Unconventional phases in a Haldane model of dice lattice

We propose a Haldane-like model of dice lattice analogous to graphene and explore its topological properties within the tight-binding formalism. The topological phase boundary of the system is identical to that of Haldane model of graphene but the phase diagram is richer than the latter due to existence of a distorted flat band. The system supports phases which have a gapped-out valence (conduction) band and an indirect overlap between the conduction (valence) band and the distorted flat band. The overlap of bands imparts metallic character to the system. These phases may be further divided into topologically trivial and nontrivial ones depending on the Chern number of the gapped-out band. The semimetallic phases exist as distinct points that are well separated from each other in the phase diagram and exhibit spin-1 Dirac-Weyl dispersion at low energies. The Chern numbers of the bands in the Chern-insulating phases are 0 and +/- 2. This qualifies the system to be candidate for quantum anomalous Hall effect with two chiral channels per edge. Counterpropagating edge states emanate from the flat band in certain topologically trivial phases. The system displays beating pattern in Shubnikov de Haas oscillations for unequal magnitude of mass terms in the two valleys. We show that the chemical potential and ratio of topological parameters of the system viz. Semenoff mass and next-neighbor hopping amplitude may be experimentally determined from the number of oscillations between the beating nodes and the beat frequency, respectively.