Edge-State Velocity and Coherence in a Quantum Hall Fabry-Pérot Interferometer

We investigate nonlinear transport in electronic Fabry-Pérot interferometers in the integer quantum Hall regime. For interferometers sufficiently large that Coulomb blockade effects are absent, a checkerboardlike pattern of conductance oscillations as a function of dc bias and perpendicular magnetic field is observed. Edge-state velocities extracted from the checkerboard data are compared to model calculations and found to be consistent with a crossover from skipping orbits at low fields to $\overrightarrow{E}\times \overrightarrow{B}$ drift at high fields. Suppression of visibility as a function of bias and magnetic field is accounted for by including energy- and field-dependent dephasing of edge electrons.

Figure 1

(a) With a current bias $I$ applied at one end of the Hall bar, voltage $V_D$ is measured directly across its width. Surface gates are shown in increasing detail, with a box indicating the region shown in (b). (b) Gate layout of the $18\mu {\mathrm{m}}^2$ device, which is operated as an interferometer by depleting all gates except $V_C$. (c) Schematic diagram of possible transmission paths through the device in the quantum Hall regime.

Figure 2

(a) $G_D$ as a function of $B$ and $V_D$ in the $18\mu {\mathrm{m}}^2$ device near $B=0.47\mathrm{T}$. (b) Result of subtracting a smooth background from the data in (a). (c) $\delta G_D$ calculated from Eq. (1), multiplied by the damping factor from Eq. (2), with $\Delta B=0.25\mathrm{mT}$, $\Delta V_D=56\mu \mathrm{V}$, and $\alpha =0.2$.

Figure 3

(a) $G_D$ as a function of $V_D$ (black dots) at a field of $B=0.22\mathrm{T}$, with a fit of Eq. (2) (solid curve) yielding $\Delta V_D=76\mu \mathrm{V}$ and $\alpha =0.063$. (b) Same as (a) but at $B=1.26\mathrm{T}$ and yielding $\Delta V_D=47\mu \mathrm{V}$ and $\alpha =0.34$. (c) Black dots indicate edge velocities (left axis) determined from measured $\Delta V_D$ (right axis) as a function of $1/B$. Curves indicate theoretical calculations: at low $1/B$, the diagonal dashed line indicates the drift velocity corresponding to $E=8\times {10}^4\mathrm{V}/\mathrm{m}$; at high $1/B$, the top and bottom solid curves indicate the predicted skipping-orbit velocities corresponding to the lowest and highest constriction densities, respectively. (d) Best-fit damping parameter $\alpha$ as a function of $B$, with a linear fit of slope $0.26{\mathrm{T}}^{-1}$ constrained through the origin. Inset: $\gamma =2\pi \alpha /e\Delta V_D$ as a function of $B$, with a linear fit of slope $31(\mathrm{meV}·\mathrm{T}{)}^{-1}$ constrained through the origin.

Figure 4

$G_D$ as a function of $B$ and $V_D$ in the $2\mu {\mathrm{m}}^2$ device.