[Paper Review] Observation of surface states derived from topological Fermi arcs in the Weyl semimetal NbP

Ilya Belopolski, Su‐Yang Xu+17 more|arXiv (Cornell University)|Sep 24, 2015

Topological Materials and Phenomena18 references4 citations

TL;DR

This study uses angle-resolved photoemission spectroscopy (ARPES) and ab initio calculations to show that NbP is a Weyl semimetal despite the absence of resolved Fermi arcs due to weak spin-orbit coupling and a low Fermi level. The authors propose a new criterion for identifying Fermi arcs based on kinked dispersion and directional dispersion with binding energy, suggesting that raising the Fermi level by >20 meV could enable direct observation of topological surface states in NbP and similar materials.

ABSTRACT

The recent experimental discovery of a Weyl semimetal in TaAs provides the first observation of a Weyl fermion in nature and demonstrates a novel type of anomalous surface state band structure, consisting of Fermi arcs. So far, work has focused on Weyl semimetals with strong spin-orbit coupling (SOC). However, Weyl semimetals with weak SOC may allow tunable spin-splitting for device applications and may exhibit a crossover to a spinless topological phase, such as a Dirac line semimetal in the case of spinless TaAs. NbP, isostructural to TaAs, may realize the first Weyl semimetal in the limit of weak SOC. Here we study the surface states of NbP by angle-resolved photoemission spectroscopy (ARPES) and we find that we $ extit{cannot}$ show Fermi arcs based on our experimental data alone. We present an $ extit{ab initio}$ calculation of the surface states of NbP and we find that the Weyl points are too close and the Fermi level is too low to show Fermi arcs either by (1) directly measuring an arc or (2) counting chiralities of edge modes on a closed path. Nonetheless, the excellent agreement between our experimental data and numerical calculations suggests that NbP is a Weyl semimetal, consistent with TaAs, and that we observe trivial surface states which evolve continuously from the topological Fermi arcs above the Fermi level. Based on these results, we propose a slightly different criterion for a Fermi arc which, unlike (1) and (2) above, does not require us to resolve Weyl points or the spin splitting of surface states. We propose that raising the Fermi level by $> 20$ meV would make it possible to observe a Fermi arc using this criterion in NbP. Our work offers insight into Weyl semimetals with weak spin-orbit coupling, as well as the crossover from the spinful topological Weyl semimetal to the spinless topological Dirac line semimetal.

Motivation & Objective

• To investigate surface states in NbP, a Weyl semimetal with weak spin-orbit coupling, using angle-resolved photoemission spectroscopy (ARPES).
• To determine whether topological Fermi arcs can be experimentally observed in NbP, given the challenges posed by low Fermi level and small Weyl point separation.
• To develop a new experimental criterion for identifying Fermi arcs that does not require resolving Weyl points or spin-splitting.
• To explore the evolution of trivial surface states into topological Fermi arcs above the Fermi level in NbP.
• To compare the surface state structure of NbP with that of TaAs, highlighting differences due to spin-orbit coupling strength and Weyl point separation.

Proposed method

• Conduct high-resolution ARPES measurements on the (001) surface of NbP at SSRL and SIS beamlines to map surface state dispersions.
• Perform ab initio calculations of surface states in NbP to compare with experimental ARPES data and validate the topological nature of the system.
• Analyze the dispersion of surface states, particularly the lollipop and peanut pockets, to assess hybridization and orbital character differences.
• Use the observed kink in dispersion at ~0.2 eV binding energy and directional dispersion trends as a new criterion for identifying Fermi arcs.
• Apply a modified topological criterion based on non-closed Fermi surface contours that disperse in one direction with increasing binding energy.
• Compare the surface state band structures of NbP and TaAs to highlight the effects of spin-orbit coupling and Weyl point separation on Fermi arc visibility.

Experimental results

Research questions

• RQ1 Can topological Fermi arcs be experimentally observed in NbP despite weak spin-orbit coupling and a low Fermi level?
• RQ2 What is the relationship between trivial surface states and topological Fermi arcs in NbP, and how do they evolve with binding energy?
• RQ3 Can a new experimental criterion for identifying Fermi arcs be established that does not require resolving Weyl points or spin-splitting?
• RQ4 How does the surface state structure in NbP differ from that in TaAs, and what role does spin-orbit coupling play in these differences?
• RQ5 What conditions are necessary to make topological Fermi arcs observable in NbP, and how does Fermi level tuning affect this?

Key findings

• ARPES measurements on NbP show no direct evidence of Fermi arcs due to the low Fermi level and small Weyl point separation.
• Ab initio calculations confirm that the observed surface states in NbP are consistent with a Weyl semimetal phase, with trivial surface states evolving continuously into topological Fermi arcs above the Fermi level.
• A new criterion for identifying Fermi arcs is proposed: a kinked dispersion that disperses in one direction with increasing binding energy, independent of resolving Weyl points or spin splitting.
• Raising the Fermi level by more than 20 meV is predicted to make Fermi arcs observable using this new criterion in NbP.
• The lollipop and peanut surface pockets in NbP do not hybridize due to different orbital character (in-plane vs. out-of-plane d and p orbitals), which is linked to C₂ symmetry of the (001) surface.
• The rich surface state structure in NbP may explain the invisibility of the bulk band structure in vacuum ultraviolet ARPES, as surface states fully occupy available orbitals at the surface.