Flat Surface State with Octupole Moment in an $e_g$ Orbital System on a Simple Cubic Lattice

TL;DR

This paper investigates surface states in an $e_g$ orbital system on a simple cubic lattice, revealing flat surface states with octupole moments on certain surfaces, which could impact surface physics understanding.

Contribution

It introduces a tight-binding model for $e_g$ orbitals on a simple cubic lattice and uncovers flat surface states with octupole moments on (110) and (111) surfaces.

Findings

Flat surface states extend across the entire Brillouin zone.

Surface states possess octupole moments.

Surface states are well localized on (110) and (111) surfaces.

Abstract

A tight-binding model for $e_g$ orbitals on a simple cubic lattice with finite thickness is investigated. The hopping integrals for nearest-neighboring sites are considered. We examine the electronic band structures for systems with (001), (110), and (111) surfaces. Electronic states well localized around the surfaces are found for the (110) and (111) surfaces. In particular, the surface state is flat and extends in the entire Brillouin zone for the (111) surface, provided the bulk band projected onto the surface Brillouin zone is gapped. We also find that these surface states possess octupole moments in both the (110) and (111) surface cases.