Observation of Aharonov-Bohm conductance oscillations in a graphene ring

We investigate experimentally transport through ring-shaped devices etched in graphene and observe clear Aharonov-Bohm conductance oscillations. The temperature dependence of the oscillation amplitude indicates that below $1\mathrm{K}$, the phase coherence length is comparable to or larger than the size of the ring. An increase in the amplitude is observed at high magnetic field, when the cyclotron diameter becomes comparable to the width of the arms of the ring. By measuring the dependence on gate voltage, we find that the Aharonov-Bohm effect vanishes at the charge neutrality point, and we observe an unexpected linear dependence of the oscillation amplitude on the ring conductance.

Figure 1

(Color online) (a) The main panel shows the two-probe measurement of the ring resistance versus back gate voltage at $T=150\mathrm{mK}$. The charge neutrality point is at $+4\mathrm{V}$. Left inset: temperature dependence of the conductance measured for different values of gate voltage. Right inset: scanning electron microscopy image of a ring-shaped device etched in graphene similar to the one used in our measurements. (b) Magnetoconductance of the graphene ring measured at $T=150\mathrm{mK}$ and $V_G=+30\mathrm{V}$. On top of the aperiodic conductance fluctuations, periodic oscillations are clearly visible as also highlighted in the inset.

Figure 2

(Color online) (a) Aharonov-Bohm conductance oscillations measured at $V_G=+30\mathrm{V}$ for different temperatures (curves are offset for clarity). (b) Fourier spectrum of the oscillations measured at $T=150\mathrm{mK}$ shown in panel (a). The vertical dashed lines indicate the expected position of the h/e peak, as determined from the inner and outer radii of the ring. In the inset: temperature dependence of the root mean squared amplitude of the AB conductance oscillations, obtained from the measurements shown in panel (a).

Figure 3

(Color online) (a) AB conductance oscillations measured at $T=150\mathrm{mK}$ for different values of the back gate voltage, as indicated by the dashed lines on panel (b). Panel (b) shows the dependence of the ring resistance (in logarithmic scale) on gate voltage, measured at $T=150\mathrm{mK}$. (c) rms amplitude of the AB conductance oscillations as a function of gate voltage. In panel (d), the same data are plotted as a function of the ring conductance. The red line is a guide to the eye.

Figure 4

(Color online) Panels (a)–(c) show the AB conductance oscillations measured at $V_G=+30\mathrm{V}$ in different magnetic field ranges. For $B\sim 3\mathrm{T}$ a clear increase of AB amplitude is observed. (d) Fourier spectrum of the AB oscillations measured between 4 and $5\mathrm{T}$. The dashed lines indicate the position of the h/e and h/2e peaks expected from the device geometry. The inset shows the magnetoconductance of the ring. All measurements were taken at $150\mathrm{mK}$.

Figure 5

(Color online) Panels (a) and (b) show the rms amplitude of the AB conductance oscillations determined on an interval of 50 periods as a function of magnetic field and for two different temperatures ($T=150\mathrm{mK}$, red line and $800\mathrm{mK}$, black line), measured at $V_G=+20$ and $+30\mathrm{V}$. The blue curves are obtained by smoothing the corresponding data over 20 points. The arrows indicate the position in field where the oscillation amplitude starts to saturate, slightly higher at $V_G=+30$. Panel (c) shows the temperature dependence of the amplitude of the h/e and h/2e components of the AB conductance oscillations measured between 4 and $5\mathrm{T}$. The continuous lines are linear fits with slopes $-0.5\pm 0.07$. Panel (d) shows that the rms values of the AB oscillations measured between 4 and $5\mathrm{T}$ (at $V_G=+4$, $+20$, and $+30\mathrm{V}$) scales linearly with the conductance of the device.