Graphene single-electron transistor as a spin sensor for magnetic adsorbates

We study single-electron transport through a graphene quantum dot with magnetic adsorbates. We focus on the relation between the spin order of the adsorbates and the linear conductance of the device. The electronic structure of the graphene dot with magnetic adsorbates is modeled through numerical diagonalization of a tight-binding model with an exchange potential. We consider several mechanisms by which the adsorbate magnetic state can influence transport in a single-electron transistor: tuning the addition energy, changing the tunneling rate, and in the case of spin-polarized electrodes, through magnetoresistive effects. Whereas the first mechanism is always present, the others require that the electrode has to have either an energy- or spin-dependent density of states. We find that graphene dots are optimal systems to detect the spin state of a few magnetic centers.

Figure 1

(a) Scheme of a graphene constriction with randomly distributed magnetic centers. (b) Diagram with the system energy levels and graphene density of states where $E_D$ is the energy of the Dirac point, $E_F$ is the Fermi level of the graphene electrodes, $V_{\mathrm{bias}}$ is the bias voltage, $V_g$ is the gate voltage that controls the energy levels in the quantum dot and $\delta$ is the spin splitting of the transport level.

Figure 2

Spin splitting $\delta$ for a sample of dimensions $L_y=N_{y}a$ and $L_x=N_x\sqrt{3}a$, with $N_x=15$ and $N_y=17$, being $a=2.46$ Å the lattice constant of graphene. $\delta$ vs total magnetization $M_T$ for a single spatial distribution of $N=10$ magnetic impurities with (a) $J=5$ and (b) 10 meV. The red solid line indicates the average value ${\langle \delta \rangle }_{\mathrm{pos}}$. Average ${\langle \delta \rangle }_{\mathrm{pos}}^{\mathrm{FM}}$ vs number of magnetic molecules $N$ for $J=5$ meV (c) and exchange energy $J$ for $N=4$ (d). The error bars correspond to the standard deviation.

Figure 3

(a) Scheme showing the transport level energy splitting. Scheme of spin dependence of transport due to (b) detuning of the transport level with respect to the electrode Fermi energy, (c) magnetoresistance associated to spin polarized electrode(s), and (d) energy dependent tunneling rates.

Figure 4

Conductance in units of $g_0=G_0\beta \Gamma$ as a function of the gate voltage $e{V}_g$ and the level splitting $\delta$. (a) The normalized conductance as a function of the gate potential $e\beta V_g$, where the labels corresponds to the different $\beta \delta$ values. (b) The conductance as a function of $\beta \delta$ for several values of the gate $e\beta V_g$. For the sake of clarity, all curves have been displaced by $0.1$. In (c) and (d), we present a contour plot of the dot charge (defined as $Q=P_{\uparrow }+P_{\downarrow }$) and the dot magnetization ($m=P_{\uparrow }-P_{\downarrow }$) as a function of the gate voltage $e{V}_g$ and level splitting $\delta$.

Figure 5

Normalized conductance for ferromagnetic electrodes as a function of the level splitting $\delta$ for several gate values. In (a) and (c), the density of states depends of the polarization $\rho ={\rho }_0(1+\sigma \mathcal{P})$, in this particular case, we take a polarization of $\mathcal{P}=0.9$. In (b) and (d), the electrode density of states is linear with the energy, $\rho \left({\Delta }_{\sigma }\right)=\rho ({\epsilon }_0+\sigma \delta /2-E_D)$. For the sake of clarity the conductance curves in (c) and (d) have been displaced by $0.2$ and 4 units, respectively.