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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 modes of graphene.
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Figure 1: Zigzag edge modes of graphene.

Mentions: Tight-binding implementation allows for giving a precise meaning to two representative edge geometries on hexagonal lattice: armchair and zigzag edges (a general edge geometry is a mixture of the two). Different geometries correspond to different ways of projecting the bulk band structure to 1D edge axis. In the armchair edge, the two Dirac points and reduce to an equivalent point whereas in the zigzag edge, they are projected onto inequivalent points on the edge, i.e., . Figures 1 and 2 show the energy spectrum of graphene (Figure 1) and of the Kane-Mele model (Figure 2) in the zigzag ribbon geometry. t2/t1 ratios are chosen as t2/t1 = 0 and t2/t1 = 0.05 in the above two cases, respectively (t1 is fixed at unity). Dotted lines represent projection of and . In the Kane-Mele model (with a finite t2) the existence of a pair of gapless helical edge modes is ensured by bulk-edge correspondence [20].


Flat edge modes of graphene and of Z2 topological insulator.

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

Zigzag edge modes of graphene.
© Copyright Policy - open-access
Related In: Results  -  Collection

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

Figure 1: Zigzag edge modes of graphene.
Mentions: Tight-binding implementation allows for giving a precise meaning to two representative edge geometries on hexagonal lattice: armchair and zigzag edges (a general edge geometry is a mixture of the two). Different geometries correspond to different ways of projecting the bulk band structure to 1D edge axis. In the armchair edge, the two Dirac points and reduce to an equivalent point whereas in the zigzag edge, they are projected onto inequivalent points on the edge, i.e., . Figures 1 and 2 show the energy spectrum of graphene (Figure 1) and of the Kane-Mele model (Figure 2) in the zigzag ribbon geometry. t2/t1 ratios are chosen as t2/t1 = 0 and t2/t1 = 0.05 in the above two cases, respectively (t1 is fixed at unity). Dotted lines represent projection of and . In the Kane-Mele model (with a finite t2) the existence of a pair of gapless helical edge modes is ensured by bulk-edge correspondence [20].

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.