Tuning of quantum interference in top-gated graphene on SiC

We report on quantum-interference measurements in top-gated Hall bars of monolayer graphene epitaxially grown on the Si face of SiC, in which the transition from negative to positive magnetoresistance was achieved varying temperature and charge density. We perform a systematic study of the quantum corrections to the magnetoresistance due to quantum interference of quasiparticles and electron-electron interaction. We analyze the contribution of the different scattering mechanisms affecting the magnetotransport in the $-2.0\times {10}^{10}$ cm${}^{-2}$ to $3.75\times {10}^{11}$ cm${}^{-2}$ density region and find a significant influence of the charge density on the intravalley scattering time. Furthermore, we observe a modulation of the electron-electron interaction with charge density not accounted for by present theory. Our results clarify the role of quantum transport in SiC-based devices, which will be relevant in the development of a graphene-based technology for coherent electronics.

Figure 1

(a) Schematic of our device and measurement setup. Gray: graphene; blue: top gate; yellow: ohmic contacts. The longitudinal and transversal resistances, $R_{xx}^{23}=V_{xx}^{23}/I_{SD}$ and $R_{xy}^{36}=V_{xy}^{36}/I_{SD}$, respectively, are recorded while the charge density in the device is independently set by the application of a top-gate voltage $V_{TG}$. (b) Half-integer quantum Hall effect measured at $T=250$ mK and $B=1.6$ T, clearly showing plateaus in $R_{xy}^{36}$ at filling factor $\nu =\pm 2$ and a change of carrier polarity at $V_{TG}=V_{CNP}\approx -27$ V.

Figure 2

Dependence of mobility $\mu$ on carrier density $n$ obtained in the temperature range $0.25–45$ K with the procedure described in the text. $\mu -n$ points obtained from $R_{xx}\left(0\right)$ and $R_{xy}\left(B\right)$ are shown as empty squares. Inset: zero-field longitudinal resistance $R_{xx}$ as a function of $V_{TG}$ measured at $T=250$ mK. The four values of $V_{TG}$ selected to study the magnetoresistance are indicated by symbols. The corresponding carrier density values are I ($3.75\times {10}^{11}$ cm${}^{-2}$), II ($1.43\times {10}^{11}$ cm${}^{-2}$), III ($2.02\times {10}^{10}$ cm${}^{-2}$), and IV ($-2.03\times {10}^{10}$ cm${}^{-2}$).

Figure 3

Longitudinal magnetoresistance at different temperatures measured for (a) point I ($V_{TG}=0$ V) and (b) at the CNP ($V_{TG}=-27$ V). The range of magnetic field in which the different contributions to the magnetoresistance are dominant is highlighted in (a).

Figure 4

Extraction of the EEI contribution to the magnetoresistance for density points (a) I and (b) III. For all temperatures, the magnetoresistance is normalized to $(R_{xx}-R_0)/R_0^2$, and then fit parabolas according to Eq. (1). Note the different $B$ range displayed in (a) and (b).

Figure 5

Dependence of the interaction parameter $K_{ee}$ on carrier density $n$, obtained from the linear fits (dashed lines) of the curvatures $A$ shown in the inset. The error bars are the standard deviations of the fits. In the electron region $(n>0)$, the error bars are smaller than the square symbols.

Figure 6

Fit of the quantum interference contribution to the magnetoresistance, at different temperatures, for the density points (a) I and (b) III. The fits are shown as dashed lines. Note the different $B$ range displayed in (a) and (b).

Figure 7

Temperature dependence of the scattering times obtained from the fits of the WL corrections. A $\propto T^{-1}$ curve and a constant one, shown as dashed lines in (a), are a guide to the eye. The uncertainty in the scattering times, expressed by the error bars, is estimated as the maximum variation in the values which allow one to retain a satisfactory fit.

Figure 8

Dependence of the intravalley time ${\tau }_{*}$ on charge density $n$ (same error bars as in Fig. 7). The data are compared with the $\propto n^{-2}$ dependence predicted for the scattering time due to trigonal warping. A $\propto n^{-1/2}$ curve is also shown.

Figure 9

Comparison between the magnetoresistances $R_{xx}^{23}\left(B\right)$ and $R_{xx}^{56}\left(B\right)$, shown as solid lines, with $R_{xx}^{23}(-B)$ and $R_{xx}^{56}(-B)$, displayed as dashed line, obtained after the inversion of polarity of magnetic field.

Figure 10

Coefficients of correction to the magnetoresistance due to nonlinear variation of the charge density. Note the different scale of the quadratic term $C_Q$ (upper panel) compared to the other terms.