Fizika Nizkikh Temperatur: Volume 44, Number 12 (December 2018), p. 1678-1691    ( to contents , go back )

Electronic states of pseudospin-1 fermions in dice lattice ribbon

D.O. Oriekhov1, E.V. Gorbar1,2, and V.P. Gusynin2

1Department of Physics, Taras Shevchenko National University of Kyiv, Kyiv 03680, Ukraine

2Bogolyubov Institute for Theoretical Physics, Kyiv 03680, Ukraine
E-mail: vgusynin@bitp.kiev.ua

Received July 20, 2018, published online October 26, 2018

Abstract

Boundary conditions for the two-dimensional fermions in ribbons of the hexagonal lattice are studied in the dice model whose energy spectrum in infinite system consists of three bands with one completely flat band of zero energy. Like in graphene the regular lattice terminations are of the armchair and zigzag types. However, there are four possible zigzag edge terminations in contrast to graphene where only one type of zigzag termination is possible. Determining the boundary conditions for these lattice terminations, the energy spectra of pseudospin-1 fermions in dice model ribbons with zigzag and armchair boundary conditions are found. It is shown that the energy levels for armchair ribbons display the same features as in graphene except the zero energy flat band inherent to the dice model. In addition, unlike graphene, there are no propagating edge states localized at zigzag boundary and there are specific zigzag terminations which give rise to bulk modes of a metallic type in dice model ribbons. We find that the existence of the flat zero-energy band in the dice model is very robust and is not affected by the zigzag and armchair boundaries.

Key words: pseudospin-1, two-dimensional fermions, dice lattice.

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