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Flat edge modes of graphene and of Z2 topological insulator.

Imura K, Mao S, Yamakage A, Kuramoto Y - Nanoscale Res Lett (2011)

Bottom Line: We argue that the appearance of such edge modes are naturally understood by regarding graphene as the gapless limit of a Z2 topological insulator.To illustrate this idea, we consider both Kane-Mele (graphene-based) and Bernevig-Hughes-Zhang models: the latter is proposed for HgTe/CdTe 2D quantum well.Much focus is on the role of valley degrees of freedom, especially, on how they are projected onto and determine the 1D edge spectrum in different edge geometries.

View Article: PubMed Central - HTML - PubMed

Affiliation: Department of Quantum Matter, AdSM, Hiroshima University, Higashi-Hiroshima, 739-8530, Japan. imura@hiroshima-u.ac.jp.

ABSTRACT
A graphene nano-ribbon in the zigzag edge geometry exhibits a specific type of gapless edge modes with a partly flat band dispersion. We argue that the appearance of such edge modes are naturally understood by regarding graphene as the gapless limit of a Z2 topological insulator. To illustrate this idea, we consider both Kane-Mele (graphene-based) and Bernevig-Hughes-Zhang models: the latter is proposed for HgTe/CdTe 2D quantum well. Much focus is on the role of valley degrees of freedom, especially, on how they are projected onto and determine the 1D edge spectrum in different edge geometries.

No MeSH data available.


Zigzag edge geometry.
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Figure 4: Zigzag edge geometry.

Mentions: Figures 3 and 4 shows two representative edge geometries on a 2D square lattice: straight (Figure 3) vs. zigzag (Figure 4) edge geometries. In analogy to the projection of K- and K'-points onto the edge in armchair and zigzag edge geometries, notice that here in the straight edge, Γ and X2 are superposed on the kx-axis. Similarly, X1 and M are projected onto the same point. In the zigzag edge of BHZ model, Γ and M are superposed, whereas X1 and X2 reduce to an equivalent point at the zone boundary.


Flat edge modes of graphene and of Z2 topological insulator.

Imura K, Mao S, Yamakage A, Kuramoto Y - Nanoscale Res Lett (2011)

Zigzag edge geometry.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC3211448&req=5

Figure 4: Zigzag edge geometry.
Mentions: Figures 3 and 4 shows two representative edge geometries on a 2D square lattice: straight (Figure 3) vs. zigzag (Figure 4) edge geometries. In analogy to the projection of K- and K'-points onto the edge in armchair and zigzag edge geometries, notice that here in the straight edge, Γ and X2 are superposed on the kx-axis. Similarly, X1 and M are projected onto the same point. In the zigzag edge of BHZ model, Γ and M are superposed, whereas X1 and X2 reduce to an equivalent point at the zone boundary.

Bottom Line: We argue that the appearance of such edge modes are naturally understood by regarding graphene as the gapless limit of a Z2 topological insulator.To illustrate this idea, we consider both Kane-Mele (graphene-based) and Bernevig-Hughes-Zhang models: the latter is proposed for HgTe/CdTe 2D quantum well.Much focus is on the role of valley degrees of freedom, especially, on how they are projected onto and determine the 1D edge spectrum in different edge geometries.

View Article: PubMed Central - HTML - PubMed

Affiliation: Department of Quantum Matter, AdSM, Hiroshima University, Higashi-Hiroshima, 739-8530, Japan. imura@hiroshima-u.ac.jp.

ABSTRACT
A graphene nano-ribbon in the zigzag edge geometry exhibits a specific type of gapless edge modes with a partly flat band dispersion. We argue that the appearance of such edge modes are naturally understood by regarding graphene as the gapless limit of a Z2 topological insulator. To illustrate this idea, we consider both Kane-Mele (graphene-based) and Bernevig-Hughes-Zhang models: the latter is proposed for HgTe/CdTe 2D quantum well. Much focus is on the role of valley degrees of freedom, especially, on how they are projected onto and determine the 1D edge spectrum in different edge geometries.

No MeSH data available.