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In this talk I will review the properties of the diamond-chain [1]. This is a
quasi-one-dimensional lattice: a linear chain with a basis containing three
lattice point in the unit cell. This lattice presents a flat band at zero
energy. This energy state correspond to a wave function that is localized on
the lattice sites with lower coordination number [2]. In addition, the full
spectrum can be reduced to a set of three flat bands by under the action of
orbital magnetic fields or spin-orbit interactions [1-3]. The basic feature of
this quasi-one-dimensional system can be extended to two-dimensions by
considering two different lattices: The face-centered square lattice, also
know as Lieb-lattice [4], and the Rhombille tiling, also know as T_3 lattice
[2,3]. Both presents flat bands with Dirac-like cones characterized by integer
pseudo-spin [4,5]. However, only in the case of the T_3 lattice the action of
the magnetic field can reduce the spectrum to a set of three flat bands
[2]. On the contrary in the presence of a second-next neighbor spin-orbit
interaction - Kane-Mele-like - only the Lieb lattice is showing the typical
protected edge stets of topological insulators [5,6].
[1] Bercioux et al., Phys. Rev. Lett. 93, 56802 (2004). [2] J. Vidal et al., Phys. Rev. B 64, 155306 (2001). [3] Bercioux et al., Phys. Rev. B 72, 075305 (2005). [4] N. Goldman, D. F. Urban, and D. Bercioux, Phys. Rev. A 83, 063601 (2011). [5] Bercioux et al.,Phys. Rev. A 80, 063603 (2009). [6] C. Weeks and M. Franz, Phys. Rev. B 82, 085310 (2010). |
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