Field-effect-driven half-metallic multilayer graphene

Rhombohedral stacked multilayer graphene displays the occurrence of a magnetic surface state at low temperatures. Recent angular resolved photoemission experiments demonstrate the robustness of the magnetic state in long sequences of ABC graphene. Here, by using first-principles calculations, we show that field-effect doping of these graphene multilayers induces a nonrigid electronic structure deformation and stabilizes a perfect half-metallic behavior with nearly 100% of spin current polarization and sizable conductivity already at dopings attainable in conventional field-effect transistors with solid state dielectrics. At high doping, magnetism disappears and a flat electronic band prone to correlated, charge density wave, or superconducting instabilities occurs at the Fermi level. Our work demonstrates the realizability of a new kind of spintronic devices where the transition between the low resistance and the high resistance state is driven only by electric fields.

Figure 1

Calculated electronic structure using the PBE0 [29] functional of rhombohedral 12-layer graphene close to the $K$ point ($\tilde{k}=k-K$). In the insets we show a schematic view of the charged state considered in the calculation. The blue and red colors label the layers contributing to the surface bands. The Fermi level is determined with a temperature $T=40$ K and labeled ${\epsilon }_F$. (a) Neutral antiferromagnetic ground state in the absence of external electric fields. (b) Electronic structure under the effect of an external electric field perpendicular to the layers in double gate configuration. The electric field is simulated adding a layer of positive (negative) point charges at 3.35 Å from the bottom (top) layer and keeping the multilayer graphene sample neutral, as shown in the inset. The surface charge density for each gate is $\pm 0.8\times {10}^{12}{\text{cm}}^{-2}$. (c) and (d) Electronic structure in field-effect configuration at two different doping values $n$. In this case the system formed by the charged layer and the graphene multilayer is kept neutral (see insets). Continuous (dashed) lines label majority (minority) spin components. Blue (red) color label the dominant projection of the band structure over $p_z$ orbitals of the atoms in the graphene layer close (opposite) to the charged layer.

Figure 2

As Fig. 1, but on a larger scale including the valence band maximum.

Figure 3

Calculated electronic structure using the PBE0 functional of rhombohedral multilayer graphene close to the $K$ point ($\tilde{k}=k-K$): comparison between 6 and 12 layers. The Fermi level is determined with a temperature $T=40$ K labeled ${\epsilon }_F$. (a) and (c) Neutral antiferromagnetic ground state in the absence of external electric fields. (b) and (d) Electronic structure in field-effect configuration at the same doping value $n$. Continuous (dashed) lines label majority (minority) spin components. Blue (red) color label the dominant projection of the band structure over $p_z$ orbitals of the atoms in the graphene layer close (opposite) to the charged layer.

Figure 4

Magnetic and transport properties of 12-layer (left) and 6-layer (right) RMG as a function of field-effect doping at $T=40$ K. (a) Antiferromagnetic order parameter ${\sum }_i\left|m_i\right|$, where $m_i$ is the atomic magnetic moment. (b) and (c) Energy distance of the minority (majority) spin bands from the Fermi level (${\epsilon }_F$). The full colored regions represents the dominant projection of valence/conduction bands onto atomic states of the multilayer surfaces: blue for the layer closest to the charged layer, red for the opposite surface (see also Fig. 1). (d) Spin-polarized conduction with respect to the graphene conductivity at the same $k_F$ (left axis). The percentage of polarization of the conductivity is displayed on the right axis.

Figure 5

Transport properties of 6-layer graphene with rhombohedral stacking as a function of field-effect doping at $T=80\mathrm{K}$: spin-polarized conduction with respect to the graphene conductivity at the same $k_F$ (left axis) and percentage of polarization of the conductivity (right axis).