Charge Number Dependence of the Dephasing Rates of a Graphene Double Quantum Dot in a Circuit QED Architecture

We use an on-chip superconducting resonator as a sensitive meter to probe the properties of graphene double quantum dots at microwave frequencies. Specifically, we investigate the charge dephasing rates in a circuit quantum electrodynamics architecture. The dephasing rates strongly depend on the number of charges in the dots, and the variation has a period of four charges, over an extended range of charge numbers. Although the exact mechanism of this fourfold periodicity in dephasing rates is an open problem, our observations hint at the fourfold degeneracy expected in graphene from its spin and valley degrees of freedom.

Figure 1

(a) Micrograph of the DQD gate structure. (b) Sample structure of a typical etched graphene DQD. The dc voltages used to control the charge numbers in the DQD are applied via left and right plunger (LP and RP) gates. A quantum point contact with a source ($S_Q$) and drain ($D_Q$) channel and a tuning gate ($Q$) is integrated near the DQD. (c) Circuit schematic of the hybrid device. The half-wavelength reflection line resonator is connected to DQD’s left dot (LD) at one end of its two strip lines. The right dot (RD) is connected to the drain. A microwave signal is applied to the other end of the resonator, and the reflected signal is detected using a network analyzer.

Figure 2

(a) The charge stability diagram measured using transport. (b),(c) The charge stability diagram measured by the amplitude (b) and phase (c) response of the reflection line resonator. The three charge stability diagrams show a direct correspondence. (d) Amplitude response of the resonator, corresponding to points $A$ and $B$ in (b). (e) Phase response of the resonator. The resonance frequency and quality factor ($Q$) of the resonator can be extracted. (f) Fit of the phase response as a function of the detuning, thus $2t_C$, $g_C$ and ${\gamma }_2$ can be obtained.

Figure 3

(a) Charge stability diagram of device $A$. The diagram contains about $5\times 12$ honeycomb cells, which indicates the region for our charge-number-dependence study, since the shape of the honeycombs is well defined and the resonator signal is sufficiently strong in this region. The charge numbers are indicated for both the left and right dots. (b) The dephasing rates as a function of hole number in the right dot for 12 consecutive holes (from $n$ to $n+11$). Five columns (from $m$ to $m+4$) are studied. To assist readers, the approximate periodicity has been guided by different background colors. (c) The averaged dephasing rates of (b) shows a periodicity.