[Paper Review] Theoretical Discovery/Prediction: Weyl Semimetal states in the TaAs material (TaAs, NbAs, NbP, TaP) class

Shin-Ming Huang, Su‐Yang Xu+10 more|arXiv (Cornell University)|Jan 5, 2015

Topological Materials and PhenomenaPhysics and Astronomy30 references641 citations

TL;DR

This paper theoretically predicts the existence of Weyl semimetal states in stoichiometric, inversion-symmetry-breaking materials such as TaAs, NbAs, NbP, and TaP. Using first-principles calculations, it identifies spin-polarized Weyl cones and topologically protected Fermi arc surface states, demonstrating that these materials host robust, intrinsic Weyl fermions without requiring fine-tuning of composition or magnetic order, establishing TaAs as the first candidate for a topological semimetal phase in a real material system.

ABSTRACT

The recent discoveries of Dirac fermions in graphene and on the surface of topological insulators have ignited worldwide interest in physics and materials science. A Weyl semimetal is an unusual crystal where electrons also behave as massless quasi-particles but interestingly they are not Dirac fermions. These massless particles, Weyl fermions, were originally considered in massless quantum electrodynamics but have not been observed as a fundamental particle in nature. A Weyl semimetal provides a condensed matter realization of Weyl fermions, leading to unique transport properties with novel device applications. Here, we THEORETICALLY identify the first Weyl semimetal in a class of stoichiometric materials (TaAs, NbAs, NbP, TaP), which break crystalline inversion symmetry, including TaAs, TaP, NbAs and NbP. Our first-principles calculation-based predictions on TaAs reveal the spin-polarized Weyl cones and Fermi arc surface states in this compound. We also observe pairs of Weyl points with the same chiral charge which project onto the same point in the surface Brillouin zone, giving rise to multiple Fermi arcs connecting to a given Weyl point. Our results show that TaAs is the first topological semimetal identified which does not depend on fine-tuning of chemical composition or magnetic order, greatly facilitating an exploration of Weyl physics in real materials. (Note added: This theoretical prediction of November 2014 (see paper in Nature Communications) was the basis for the first experimental discovery of Weyl Fermions and topological Fermi arcs in TaAs recently published in Science (2015) at http://www.sciencemag.org/content/early/2015/07/15/science.aaa9297.full.pdf)

Motivation & Objective

• To identify a class of stoichiometric, non-magnetic, inversion-asymmetric materials that host intrinsic Weyl semimetal states.
• To demonstrate that Weyl fermions can emerge as robust quasiparticles in a real crystalline solid without requiring external tuning or magnetic order.
• To establish the existence of topologically protected Fermi arc surface states in these materials, which are signatures of non-trivial topology in a semimetal.
• To provide a theoretical foundation for the experimental discovery of Weyl fermions and their unique transport phenomena in real materials.

Proposed method

• First-principles density functional theory (DFT) calculations using the GGA functional and norm-conserving pseudopotentials.
• Inclusion of spin-orbit coupling via j-dependent pseudopotentials to capture spin-polarized band structures.
• Construction of symmetry-respecting Wannier functions for As p and Ta d orbitals to generate a real-space tight-binding Hamiltonian.
• Use of a 80-atomic-layer slab model with Ta-terminated and As-terminated surfaces to compute surface states.
• Employment of a (17×17×5) k-point mesh for Brillouin zone sampling and a 1000 Ry real-space cutoff for numerical integration.
• Analysis of band structures and Fermi surface contours to identify Weyl points and their topological properties.

Experimental results

Research questions

• RQ1 Can Weyl semimetal states emerge in stoichiometric, non-magnetic, inversion-asymmetric materials like TaAs without requiring fine-tuning of chemical composition or magnetic order?
• RQ2 What is the nature of the surface states in such materials, and do they exhibit topologically protected Fermi arcs as predicted by theory?
• RQ3 How do Weyl points with opposite chiral charge project onto the surface Brillouin zone, and what is the resulting surface state connectivity?
• RQ4 What is the role of bulk band topology in generating closed Fermi surface contours on the surface, and how does this relate to the annihilation of Weyl points?
• RQ5 Can electron transport along constant energy contours exhibit exotic behavior due to the interplay between surface arcs and bulk Weyl points?

Key findings

• First-principles calculations confirm the presence of spin-polarized Weyl cones in TaAs, with linear dispersion in all three momentum directions around Weyl points.
• Multiple Fermi arc surface states are observed, with pairs of Weyl points of the same chiral charge projecting onto the same point in the surface Brillouin zone.
• The Weyl semimetal phase in TaAs is robust and intrinsic, arising from crystalline inversion symmetry breaking without requiring tuning of chemical composition or magnetic order.
• Fermi arc surface states connect Weyl points in a way that enables a novel electron trajectory: from a surface arc, through the bulk to the opposite surface, and back via another arc, forming a closed loop.
• Theoretical analysis shows that annihilating Weyl points in pairs can lead to either a trivial or topological insulator phase, depending on the annihilation path, with implications for the observed closed Fermi surfaces near the X̄′ point on the bottom surface.
• The predicted surface transport behavior—where electrons traverse surface arcs and Weyl points in a loop—suggests exotic non-local and chiral transport phenomena, consistent with theoretical proposals for Weyl semimetal devices.