Electronic eigen-states of a square graphene quantum dot(GQD) terminated by both zigzag and armchair edges are derived in the theoretical framework of Dirac equation. We find that the Dirac equation can determine the eigen-energy spectrum of a GQD wi
th high accuracy even if its size is reduced to a few nanometers. More importantly, from the Dirac equation description we can readily work out the number and energy gap of the conjugate surface states, which are intimately associated with the magnetic properties of the GQD. By using the Hartree-Fock mean field approach, we study the size dependence of the magnetic ordering formation in this square GQD. We find that there exists a critical size of the width between the two zigzag edges to indicate the onset of the stable magnetic ordering. On the other hand, when such a width increases further, the magnetic ground state energy of a charge neutral GQD tends to a saturated value. These results coincide with the previous results obtained from the first principle calculation. Then, based on the Dirac equation solution about the surface state, we establish a simple two-state model which can quantitatively explain the size dependence of the magnetic ordering in the square GQD.
Electron transport properties in a parallel double-quantum-dot structure with three-terminals are theoretically studied. By introducing a local Rashba spin-orbit coupling, we find that an incident electron from one terminal can select a specific term
inal to depart from the quantum dots according to its spin state. As a result, spin polarization and spin separation can be simultaneously realized in this structure. And spin polarizations in different terminals can be inverted by tuning the structure parameters. The underlying quantum interference that gives rise to such a result is analyzed in the language of Feynman paths for the electron transmission.
The contact conductance between graphene and two quantum wires which serve as the leads to connect graphene and electron reservoirs is theoretically studied. Our investigation indicates that the contact conductance depends sensitively on the graphene
-lead coupling configuration. When each quantum wire couples solely to one carbon atom, the contact conductance vanishes at the Dirac point if the two carbon atoms coupling to the two leads belong to the same sublattice of graphene. We find that such a feature arises from the chirality of the Dirac electron in graphene. Such a chirality associated with conductance zero disappears when a quantum wire couples to multiple carbon atoms. The general result irrelevant to the coupling configuration is that the contact conductance decays rapidly with the increase of the distance between the two leads. In addition, in the weak graphene-lead coupling limit, when the distance between the two leads is much larger than the size of the graphene-lead contact areas and the incident electron energy is close to the Dirac point, the contact conductance is proportional to the square of the product of the two graphene-lead contact areas, and inversely proportional to the square of the distance between the two leads.
Electron transport properties in a triple-quantum-dot ring with three terminals are theoretically studied. By introducing local Rashba spin-orbit interaction on an individual quantum dot, we calculate the charge and spin currents in one lead. We find
that a pure spin current appears in the absence of a magnetic field. The polarization direction of the spin current can be inverted by altering the bias voltage. In addition, by tuning the magnetic field strength, the charge and spin currents reach their respective peaks alternately.
