[Paper Review] Two-dimensional Dirac nodal-line semimetal protected by symmetry

Xingxia Cui, Yafei Li+13 more|arXiv (Cornell University)|Dec 30, 2020

Topological Materials and Phenomena50 references4 citations

TL;DR

This paper reports the first experimental realization of a two-dimensional Dirac nodal-line semimetal (2D DNLS) protected by intrinsic crystalline symmetry, specifically in a 3-atomic-layer bismuth (3-AL Bi(110)) film grown epitaxially on black phosphorus. The non-symmorphic space group symmetry of the 3-AL Bi(110) structure topologically protects the Dirac nodal line from spin-orbit coupling, enabling robust linearly dispersing Dirac bands with four-fold degeneracy, confirmed by molecular beam epitaxy, STM, nc-AFM, DFT, and space group analysis.

ABSTRACT

Dirac nodal line semimetals (DNLSs) host relativistic quasiparticles in their one-dimensional (1D) Dirac nodal line (DNL) bands that are protected by certain crystalline symmetries. Their novel low-energy fermion quasiparticle excitations and transport properties invite studies of relativistic physics in the solid state where their linearly dispersing Dirac bands cross at continuous lines with four-fold degeneracy. In materials studied up to now, the four-fold degeneracy, however, has been vulnerable to suppression by the ubiquitous spin-orbit coupling (SOC). Despite the current effort to discover 3D DNLSs that are robust to SOC by theory, positive experimental evidence is yet to emerge. In 2D DNLSs, because of the decreased total density of states as compared with their 3D counterparts, it is anticipated that their physical properties would be dominated by the electronic states defined by the DNL. It has been even more challenging, however, to discover robust 2D DNLSs against SOC because of their lowered symmetry; no such materials have yet been predicted by theory. By combining molecular beam epitaxy growth, STM, nc-AFM characterisation, with DFT calculations and space group theory analysis, here we reveal a novel class of 2D crystalline DNLSs that host the exact symmetry that protects them against SOC. The discovered quantum material is a brick phase 3-AL Bi(110), whose symmetry protection and thermal stability are imparted by the compressive vdW epitaxial growth on black phosphorus substrates. The BP substrate templates the growth of 3-AL Bi(110) nano-islands in a non-symmorphic space group structure. This crystalline symmetry protects the DNL electronic phase against SOC independent of any orbital or elemental factors. We theoretically establish that this intrinsic symmetry imparts a general, robust protection of DNL in a series of isostructural 2D quantum materials.

Motivation & Objective

• To discover a two-dimensional Dirac nodal-line semimetal (2D DNLS) that is robust against spin-orbit coupling (SOC), a major challenge in 2D systems due to reduced symmetry.
• To identify a crystalline symmetry mechanism that intrinsically protects the Dirac nodal line (DNL) without relying on orbital or elemental factors.
• To demonstrate that such symmetry protection enables stable, four-fold degenerate DNL bands in a 2D quantum material with linear dispersion.

Proposed method

• Molecular beam epitaxy (MBE) was used to grow 3-atomic-layer bismuth (3-AL Bi(110)) nano-islands on black phosphorus substrates.
• Scanning tunneling microscopy (STM) and non-contact atomic force microscopy (nc-AFM) were employed to characterize the atomic structure and surface morphology of the 3-AL Bi(110) islands.
• Density functional theory (DFT) calculations were performed to analyze the electronic band structure and confirm the presence of a Dirac nodal line with four-fold degeneracy.
• Space group theory analysis was applied to identify the non-symmorphic symmetry (specifically, the I4/mmm space group) responsible for topological protection of the DNL.
• The epitaxial strain from the black phosphorus substrate was shown to stabilize the 3-AL Bi(110) phase and enforce the symmetry that protects the DNL.
• Theoretical modeling established that this symmetry protection is generalizable to a class of isostructural 2D materials.

Experimental results

Research questions

• RQ1 Can a two-dimensional Dirac nodal-line semimetal be stabilized in a 2D system with robust protection against spin-orbit coupling?
• RQ2 What specific crystalline symmetry in 2D materials can provide intrinsic topological protection for a Dirac nodal line independent of electronic or elemental factors?
• RQ3 How does the epitaxial growth on black phosphorus influence the formation of a 3-AL Bi(110) phase with non-symmorphic symmetry?
• RQ4 To what extent does the non-symmorphic space group symmetry in 3-AL Bi(110) prevent the lifting of four-fold degeneracy at the Dirac nodal line?
• RQ5 Is the symmetry protection mechanism observed in 3-AL Bi(110) generalizable to other 2D materials with similar crystal structures?

Key findings

• The 3-AL Bi(110) film grown on black phosphorus exhibits a Dirac nodal line (DNL) with four-fold degeneracy, confirmed by DFT calculations and STM measurements.
• The DNL is topologically protected by the non-symmorphic space group symmetry (I4/mmm) of the 3-AL Bi(110) structure, which prevents splitting due to spin-orbit coupling.
• The epitaxial growth on black phosphorus induces compressive strain that stabilizes the 3-AL Bi(110) phase and enforces the symmetry responsible for DNL protection.
• Theoretical analysis confirms that this symmetry protection is general and applies to a series of isostructural 2D materials beyond bismuth.
• The 3-AL Bi(110) system exhibits high thermal stability and well-defined atomic layers, enabling robust observation of the DNL phase.
• The absence of spin-orbit coupling splitting in the DNL is attributed solely to the crystalline symmetry, not to material-specific electronic or orbital characteristics.