Zero modes of tight-binding electrons on the honeycomb lattice
By Y. Hasegawa, R. Konno, H. Nakano, M. Kohmoto. 2006
164 citations recorded by the source corpus.
Tight binding electrons on the honeycomb lattice are studied where nearest neighbor hoppings in the three directions are $t_a,t_b$ and $t_c$, respectively. For the isotropic case, namely for $t_a=t_b=t_c$, two zero modes exist where the energy dispersions at the vanishing points are linear in momentum $k$. Positions of zero modes move in the momentum space as $t_a,t_b$ and $t_c$ are varied. It is shown that zero modes exist if $||\frac{t_b}{t_a}| -1| \leq |\frac{t_c}{t_a}| \leq ||\frac{t_b}{t_a}|+1|$. The density of states near a zero mode is proportional to $|E|$ but it is propotional to $\sqrt{|E|}$ at the boundary of this condition.
Subfields: Atomic and Molecular Physics, and Optics, Condensed Matter Physics
View Paper: https://www.semanticscholar.org/paper/cd990a641236d06a6a44029671bedd59ae7b3864
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Atomic and Molecular Physics, and Optics
In Condensed Matter Physics
Citations in the corpus
- Colloquium: The transport properties of graphene: An introduction (2010, background): “The different types of states are a result of the different shifts of the two Dirac cones over the Brillouin zone (Hasegawa et al., 2006; Montam- 19 baux et al., 2009), induced by the strain and governing the vector potential of Eq.”
- Electronic properties of graphene in a strong magnetic field (2010, unknown): “The hopping t′ along δ3 is then different from that t along δ1 and δ2 (Dietl et al., 2008; Farjam and Rafii-Tabar, 2009; Goerbig et al., 2008; Hasegawa et al., 2006; Wunsch et al., 2008; Zhu et al., 2007), t→ t′ = t+ ∂t ∂a δa.”
- Strain effects in graphene and graphene nanoribbons: The underlying mechanism (2010, methodology): “It was previously suggested using an analytical model that a realistic band gap will be opened under such a collision [43], and a similar effect has also been observed in TB and DFT calculations [26, 30, 31].”
- Creating, moving and merging Dirac points with a Fermi gas in a tunable honeycomb lattice (2011, methodology): “7(5)Hz, as calibrated from dipole oscillations of the cloud.”
- Colloquium: Graphene spectroscopy (2014, background): “The defining topology feature of the graphene electronic band, namely, the degeneracy of conical electron and hole bands at Dirac points, is protected by the inversion symmetry of graphene lattice (Hasegawa et al., 2006; Kishigi, Takeda, and Hasegawa, 2008; Wunsch, Guinea, and Sols, 2008).”