Scanning tunneling microscopy currents on locally disordered graphene

We study the local density of states at and around a substituting impurity, and use these results to compute current versus bias characteristic curves of scanning tunneling microscopy (STM) experiments done on the surface of graphene. This allows us to detect the presence of substituting impurities on graphene. The case of vacancies is also analyzed. We find that the shape and magnitude of the STM characteristic curves depend on the position of the tip and on the nature of the defect, with the strength of the binging between the impurity and the carbon atoms playing an important role. Also the nature of the last atom of the tip has an influence on the shape of the characteristic curve.

Figure 1

(Color online) The honeycomb lattice with a substituting atom replacing a carbon atom. The local hopping parameter changes from $t$ to $t-t_0$ around the $A$ atom. We assume all over $t=3\text{eV}$.

Figure 2

(Color online) Local density of states (LDOS) at the unit cell $\mathit{R}=0$ for the $A$ and $B$ atoms, and different values of $t_0$ in electron volt. In panel (a) we plot the density of states of clean graphene and the LDOS at the $B$ atom near a vacancy at the $A$ atom of the same unit cell. For $t_0=1$, ${\rho }_B\left(0,\omega \right)$ is multiplied by ten for clarity.

Figure 3

(Color online) LDOS at distance $R$ from unit cell $\mathit{R}=0$, where the impurity is located for different values of $t_0$. The energy is $\hslash \omega =0.5\text{eV}$. The case of the vacancy is also illustrated.

Figure 4

(Color online) Transmission coefficient $T\left(E\right)$ as function of the energy for zero bias. The fixed parameters are $t=3.0$, $V=1$, $W_1=0.9$, and $W_2=0.2$, all in electron volt. Panel (a) depicts the case of clean graphene and two different values of ${ϵ}_0$. Panel (b) depicts $T\left(E\right)$ through a $B$ site when a vacancy sits at the $A$ site. Panel (c) depicts $T\left(E\right)$ through $A$ and $B$ sites, when an impurity sits at the $A$ site, taking $t_0=1\text{eV}$ and ${ϵ}_0=0$. Panel (d) is the same as panel (c) for $t_0=-1\text{eV}$.

Figure 5

(Color online) Transmission coefficient $T\left(E\right)$ as function of the energy for finite bias $V_b=0.5\text{V}$. The parameters and the description are the same as those listed in the caption of Fig. 4. The energy scale in the case of the vacancy was increased in order to see the low-energy behavior close to the Dirac point.

Figure 6

(Color online) Current $J$ as function of the bias voltage $V_b$. The parameters are the same as those listed in the caption of Fig. 4 and ${ϵ}_0=0.2\text{eV}$. Panel (a) represents the clean case for two values of the chemical potential $\mu$. The case of the vacancy is represented in panel (b), also for two values of the chemical potential. Panel (c) represents the case $t_0=1\text{eV}$ for $\mu =0.3\text{eV}$, and panel (d) is the same as (c) for $t_0=-1\text{eV}$. In panels (c) and (d), $A$ and $B$ refer to tunneling through the atom sitings on sublattice $A$ or $B$, respectively.

Figure 7

(Color online) Fano factor $F$ as function of the bias voltage $V_b$. The parameters are the same as those listed in the caption of Fig. 4 and ${ϵ}_0=0.2\text{eV}$. Panel (a) represents the clean case for two values of the chemical potential $\mu =0$ and $\mu =0.3\text{eV}$. The case of the vacancy is represented in panel (b), also for two values of the chemical potential. Panel (c) represents the case $t_0=1\text{eV}$ for $\mu =0.3\text{eV}$, and panel (d) is the same as (c) for $t_0=-1\text{eV}$. In panels (c) and (d), $A$ and $B$ refer to tunneling through the atom sitings on sublattice $A$ or $B$, respectively.