Universality of bias- and temperature-induced dephasing in ballistic electronic interferometers

We performed a transport measurement in a ballistic Aharonov-Bohm ring and a Fabry-Pérot-type interferometer. In both cases we found that the interference signal is reversed at a certain bias voltage and that the visibility decays exponentially as a function of temperature, being in a strong analogy with recent reports on the electronic Mach-Zehnder interferometers. By analyzing the data including those in the previous works, the energy scales that characterize the dephasing are found to be dominantly dependent on the interferometer size, implying the presence of a universal behavior in ballistic interferometers in both linear and nonlinear transport regimes.

Figure 1

(Color online) (a) Conductance of the ABR at 125 mK as a function of $B$. Inset: AFM image of the sample, white lines are oxidized area, under which the 2DEG is depleted (Ref. 14). (b) Image plot of the conductance as a function of $V_{sd}$ and $B$. The color scale is shown in units of $2e^2/h$. (c) The upper panel shows the line profiles at the fixed magnetic field indicated by “A” and “B” in (b). The lower panel shows the corresponding visibility as a function of $V_{sd}$ at $T=125$, 500, and 800 mK. The solid lines are the result of the fitting to Eq. (1). They are vertical offset upward for clarity. (d) Electron temperature dependence of the zero-bias visibility for 0 and 1.6 T (applied perpendicular to 2DEG) plotted in a semilogarithmic scale. The solid and dashed lines show the exponential decay function of $T$.

Figure 2

(Color online) (a) The oscillating components in the conductance of the FPI $\left(\Delta G_{AB}\right)$ as a function of $B$ (dashed line) and the center gate voltage (solid line). The insets show the SEM image of the sample in the left and the schematic drawing of the edge channels to construct the FPI in the right. (b) Image plot of the conductance as a function of $V_{sd}$ and the center gate voltage. The color scale is shown in units of $2e^2/h$. (c) The upper panel shows the line profiles at the fixed gate voltages indicated by “A” and “B” in (b). The lower panel shows the corresponding visibility as a function of $V_{sd}$ at $T=125$, 300, and 450 mK. The solid lines are the result of the fitting to Eq. (1). They are vertically offset upward for clarity. (d) Electron temperature dependence of the zero-bias visibility is plotted in a semilogarithmic scale. The line shows the exponential decay function of $T$.

Figure 3

(a) The energy scale $\left({ϵ}_0\right)$ of the lobe structure is plotted as a function of the arm length $\left(L\right)$ by using the data for the present ABR at 0 and 1.6 T, the present FPI, the ABR at 0 T reported by Yacoby et al. (Ref. 19), and MZI by Roulleau et al. (Refs. 5, 9), Litvin et al. (Ref. 7), and Neder et al. (Ref. 8). Open points represent the data at zero magnetic field, and filled points in the IQH regime. The arm length of MZI by Neder et al. (Ref. 8) is estimated from the SEM image of their sample. Different points with the same mark correspond to data obtained at different conditions of the magnetic field, the opening of the beam splitters, and so on. The two dashed lines indicate ${ϵ}_0=\alpha /L$ with $\alpha =150$ and $250\mu \text{eV}\mu \text{m}$. (b) The plot of ${ϵ}_L$ vs ${ϵ}_0$ shows that the two values are almost in the same range for a wide parameter range.

Figure 4

The dependence of $T_0$ on the arm length $\left(L\right)$ of the interferometers is plotted by using the data obtained for the present ABR at 0 T and 1.6 T, the present FPI, the FPI by Bird et al. (Ref. 17), the ABR by Cassé et al. (Ref. 24), Hansen et al. (Ref. 22) and Kobayashi et al. (Ref. 23) and MZI by Roulleau et al. (Refs. 5, 9), Litvin et al. (Ref. 7). Filled points were those obtained under IQH regime, while opened points were at zero magnetic field.