Disordered Fermi Liquid in Epitaxial Graphene from Quantum Transport Measurements

We have performed magnetotransport measurements on monolayer epitaxial graphene and analyzed them in the framework of the disordered Fermi liquid theory. We have separated the electron-electron and weak-localization contributions to resistivity and demonstrated the phase coherence over a micrometer length scale, setting the limit of at least 50 ps on the spin relaxation time in this material.

Figure 1

Magnetotransport measurements in monolayer $\mathrm{SiC}/\mathrm{G}$. (a) Temperature dependence of the characteristic scattering lengths and (b) decoherence rate (${\tau }_{\varphi }^{-1}$) for samples $S1$ (open markers) and $S2$ (solid markers). Dotted line is the fit to ${\tau }_{\varphi }^{-1}={\tau }_s^{-1}+AT$, with ${\tau }_s^{-1}=0.02{\mathrm{ps}}^{-1}$ and $A=0.036{\mathrm{ps}}^{-1}{\mathrm{K}}^{-1}$. (c) Half-integer QHE proving the monolayer nature of $\mathrm{SiC}/\mathrm{G}$. Inset: Micrograph of one of the devices. (d) Weak localization peak at different temperatures.

Figure 2

Magnetic field and temperature dependence of the full resistivity tensor for sample $S1$. (a), top. Temperature dependence of ${\tilde{\rho }}_{xx}$ where WL effects have been suppressed analytically (labeled as “WL corrected”) and experimentally. WL was substantially suppressed at $B=300\mathrm{mT}$ and for $B=1\mathrm{T}$, $\Delta {\tilde{\rho }}_{\mathrm{WL}-\mathrm{Fit}}\approx \Delta {\tilde{\rho }}_{\mathrm{WL}-\mathrm{Exp}}$. (a), bottom. The corresponding conductivity, ${\sigma }_{xx}={\tilde{\rho }}_{xx}/({\tilde{\rho }}_{xx}^2+{\rho }_{xy}^2)$, in units of ${\sigma }_0=2e^{2}h\approx (12906.4\Omega {)}^{-1}$. (b), top. Temperature dependence of the Hall coefficient $R_H$ and the transversal conductivity (bottom) ${\sigma }_{xy}={\rho }_{xy}/({\tilde{\rho }}_{xx}^2+{\rho }_{xy}^2)$ in units of ${\sigma }_0$.

Figure 3

The conductivity in $\mathrm{SiC}/\mathrm{G}$ as described by the AA theory for electron transport in disordered systems. Top: The finite ratio $\gamma =(\Delta {\tilde{R}}_H/R_H)/(\Delta {\tilde{\rho }}_{xx}/{\tilde{\rho }}_{xx})$ for the analytical and experimental WL corrected ${\rho }_{xx}$ confirms unequivocally the presence of electron-electron interactions in $\mathrm{SiC}/\mathrm{G}$ for the range $2\mathrm{K}<T<30\mathrm{K}$ for the two samples, $S1$ (open circles) and $S2$ (solid circles). Bottom: The WL-corrected conductivity displays a logarithmic dependence in temperature out of which the strength of the electron interaction can be extracted. For $S1$, $A(F_0)\approx 0.758$ yielding $F_0\approx -0.066$ while for $S2$ $F_0\approx -0.085$ for $A(F_0)\approx 0.686$ using $c=7$ triplet channels, implying the high-$\kappa$ substrate (${\kappa }_{\mathrm{SiC}}\approx 10$) does not screen interactions efficiently.