Reverse strain-induced snake states in graphene nanoribbons

Strain can tailor the band structures and properties of graphene nanoribbons (GNRs) with the well-known emergent pseudomagnetic fields and the corresponding pseudo Landau levels. We design one type of the zigzag GNR with reverse strains, producing pseudomagnetic fields with opposite signs in the lower and upper half planes. Therefore, electrons propagate along the interface as “snake states,” experiencing opposite Lorentz forces as they cross the zero field border line. By using the Landauer-Büttiker formalism combined with the nonequilibrium Green's function method, the existence and robustness of the reverse strain-induced snake states are further studied. Furthermore, the realization of long-thought pure valley currents in monolayer graphene systems is also proposed in our device.

Figure 1

(a) and (d) are the schematic diagrams of the ZGNR with MIS and SS, respectively. The blue dotted rectangle represents a primitive cell for the ZGNR, and the red (blue) arrows depict the current for the $K$ ($K^{\prime }$) valley. (b) and (c) [(e) and (f)] are energy bands and the distributions of wave functions for the ZGNR with MIS (SS).

Figure 2

(a) and (b) show the QH edge states, where the electrons take circular motions under the perpendicular magnetic field. (c) and (d) show the QVH edge states, where the electrons take circular motions under the perpendicular pseudomagnetic fields. Because the electrons experience opposite Lorentz forces as they cross the zero field border line, the snake states propagate along the interface.

Figure 3

Schematic diagram showing (a) two-terminal and (b) four-terminal measurement geometries. In (a) a charge current $I^c=4e^{2}V/h$ flows into the right lead. In (b) a valley current $I^v=e^{2}V/h$ flows into the right lead.

Figure 4

Conductances versus Fermi energy for the strained ZGNRs. (a) is the schematic diagram of the two-terminal device. (b) shows the conductance plateaus for the ZGNR without strain, ZGNR with SS, and ZGNR with MIS, respectively. (c) illustrates the conductances of the ZGNR with SS for different strain strength. (d)–(f) show the influences of Anderson disorders on conductances with (e) and (f) from (d).

Figure 5

(a) The band structure adopted from Fig. 1. (b) The comparison between the energy points marked by green circles in (a) and the Landau levels generated by the real magnetic field.

Figure 6

Spatial distributions of the eigenstates belong to $E=0.33$ eV, $E=0.275$ eV, and $E=0.255$ eV, respectively.