Local electronic signatures of impurity states in graphene

Defects in graphene are of crucial importance for its electronic and magnetic properties. Here, impurity effects on the electronic structure of surrounding carbon atoms are considered and the distribution of the local densities of states is calculated. As the full range from near field to the asymptotic regime is covered, our results are directly accessible by scanning tunneling microscopy. We also include exchange scattering at magnetic impurities and elucidate how strongly spin-polarized impurity states arise.

Figure 1

(Color online) The energy $E_{\mathrm{imp}}$ of the impurity resonance as a function of the potential strength $U_0$ is shown for single impurities and double impurities with $U_1=0$. For the single scatterer, $E_{\mathrm{imp}}$ obtained from our tight-binding calculation is compared to the result obtained from the fully linearized band structure [Eq. (1)] with fitted bandwidth $W=6.06\mathrm{eV}$.

Figure 2

(Color online) $r$-dependent LDOS at $E=E_{\mathrm{imp}}=-0.1\mathrm{eV}$ for a single impurity with $U_0=45\mathrm{eV}$ (left) and for a scalar double impurity with $U_0=6.9\mathrm{eV}$ (right) encoded corresponding to color bar. The impurity sites are marked as big dots in the center of the images.

Figure 3

(Color online) LDOSs at the impurity site (left), NN site (middle), and NNN site (right) are shown for a single impurity with potentials $U_0=\left(\mathrm{a}\right)$ $10\mathrm{eV}$, (b) $20\mathrm{eV}$, and (c) $40\mathrm{eV}$.

Figure 4

(Color online) As in Fig. 3 but for scalar double impurity with $U_0=\left(\mathrm{a}\right)$ $4\mathrm{eV}$ and (c) $6\mathrm{eV}$ as well as for double impurity with $U_0=4\mathrm{eV}$ and $U_1=\left(\mathrm{b}\right)$ $-2\mathrm{eV}$.

Figure 5

(Color online) SP-LDOSs at the impurity site (left) and a NN site (right) are shown for a single magnetic impurity with $U_0=12\mathrm{eV}$ and $J=2\mathrm{eV}$.

Figure 6

(Color online) SP-LDOSs at a NN site of a double impurity with $U_0=5\mathrm{eV}$, $U_1=-2\mathrm{eV}$, and $J=1\mathrm{eV}$ (left) and $2\mathrm{eV}$ (right) are shown.