Transport study of graphene adsorbed with indium adatoms

Enhancement of the spin-orbit coupling in graphene may lead to various topological phenomena and also find applications in spintronics. Adatom adsorption has been proposed as an effective way to achieve the goal. In particular, great hope has been held for indium in strengthening the spin-orbit coupling and realizing the quantum spin Hall effect. To search for evidence of the spin-orbit coupling in graphene adsorbed with indium adatoms, we carry out extensive transport measurements. It is found that indium adatoms dope graphene and introduce significant Coulomb scattering. No signature of the spin-orbit coupling is observed in the weak localization magnetoconductance and nonlocal spin Hall effect. Possible explanations are discussed.

Figure 1

Magnetotransport of a graphene Hall bar device before indium deposition. (a) Longitudinal resistivity and the transverse conductivity vs the gate voltage in 9 T at 150 mK. The inset is a scanning electron microscopy picture of the device. (b) Low-field magnetoresistivity exhibits two features, the weak localization peak at $B=0$ and the universal conductance fluctuations. (c) Fits to Eq. (1) for the low-field magnetoconductivity at different carrier densities, $n=2.15,1.43,0.77,0.50\times {10}^{12}{\mathrm{cm}}^{-2}$. (d) The mean free path $l$ and the phase coherence length $l_{\varphi }$ as a function of $n_s$.

Figure 2

Deposition of indium. (a) The conductivity $\sigma$ vs gate voltage $V_g$ curves for the device after each deposition. The solid lines are linear fits, from which the field effect mobility is obtained. (b) The dependence of the mean free path $l$ and mobility $\mu$ on the shift of the Dirac point $\Delta V_{\mathrm{D}}$.

Figure 3

Low-field magnetoconductivity after the third deposition. (a) Fits of the low-field magnetoconductivity to Eqs. (1) and (2). The circles are experimental data. The solid lines are the best fits to the equations, red for Eq. (1) and blue for Eq. (2). The dotted lines are plots of two equations, assuming a spin-orbit scattering time ${\tau }_{\mathrm{so}}={\tau }_{\varphi }$. (b) Magnetoconductivity data and fits to Eq. (1) at different gate voltages relative to the Dirac point $(V_g-V_{\mathrm{D}})$.

Figure 4

Magnetotransport of a graphene Hall bar device before Mg deposition. (a) Longitudinal resistivity and the transverse conductivity vs the gate voltage in 9 T at 150 mK, showing the half-integer quantum Hall effect. (b) Low-field magnetoresistivity exhibits two features, the weak localization peak at $B=0$ and the universal conductance fluctuations. (c) Fits to Eq. (1) for the low-field magnetoconductivity at different carrier densities. (d) The mean free path $l$ and the phase coherence length $l_{\varphi }$ as a function of $n_s$. $l_{\varphi }$ is obtained from the fits in (c).

Figure 5

Deposition of magnesium. (a) The conductivity $\sigma$ vs gate voltage $V_g$ curves for the device after each deposition. The solid lines are linear fits, from which the field effect mobility is obtained. (b) The dependence of the mean free time $\tau$ at a carrier density of $1.7\times {10}^{12}{\mathrm{cm}}^2$/Vs and the field effect mobility $\mu$ on the shift of the Dirac point $\Delta V_{\mathrm{D}}$.

Figure 6

Low-field magnetoconductivity after the fourth deposition of Mg. (a) Fit of the low-field magnetoconductivity at a carrier density of $1.7\times {10}^{12}{\mathrm{cm}}^2$/Vs to Eq. (1) and Eq. (2). The circles are experimental data. The solid lines are the best fits to the equations, red for Eq. (1) and blue for Eq. (2). The dotted lines are plots of two equations, assuming a spin-orbit scattering time ${\tau }_{\mathrm{so}}={\tau }_{\varphi }$. (b) Magnetoconductivity data and fits to Eq. (1) at different gate voltages relative to the Dirac point. The fluctuations of the conductivity are reproducible and due to universal conductance fluctuations.

Figure 7

Nonlocal SHE measurements. The nonlocal signal is very weak, on a level comparable to noise. No substantial change occurs after indium deposition.