Quantum blockade and loop currents in graphene with topological defects

We investigate the effect of topological defects on the transport properties of a narrow ballistic ribbon of graphene with zigzag edges. Our results show that the longitudinal conductance vanishes at several discrete Fermi energies where the system develops loop orbital electric currents with certain chirality. The chirality depends on the direction of the applied bias voltage and the sign of the local curvature created by the topological defects. This quantum localization phenomenon provides a way to generate a magnetic moment by an external electric field, which can prove useful in nanotronics.

Figure 1

(Color online) The process of constructing a pentagon $\left[\left(a\right)\to \left(b\right)\to \left(c\right)\right]$ and a heptagon $\left[\left(a\right)\to \left(d\right)\to \left(e\right)\right]$ by “cut” and “paste” from a perfect graphene sheet. Positive (negative) curvature is induced by a pentagon (heptagon) in the realistic three-dimensional space. Notice that after the cut and paste, a single pentagon (heptagon) will give rise to a global change of the lattice structure, which is explained in the text.

Figure 2

(Color online) Conductance of the topologically disordered sample with a pentagon $G$ (black solid), averaged loop current $⟨i_L⟩$ (blue dashed dot), and induced magnetic moment $m$ (red solid) of the pentagon as functions of Fermi energy $E$. The conductance for a perfect graphene sample $G_0$ (black dashed) with the same dimensions is also plotted for reference.

Figure 3

(Color online) The spatial distribution of LDOS of the sites (blue circles), local current density of the bonds (arrows), and induced magnetic moment of carbon rings (green disks and crosses) near the pentagon. The size of each symbol is proportional to the local value of the corresponding quantity. (a) $E=-0.1t$, corresponding to point $J$ in Fig. 2, far away from the antiresonance. (b) $E=0.1t$, corresponding to point $H$ in Fig. 2, near the antiresonance. (c) $E=0.2t$, corresponding to point $Q$ in Fig. 2, on the other side of the antiresonance. Some circular loop currents around the pentagon are stressed in purple arrows. Note that circular loop currents can also be observed on some hexagons near the defect.

Figure 4

(Color online) Conductance of the topologically disordered sample with a heptagon $G$ (black solid), averaged loop current $⟨i_L⟩$ (blue dashed dot), and induced magnetic moment $m$ (red solid) of the pentagon as functions of Fermi energy $E$. The conductance for a perfect graphene sample $G_0$ (black dashed) with the same dimensions is also plotted for reference.

Figure 5

(Color online) The spatial distribution of LDOS of the sites (blue circles), local current density of the bonds (arrows), and induced magnetic moment of carbon rings (green disks and crosses) near the heptagon. The size of each symbol is proportional to the local value of the corresponding quantity. (a) $E=0.17t$, corresponding to point A in Fig. 4, far away from the antiresonance. (b) $E=-0.15t$, corresponding to point B in Fig. 4, near the antiresonance. (c) $E=-0.12t$, corresponding to point C in Fig. 4, on the other side of the antiresonance. Some loop currents around the pentagon are stressed in purple arrows. Note that circular loop currents can also be observed on some hexagons near the defect.

Figure 6

(Color online) Conductance $G$ (black solid) of the topologically disordered sample with a pentagon-heptagon pair, averaged loop current of the pentagon ${⟨i_L⟩}_{\text{pen}}$ (blue dashed dot) and the heptagon ${⟨i_L⟩}_{\text{hep}}$ (red solid) as functions of Fermi energy $E$.

Figure 7

(Color online) The spatial distribution of LDOS of the sites (blue circles), local current density of the bonds (arrows) near the pentagon-heptagon pair. (a) $E=-0.18t$, corresponding to point A in Fig. 6. (b) $E=0.2t$, corresponding to point B in Fig. 6. Some loop currents near the defect are plotted in purple arrows.