[Paper Review] Anisotropic Dirac fermions in a Bi square net of SrMnBi2

J. Park, G. Lee+9 more|arXiv (Cornell University)|Apr 27, 2011

Quantum Chromodynamics and Particle Interactions15 citations

TL;DR

This study identifies highly anisotropic Dirac fermions in the Bi square net of SrMnBi2 through first-principles calculations, angle-resolved photoemission spectroscopy (ARPES), and quantum oscillation measurements on high-quality single crystals. The Dirac cone exhibits a Fermi velocity anisotropy ratio of ~8, distinguishing it from isotropic Dirac fermions in graphene or topological insulators, and establishes the Bi square net as a new platform for anisotropic Dirac fermions with tunable electronic properties.

ABSTRACT

We report the highly anisotropic Dirac fermions in a Bi square net of SrMnBi2, based on a first principle calculation, angle resolved photoemission spectroscopy, and quantum oscillations for high-quality single crystals. We found that the Dirac dispersion is generally induced in the (SrBi)+ layer containing a double-sized Bi square net. In contrast to the commonly observed isotropic Dirac cone, the Dirac cone in SrMnBi2 is highly anisotropic with a large momentum-dependent disparity of Fermi velocities of ~ 8. These findings demonstrate that a Bi square net, a common building block of various layered pnictides, provide a new platform that hosts highly anisotropic Dirac fermions.

Motivation & Objective

• To identify and characterize Dirac fermions in the layered pnictide SrMnBi2, particularly within its Bi square net structure.
• To investigate whether the Bi square net—a common building block in layered pnictides—can host Dirac fermions with anisotropic dispersion.
• To determine the electronic structure and Fermi velocity anisotropy of Dirac fermions in SrMnBi2 using multiple experimental and theoretical techniques.
• To explore the potential of SrMnBi2 and related compounds as tunable platforms for anisotropic Dirac fermions with coupled magnetic or superconducting orders.

Proposed method

• First-principles calculations using the full-potential linearized augmented plane wave (FP-LAPW) method within the generalized gradient approximation (GGA) to model the electronic band structure.
• Angle-resolved photoemission spectroscopy (ARPES) with 24 eV photons at UVSOR beamline 7U, performed on cleaved single crystals under ultra-high vacuum (<7×10⁻¹¹ Torr).
• Quantum oscillation measurements using 6-probe magnetotransport in high magnetic fields up to 63 T at the Dresden High Magnetic Field Laboratory and up to 33 T at NHMFL.
• Analysis of Shubnikov–de Haas (SdH) oscillations to extract Fermi surface cross-sectional area, effective mass, scattering time, and Berry’s phase.
• Use of the Onsager relation (F = (Φ₀/2π²)Aₖ) to determine the Fermi surface cross-sectional area from the quantum oscillation frequency.
• SdH fan diagram analysis to extract the Berry’s phase from the intercept of 1/Bₙ vs. Landau level index n, with a non-zero intercept indicating Dirac fermions.

Experimental results

Research questions

• RQ1 Does the Bi square net in SrMnBi2 host Dirac fermions with anisotropic dispersion, and if so, what is the degree of anisotropy in the Fermi velocity?
• RQ2 What experimental evidence confirms the presence of Dirac fermions in SrMnBi2, particularly in terms of non-zero Berry’s phase and quantum oscillations?
• RQ3 How does the electronic structure of SrMnBi2 differ from isotropic Dirac materials like graphene, particularly in terms of band dispersion and Fermi velocity anisotropy?
• RQ4 Can the anisotropic Dirac cone in SrMnBi2 be tuned via chemical substitution of alkaline earth metals or pnictogens, and how does magnetic ordering in MnBi layers affect the Dirac state?
• RQ5 What is the role of the (SrBi)+ layer and double-sized Bi square net in stabilizing the anisotropic Dirac cone?

Key findings

• The Dirac cone in SrMnBi2 exhibits a large momentum-dependent anisotropy in Fermi velocity, with a ratio of maximum to minimum v_F ≈ 8, indicating highly anisotropic Dirac fermions.
• ARPES measurements confirm a linear energy dispersion in the Bi square net, with a Dirac point located at the Γ point of the Brillouin zone.
• Quantum oscillation measurements reveal a single Fermi surface pocket with a frequency F = 152(5) T, corresponding to a cross-sectional area Aₖ = 1.45(5) nm⁻², or ~0.7% of the Brillouin zone.
• The cyclotron effective mass is measured as m_c = 0.29(2)mₑ, and the scattering time is τ = 3.5(5)×10⁻¹⁴ s⁻¹, yielding a mobility of ~250 cm²/Vs.
• The SdH fan diagram shows a non-zero intercept at n = -0.40(9), yielding a Berry’s phase of 0.5, confirming the presence of Dirac fermions with a non-trivial topological character.
• The combination of low effective mass, high mobility, and non-zero Berry’s phase establishes SrMnBi2 as a bulk Dirac material with anisotropic Dirac fermions hosted in the Bi square net.