Two-fold symmetry flattens Dirac cone of surface state at W(110)

TL;DR

This study investigates how the two-fold symmetry of W(110) surface affects the shape and spin properties of Dirac-like surface states, revealing a flattened Dirac cone caused by hybridization with bulk states, with implications for spintronic systems.

Contribution

It provides a detailed experimental and theoretical analysis of the influence of $C_{2v}$ symmetry on surface states, including the flattening of the Dirac cone and spin texture behavior.

Findings

Dirac cone appears along specific symmetry lines

Flattened Dirac cone due to hybridization with bulk states

Spin texture shows quasi-one dimensional behavior

Abstract

The $C_{2v}$ symmetry of the W(110) surface influences strongly the spin-polarized Dirac-cone-like surface state within a spin-orbit-induced symmetry gap. We present a detailed angle-resolved photoemission study with $s$- and $p$-polarized light along three different symmetry lines. The Dirac-cone-like feature appears along $\bar{\Gamma}\bar{H}$ and $\bar{\Gamma}\bar{S}$, while it is strongly deformed along $\bar{\Gamma}\bar{N}$. A two-fold $\Sigma_{3}$ symmetry of the $d$-type surface state is identified from photoemission experiments using linear polarized light. Our results are well described by model calculations based on an effective Hamiltonian with $C_{2v}$ symmetry including Rashba parameters up to third order. The flattened Dirac cone of the surface state is caused by hybridization with bulk continuum states of $\Sigma_{1}$ and $\Sigma_{2}$ symmetry. The spin texture of this state obtained from the model calculations shows a quasi-one dimensional behavior. This finding opens a new avenue in the study of $d$-electron-based persistent spin helix systems and/or weak topological insulators.