Distinct signatures for Coulomb blockade and Aharonov-Bohm interference in electronic Fabry-Perot interferometers

Two distinct types of magnetoresistance oscillations are observed in two electronic Fabry-Perot interferometers of different sizes in the integer quantum Hall regime. Measuring these oscillations as a function of magnetic field and gate voltages, we describe three signatures that distinguish the two types. The oscillations observed in a $2.0\mu {\text{m}}^2$ device are understood to arise from a Coulomb blockade mechanism and those observed in an $18\mu {\text{m}}^2$ device from an Aharonov-Bohm mechanism. This work clarifies, provides ways to distinguish, and demonstrates control over these distinct mechanisms of oscillations seen in electronic Fabry-Perot interferometers.

Figure 1

(Color online) Measurement setup and devices. (a) Diagram of the wet-etched Hall bar, surface gates, and measurement configuration. Diagonal resistance $R_D$ is measured directly across the Hall bar, with current bias $I$. Subsequent zoom ins of the surface gates are also shown; the red box encloses the detailed gate layouts for the device shown in (c). [(b) and (c)] Gate layouts for the $2.0\mu {\text{m}}^2$ and $18\mu {\text{m}}^2$ devices, respectively. The areas quoted refer to those under $V_C$.

Figure 2

(Color online) Oscillations in $R_D$ as a function of magnetic field $B$ for the $2.0\mu {\text{m}}^2$ device. (a) $R_D$ as a function of $B$, showing well-quantized integer plateaus. Different colored backgrounds indicate different numbers of fully occupied LLs ($f_0$) through the device. [(b) and (c)] Zoom ins of the data in (a), at $f_0=1$ and 2, respectively, showing oscillations in $R_D$, and their $B$ periods $\Delta B$.

Figure 3

(Color online) Magnetic field and gate-voltage periods at various $f_0$, for the $2.0\mu {\text{m}}^2$ device. (a) $\Delta B$ as a function of $1/f_0$ and a best-fit line constrained through the origin. [(b)–(d)] $R_D$ oscillations as a function of $B$, at $f_0=1$, 2, and 4, respectively. (e) $\Delta V_T$ (diamonds) and $\Delta V_C$ (circles) as a function of $1/f_0$ and their averages indicated by horizontal lines. [(f)–(h)] $R_D$ oscillations as a function of $V_C$, at $f_0=1$, 2, and 4, respectively.

Figure 4

(Color online) Magnetic field and gate-voltage periods at various $B$, for the $18\mu {\text{m}}^2$ device. (a) $\Delta B$ as a function of $1/B$ and their average indicated by a horizontal line. [(b)–(d)] $R_D$ oscillations as a function of $B$ over three magnetic field ranges. (e) $\Delta V_T$ (diamonds) and $\Delta V_C$ (circles) as a function of $1/B$ and best-fit lines constrained through the origin. [(f)–(h)] $R_D$ oscillations as a function of $V_T$, at $B=6.2\text{T}$, 2.5 T, and 0.72 T, respectively.

Figure 5

(Color online) (a) $\delta R_D$, i.e., $R_D$ with a smooth background subtracted, as a function of $B$ and $V_C$, for the $2.0\mu {\text{m}}^2$ device. (b) Same as in (a), but for the $18\mu {\text{m}}^2$ device.