# Surface states in defect-free polyatomic lattices described by a tight-binding model

## TL;DR

This paper investigates surface localization phenomena in finite defect-free polyatomic lattices using a tight-binding model, revealing conditions for surface state existence and their dependence on lattice parameters.

## Contribution

It introduces a mechanism for surface states in defect-free polyatomic lattices, highlighting the minimum unit cell size and the second-order nature of their emergence.

## Key findings

- Surface states depend on the number of atoms per unit cell.
- Surface states appear when the surface atom's energy differs from others.
- Multiple types of surface states are identified in 2D lattices.

## Abstract

We report about a mechanism for surface localization, present in finite defect-free polyatomic lattices described by a tight binding model. Numerical diagonalization and degenerated perturbation theory show that there is a minimum number of atoms within each unit cell in the lattice for which surface states may exist, provided the local energy of the surface atom is different from the rest in the unit cell. It is shown that the appearance of surface states is a second-order effect in the hopping parameter. Other kinds of surface states are identified in the two-dimensional case.