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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.


Energy spectrum of BHZ model: zigzag edge, Δ/B = 0.2.
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Figure 11: Energy spectrum of BHZ model: zigzag edge, Δ/B = 0.2.

Mentions: The edge spectrum has also a very different character from the straight edge case; typically, its slope in the vicinity of crossing points varies as a function of Δ/B (see Figures 11, 12, 13, 14, 15 and 16): Δ/B = 0.2 (red, Figure 11), Δ/B = 0.8 (green, Figure 12), Δ/B = 2 (blue, Figure 13). Δ/B = 3.2 (cyan, Figure 14), and Δ/B = 4 (magenta, Figure 15). These five plots are superposed in the last panel (Figure 16) to show that the edge spectra at different values of Δ/B are, in contrast to the straight edge case, not on the same curve. Even in the long-wave-length limit: k → 0, their slopes still differ.


Flat edge modes of graphene and of Z2 topological insulator.

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

Energy spectrum of BHZ model: zigzag edge, Δ/B = 0.2.
© Copyright Policy - open-access
Related In: Results  -  Collection

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

Figure 11: Energy spectrum of BHZ model: zigzag edge, Δ/B = 0.2.
Mentions: The edge spectrum has also a very different character from the straight edge case; typically, its slope in the vicinity of crossing points varies as a function of Δ/B (see Figures 11, 12, 13, 14, 15 and 16): Δ/B = 0.2 (red, Figure 11), Δ/B = 0.8 (green, Figure 12), Δ/B = 2 (blue, Figure 13). Δ/B = 3.2 (cyan, Figure 14), and Δ/B = 4 (magenta, Figure 15). These five plots are superposed in the last panel (Figure 16) to show that the edge spectra at different values of Δ/B are, in contrast to the straight edge case, not on the same curve. Even in the long-wave-length limit: k → 0, their slopes still differ.

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.