC1 is closed and QPC2 is opened. The peak in each curve corresponds to maximum scattering between edges in the lower MZI arm and correspond to $\nu =1.5$. Inset: Data from (a) plotted vs filling factor.

Figure 4

(a) Temperature dependencies of visibilities for large (open symbols) and small (full symbols) MZIs at different magnetic fields. The curves “a” and “b” for $B=4.8\text{T}$ correspond to different QPC half transmission points. Inset: Characteristic temperatures $T_0$ extracted from the exponential fits according to Eq. (1). The data for the large interferometer (open circles) have been multiplied by 2.

Figure 5

Differential visibility of the small MZI. (a) Lobe structures at different magnetic fields at $V_{\text{BG}}=-25\text{V}$. (b) Characteristic energies ${\epsilon }_L$ and ${\epsilon }_0$ (see text) extracted from ${\nu }_I\left(V\right)$ together with $k_B{T}_0$ as a function of magnetic field $B$.