TY - JOUR

T1 - Orbital dependent band degeneracy and edge states in single layer and AA bilayer honeycomb lattice systems with p orbital degeneracy

AU - Hayashi, Genki

AU - Mizokawa, Takashi

N1 - Funding Information:
The authors would like to thank valuable discussion with Daiki Shimaiwa. This work was partially supported by Grants-in-Aid from the Japan Society for the Promotion of Science (JSPS) (Grant No. JP19H00659).
Publisher Copyright:
© 2022 The Author(s). Published by IOP Publishing Ltd.

PY - 2022/8

Y1 - 2022/8

N2 - We have investigated band structure and edge states of single and AA bilayer honeycomb lattice systems with p orbital degeneracy which would be relevant for relatively heavy metals such as Pb and Bi. The p electrons, which are triply degenerate in the atomic limit, form quadruple degeneracy at K point in a single layer honeycomb lattice. The spin-orbit interaction splits the quartet at K point into two singlets and one doublet which are mixtures of p x, p y and p z orbitals. In the AA bilayer honeycomb lattice, the Dirac node at K point is deformed into circular line node around it. With the intermediate interlayer coupling, there is a degenerate point along Γ-K with p z character. A p x/p y type degenerate point exists under the strong interlayer coupling. This degenerate point is robust against the spin-orbit interaction and the antiferromagnetic spin arrangement only along the intralayer bonds. Without SOI, localized edge states with p x/p y or p z character are created at the zigzag edges both in the single and AA bilayer systems. In the AA bilayer system with SOI, only the p x/p y edge states exhibit the Dirac-like dispersion.

AB - We have investigated band structure and edge states of single and AA bilayer honeycomb lattice systems with p orbital degeneracy which would be relevant for relatively heavy metals such as Pb and Bi. The p electrons, which are triply degenerate in the atomic limit, form quadruple degeneracy at K point in a single layer honeycomb lattice. The spin-orbit interaction splits the quartet at K point into two singlets and one doublet which are mixtures of p x, p y and p z orbitals. In the AA bilayer honeycomb lattice, the Dirac node at K point is deformed into circular line node around it. With the intermediate interlayer coupling, there is a degenerate point along Γ-K with p z character. A p x/p y type degenerate point exists under the strong interlayer coupling. This degenerate point is robust against the spin-orbit interaction and the antiferromagnetic spin arrangement only along the intralayer bonds. Without SOI, localized edge states with p x/p y or p z character are created at the zigzag edges both in the single and AA bilayer systems. In the AA bilayer system with SOI, only the p x/p y edge states exhibit the Dirac-like dispersion.

KW - honeycomb lattice

KW - p orbital degeneracy

KW - spin-orbit interaction

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U2 - 10.1088/2399-6528/ac8855

DO - 10.1088/2399-6528/ac8855

M3 - Article

AN - SCOPUS:85137384646

VL - 6

JO - Journal of Physics Communications

JF - Journal of Physics Communications

SN - 2399-6528

IS - 8

M1 - 085011

ER -