Manifestation of the shape and edge effects in spin-resolved transport through graphene quantum dots

We report on theoretical studies of transport through graphene quantum dots weakly coupled to external ferromagnetic leads. The calculations are performed by exact diagonalization of a tight-binding Hamiltonian with finite Coulomb correlations for graphene sheet and by using the real-time diagrammatic technique in the sequential and cotunneling regimes. The emphasis is put on the role of graphene flake shape and spontaneous edge magnetization in transport characteristics, such as the differential conductance, tunneling magnetoresistance (TMR), and the shot noise. It is shown that for certain shapes of the graphene dots, a negative differential conductance and nontrivial behavior of the TMR effect can occur.

Figure 1

Scheme of a graphene quantum dot coupled to external ferromagnetic leads. We consider graphene flakes of three different shapes: (a) circular, (b) rectangular, and (c) rhombic. A particular dot is coupled to external leads with coupling strengths described by ${\Gamma }_L^{\sigma }$ and ${\Gamma }_R^{\sigma }$ for the left and right leads. It is assumed that the system can be in two magnetic configurations: the parallel and antiparallel ones, as sketched in the figure.

Figure 2

The atomic structure (a) and energy spectrum (b) of the rhombic graphene quantum dot. There are no magnetic solutions irrespective of the value of $U$, instead a quite pronounced energy gap opens.

Figure 3

The bias $V$ and gate $V_g$ voltage dependence of the differential conductance in the parallel (a) and antiparallel (b) configurations as well as the resulting TMR effect (c) calculated for rhombiclike graphene quantum dot. The parameters are the charging energy $E_C=0.15$ eV, the coupling strength $\Gamma =2$ meV, the thermal energy $k_{B}T=20$ meV, and the leads' spin polarization $p=0.5$.

Figure 4

The Fano factor in the parallel (a) and antiparallel (b) magnetic configuration as a function of the bias and gate voltages for rhombiclike graphene quantum dot. The parameters are the same as in Fig. 3.

Figure 5

The atomic structure (a) and energy spectrum (b) for circular graphene flake. In the case of $U=0$, there are no magnetic edges, while magnetic edges appear for finite $U$. Note that in the latter case, an energy gap ($\Delta E$) opens. The corresponding magnetic configuration is also displayed in (a). The maximum edge magnetic moments are equal to approximately 1/5 ${\mu }_B$. However, the total magnetic moment of the dot is equal to $1{\mu }_B$.

Figure 6

The bias and gate voltage dependence of the differential conductance in the parallel (a) and antiparallel (b) configurations as well as the resulting TMR effect (c) calculated for circular graphene quantum dot. The parameters are the same as in Fig. 3 except for thermal energy, which is $k_{B}T=10$ meV.

Figure 7

The Fano factor in the parallel (a) and antiparallel (b) magnetic configuration as a function of the bias and gate voltages for circular graphene quantum dot. The parameters are the same as in Fig. 6.

Figure 8

The same as in Fig. 5 but for the rectangular graphene quantum dot. Now, the maximum edge magnetic moments are equal to approximately 1/3 ${\mu }_B$.

Figure 9

The bias and gate voltage dependence of the differential conductance in the parallel (a) and antiparallel (b) configurations as well as the resulting TMR effect (c) calculated for rectangular graphene quantum dot. The parameters are the same as in Fig. 6.

Figure 10

The Fano factor in the parallel (a) and antiparallel (b) magnetic configuration as a function of the bias and gate voltages for rectangular graphene quantum dot. The parameters are the same as in Fig. 6.