Hamiltonian decomposition for bulk and surface states

TL;DR

This paper presents a method to decompose Hamiltonians into bulk and boundary components, revealing how next-nearest-neighbor hopping influences surface states, particularly stabilizing edge states in graphene.

Contribution

It introduces a Hamiltonian decomposition technique applicable to lattice systems, highlighting the impact of next-nearest-neighbor hopping on surface state energies and stability.

Findings

Next-nearest-neighbor hopping significantly alters surface state energies.

Decomposition method distinguishes bulk and boundary contributions.

Edge states in graphene are stabilized by next-nearest-neighbor hopping.

Abstract

We demonstrate that a tight-binding Hamiltonian with nearest- and next-nearest-neighbor hopping integrals can be decomposed into bulk and boundary parts in a general lattice system. The Hamiltonian decomposition reveals that next nearest-neighbor hopping causes sizable changes in the energy spectrum of surface states even if the correction to the energy spectrum of bulk states is negligible. By applying the Hamiltonian decomposition to edge states in graphene systems, we show that the next nearest-neighbor hopping stabilizes the edge states.