# Hybridization of topological surface states with a flat band

## TL;DR

This paper investigates how topological surface states interact with a flat bulk band, revealing transformations into different surface states and the emergence of Fermi arcs in Dirac semimetals through a combined theoretical model.

## Contribution

It introduces a hybrid model combining 3D topological and 2D pseudospin Hamiltonians to explicitly analyze surface state evolution with flat band hybridization.

## Key findings

- Hybridization converts Dirac-like states into branches below and above the flat band.
- Upper surface state branch is identified as Dyakonov-Khaetskii states.
- Fermi arcs emerge when the flat band crosses the conduction band.

## Abstract

We address the problem of hybridization between topological surface states and a non-topological flat bulk band. Our model, being a mixture of three-dimensional Bernevig-Hughes-Zhang and two-dimensional pseudospin-1 Hamiltonian, allows explicit treatment of the topological surface state evolution by continuously changing the hybridization between the inverted bands and an additional "parasitic" flat band in the bulk. We show that the hybridization with a flat band lying below the edge of conduction band converts the initial Dirac-like surface states into a branch below and one above the flat band. Our results univocally demonstrate that the upper branch of the topological surface states is formed by Dyakonov-Khaetskii surface states known for HgTe since the 1980s. Additionally we explore an evolution of the surface states and the arising of Fermi arcs in Dirac semimetals when the flat band crosses the conduction band.