Partial preservation of chiral symmetry and colossal magnetoresistance in adatom-doped graphene

We analyze the electronic properties of adatom-doped graphene in the low-impurity-concentration regime. We focus on the Anderson localized regime and calculate the localization length $\xi$ as a function of the electron doping and an external magnetic field. The impurity states hybridize with carbon's $p_z$ states and form a partially filled band close to the Dirac point. Near the impurity band center, the chiral symmetry of the system's effective Hamiltonian is partially preserved, which leads to a large enhancement of $\xi$. The sensitivity of transport properties, namely, Mott's variable range hopping scale $T_0$, to an external magnetic field perpendicular to the graphene sheet leads to a colossal magnetoresistance effect, as observed in recent experiments.

Figure 1

(a) Average local density of states near the DP for increasing values of the impurity level energy ${\varepsilon }_0/t=0,0.025,0.05,0.1$ (the inset shows a zoom out for ${\varepsilon }_0=0.05$). A peak in the density of states forms near the renormalized energy ${\overline{\varepsilon }}_0$. The impurity concentration is $n_i=1/1800$. (b) Spatial dependence of ${\langle ln|G_{ij}^r{\left(\omega \right)|}^2\rangle }_{\mathrm{avg}}$ inside the impurity band for ${\varepsilon }_0=0$. The solid lines are fits to Eq. (2) (taking $\alpha =1$) for two cases, $\omega =0.002t$ and $0.012t$. The localization length extracted from all these curves is shown in (c) for ${\varepsilon }_0/t=0$ ($•$),0.025 ($▵$), 0.05 ($▴$), and 0.1 ($\blacksquare$). Lines are guides to the eye. The arrows show the position of ${\overline{\varepsilon }}_0$. (d) Same as in (c) but including the cases of ${\varepsilon }_0/t=0.005$ ($\times$) and 0.01 ($*$) and using a logarithmic scale for $\omega$.

Figure 2

Activation temperature $T_0$ as a function of the Fermi energy ${\varepsilon }_{\text{F}}$ for $\mathcal{B}=0$ and the same parameters as in Fig. 1.

Figure 3

Average density of states for $\mathcal{B}=0$, 6, and 12 T (dotted, dashed, and solid lines, respectively) and (a) ${\varepsilon }_0=0$ and (b) ${\varepsilon }_0=0.05t$. Note the splitting of the zeroth Landau level. (c) Plot of $\xi \left(\omega \right)$ for the values of $\mathcal{B}$ shown in (a); the inset shows the spatial dependence of ${\langle ln|G_{ij}^r{|}^2\rangle }_{\mathrm{avg}}$ for $\omega /t=5\times {10}^{-3}$ and increasing values of $\mathcal{B}$. The solid lines are fits to Eq. (2) for $\mathcal{B}=0$ and 20 T. (d) Plot of $\xi \left(\omega \right)$ for two of the cases ($\mathcal{B}=0$ and 6 T) shown in (b).

Figure 4

(a) Localization length as a function of the magnetic field for the electron-hole symmetric case (${\varepsilon }_0=0$) for $\omega /t=2\times {10}^{-3}$ ($\circ$), $5\times {10}^{-3}$ ($•$), and $8\times {10}^{-3}$ ($▴$). (b) Characteristic activation temperature $T_0$ for the same energies.