Effects of edge potential on an armchair-graphene open boundary and nanoribbons

Abstract

Pseudospin flipping is found to be the key process leading to the formation of an edge-potential-induced edge state at an armchair-graphene open boundary and nanoribbons. At an open boundary, the edge potential U 0 is shown to turn on pseudospin-flipped (intravalley) scattering even though U 0 does not post an apparent breaking of the AB site (basis atoms) symmetry. For a valley-polarized incident beam, the interference between the pseudospin-conserving (intervalley) and -nonconserving (intravalley) processes in the scattering state leads to a finite out-of-plane pseudospin density. This two-wave feature in the evanescent regime leads to the formation of the edge state. The physical origin of the edge state is different from that for the Tamm states in semiconductors. For an armchair-graphene nanoribbon with a gapless energy spectrum, applying U 0 to both edges opens up an energy gap. Both edge states and energy gap opening exhibit distinct features in nanoribbon conductance.

Edge states in a ferromagnetic honeycomb lattice with armchair boundaries

“…After introducing an external on-site potential at the outermost sites, we find that the edge states are tunable. Interestingly, we find that the nature of such edge states is Tamm-like [19], in contrast with the equivalent model for the armchair graphene [8] but, as mentioned earlier, in agreement with the experiments in photonic lattices [17,18]. Furthermore, after introducing a Dzialozinskii-Moriya interaction (DMI), we find that the topologically protected edge states are sensitive to the presence of the Tamm-like states and they also become tunable.…”

“…For example, there are flat edge states connecting the two Dirac points in a lattice with zig-zag [1] or bearded edges [6]. On the contrary, there are no edge states in a lattice with armchair boundary [7], unless a boundary potential is applied [8].…”

Valley-dependent resonant inelastic transmission through a time-modulated region in graphene

“…[10][11][12][13][14][15][16][17] The two nonequivalent valleys K and K points (Dirac points) at the corners of the Brillouin zone result from the triangular Bravias lattice, and the amplitudes of the states in the sublattice constitute a pseudospin. Various anomalous phenomena ranging from the Klein tunneling, 18 quantum Hall effects, 19,20 weak (anti-) localization, [21][22][23] focusing electron flow 24,25 electron beam supercollimation, 26 and edge-states physics [27][28][29][30][31][32] are attributed to the relativistic dispersion. Exploration of valleytronics in graphene has led to studies on valley filter, [33][34][35][36][37] valley polarization detection, 38 valley physics with broken inversion symmetry, 39 valley physics in strained graphene, 36,40,41 and valley-based qubit in graphene rings 42 and in double quantum dots.…”

Helical edge states and edge-state transport in strained armchair graphene nanoribbons

“…But people found that modifications on armchair edges can induce complete flat bands, where the wavefunction has the character of valley polarization 27 . The use of edge potentials can also cause the formation of edge states, and the key is to turn on the pseudospin-flipped (intravalley) scattering processes 28 . In this case, the armchair edge bands behave similar to the zigzag ones.…”