Radio-frequency charge detection on graphene electron-hole double quantum dots

Abstract

High-fidelity detection of charge transitions in quantum dots (QDs) is a key ingredient in solid state quantum computation. We demonstrate high-bandwidth radio-frequency charge detection in bilayer graphene quantum dots (QDs) using a capacitively coupled quantum point contact (QPC). The device design suppresses screening effects and enables sensitive QPC-based charge readout. The QPC is arranged to maximize the readout contrast between two neighboring, coupled electron and hole QDs. We apply the readout scheme to a single-particle electron-hole double QD and demonstrate time-resolved detection of charge states as well as magnetic field dependent tunneling rates. This promises a high-fidelity readout scheme for individual spin and valley states, which is important for the operation of spin, valley or spin-valley qubits in bilayer graphene.

Figures (5)

• Figure 1: (a) False-colored scanning electron microscopy image of the BLG QD device. Scale bar is 500nm. Split gates (SGs) define conducting channels; finger gates G1--G3 control the potential along the narrow channel, defining and controlling QDs and gate G0 (orange) defines a QPC in the wide channel (blue) acting as charge detector. Via three ohmic contacts ($\boxtimes$) bias voltages can be applied and current through the device can be measured. One of the contacts is additionally connected to an inductor, $L=3.3\mu H$, forming an LC resonant circuit together with the stray capacitance of the bond wires, $C_\mathrm{s}\approx0.6pF$, matching the impedance of the QPC to the $50\mathrm{\Omega}$ RF line. For reflectometry measurements, an RF signal ($\mathrm{RF_{in}}$) is applied to the resonant circuit via cryogenic attenuators ($-36dB$) and a directional coupler ($-20dB$). The reflected signal is amplified ($+35dB$, Cosmic Microwave CITLF3) at $4K$, followed by additional $+28dB$ at room temperature. A lock-in amplifier (Zurich Instruments UHFLI 600MHz) is used for signal generation and homodyne detection. (b) Schematic of the gate structure together with the calculated charge carrier density $n$ induced in the BLG (scale bar is 100nm). For the calculation the gate voltages were chosen as $V_\mathrm{G1}=-4.44V$, $V_\mathrm{G2}=-4.795V$, $V_\mathrm{G3}=-3.52V$, $V_\mathrm{G4}=-4.54V$, $V_\mathrm{G0}=-4.17V$, $V_\mathrm{SG}=-3.88V$, $V_\mathrm{BG}=4V$. (c) Current $I_\mathrm{QD}$ as a function of the gate voltages $V_\mathrm{G0}$ and $V_\mathrm{G2}$ with $V_\mathrm{CD} = 250\mu V$, $V_\mathrm{QD} = 0$. Coulomb resonances of a single hole QD formed in the narrow channel close to the T-junction appear. The vertical feature (see arrow) is caused by the formation of a QPC in the wide channel. (d) Potential profiles along the narrow channel (black lines) in between bulk conduction (CB) and valence band (VB) for two different gate voltage configurations defining an electron-hole DQD (upper panel, corresponding to b) and an electron QD (lower panel). (e) Conductance $G_\mathrm{CD}$ of the charge detector operated in the QPC regime ($V_\mathrm{CD} = 80\mu V$). Here, the two channels were isolated with G1 and a single hole QD is present in the QD channel (see left schematics in panel (f)). The arrow indicates the operating point set in the following experiments. (f) Jumps in $I_\mathrm{CD}$ as a function of $V_\mathrm{G2}$ (see labels and dashed lines) show the formation of single QDs in the few hole ($V_\mathrm{G4} = -4.3V$, red) and few electron ($V_\mathrm{G4} = -5.35V$, blue, offset by $-0.5nA$ for clarity) regimes (see also corresponding schematics on the top)
• Figure 2: (a) Magnitude of the RF signal as a function of the RF carrier frequency $f$ for different voltages $V_\mathrm{G0}$ applied to the detector gate (excitation power $P = -10dBm$). At the resonance frequency $f_\mathrm{res}$ of the tank circuit, the reflected signal is minimized. (b) Signal-to-noise ratio (SNR) of the magnitude $R_\mathrm{demod}$ of the RF signal reflected off the charge detector, measured as a function of $f$ and $P$. The SNR is determined as the ratio of the step height caused by the first charge carrier in the hole QD (0h-1h) and the RMS of the noise. (c) SNR of the phase $\varphi$ of the RF signal. (d) SNR of the phase response as a function of the measurement bandwidth set by the digital first order low pass filter of the lock-in amplifier ($P = -11dBm$).
• Figure 3: (a) Charge stability diagram of the differential phase $\mathrm{d} \varphi/\mathrm{d}V_\mathrm{G2}$ of the reflected RF signal as a function of the gate voltages $V_\mathrm{G1}$ and $V_\mathrm{G2}$. A hole (electron) QD is defined under gate G1 (G2). The charge carrier occupation of electron (e) and hole (h) QD (see labels) can be tuned down to (0h,0e). (b-c) Step height $\delta\varphi_{\mathrm{step}}$ of the charge detector response at the (b) 0h-1h, (c) 1e-2e charge transition (dashed lines in (a)) as a function of $V_\mathrm{G1}$. Charge transitions of the electron QD occur at the gate voltages indicated by dashed lines. The inset depicts the corresponding charge configuration. (d-e) Line cut of the charge carrier density $\rho$ along $y=0$ in Fig. \ref{['f1']}b calculated for different $V_\mathrm{G1}$. The gate voltages $V_\mathrm{G2}$ -- $V_\mathrm{G4}$ have been chosen such that (d) the hole QD is occupied by roughly 1 hole and (e) the electron QD contains two electrons. (f-g) Average calculated potential difference $\delta\phi$ at the QPC due to a change in occupation of (f) the hole QD (g) the electron QD as a function of $V_\mathrm{G1}$ for the configurations shown in the insets of (b) and (c), respectively.
• Figure 4: (a) Charge stability diagram showing a close-up of the single-particle electron-hole transition measured in Fig. \ref{['f3']}a at $B = 0T$. $\varepsilon$ is the detuning energy between the charge states (0h,0e) and (1h,1e). A linear background caused by capacitive cross talk between the gate voltages $V_\mathrm{G1}$ and $V_\mathrm{G2}$ and the charge detector was subtracted. (b) Same as in (a) but with a perpendicular magnetic field of $B = 1.5T$ applied.
• Figure 5: (a) Time-resolved detection of (0h,0e) $\leftrightarrow$ (1h,1e) charge transitions at $B = 1.3T$ recorded in a time span of 1s with a sampling rate of 20kS/s. The data has been low pass filtered at 7.5kHz. Histograms of the data sets with a trace length of 50s are shown at the side. (b) Tunneling rates $\Gamma_\mathrm{(1h,1e)}$ (left) and $\Gamma_\mathrm{(0,0)}$ (right) for the annihilation and creation of an electron hole pair, respectively, as a function of $V_\mathrm{G1}$ and $V_\mathrm{G2}$ ($B=1.3T$). Each data point has been obtained from a single-shot measurement, as in (a). (c) Time-resolved detection in a regime of increased tunnel coupling at $B=0.9T$ in a time span of 20ms with a sampling rate of 200kS/s. The data has been low pass filtered at 77kHz. Histograms of the data sets with a trace length of 5s are shown at the side. (d) Combined tunneling rate as a function of the perpendicular magnetic field $B$, determined at $\varepsilon = 0$. Fitting a power law yields $\Gamma \propto B^{-10.0\pm0.7}$. (e) SNR determined from time-resolved charge detection as a function of the measurement bandwidth ($B = 0.7T$).