Dirac-point engineering and topological phase transitions in honeycomb optical lattices

By B. Wűnsch, Francisco Guinea, F. Sols. 2008

146 citations recorded by the source corpus.

We study the electronic structure and the phase diagram of non-interacting fermions confined to hexagonal optical lattices. In the first part, we compare the properties of Dirac points arising in the eigenspectrum of either honeycomb or triangular lattices. Numerical results are complemented by analytical equations for weak and strong confinements. In the second part, we discuss the phase diagram and the evolution of Dirac points in honeycomb lattices applying a tight-binding description with arbitrary nearest-neighbor hoppings. With increasing asymmetry between the hoppings the Dirac points approach each other. At a critical asymmetry the Dirac points merge to open an energy gap, thus changing the topology of the eigenspectrum. We analyze the trajectory of the Dirac points and study the density of states in the different phases. Manifestations of the phase transition in the temperature dependence of the specific heat and in the structure factor are discussed.

Subfields: Atomic and Molecular Physics, and Optics

View Paper: https://www.semanticscholar.org/paper/2e1c62342386682434837228a09a6372b61309c5

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

Citations in the corpus

Colloquium: Graphene spectroscopy (2014, background): “The defining topology feature of 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 et al., 2008; Wunsch et al., 2008).”
Creating, moving and merging Dirac points with a Fermi gas in a tunable honeycomb lattice (2011, background): “6(7)Hz, which is small compared with the full bandwidth,W/h5 4.”
Electronic properties of graphene in a strong magnetic field (2010, background): “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.”
Colloquium : Topological band theory (2016, unknown): “(Kotov et al. 2012) In particular, a 2D electron gas under an external hexagonal periodic potential or optical lattice has been shown to develop graphene-like massless Dirac cones both theoretically (Park and Louie 2009; Wunsch, Guinea, and Sols 2008) and experimentally.”
Novel effects of strains in graphene and other two dimensional materials (2015, background): “It also arises when applying uniaxial strain in the zigzag direction, a situation that has been discussed at length in the literature [58, 106, 244, 363].”
Designer Dirac fermions and topological phases in molecular graphene (2012, background): “Because the accessibility of this physics is predicated on the synthesis of new materials, the quest for Dirac quasi-particles has expanded to artificial systems such as lattices comprising ultracold atom”