[Paper Review] Dirac node lines in a two-dimensional bipartite square lattice

Bo Yang, Xiaoming Zhang+1 more|arXiv (Cornell University)|Dec 20, 2016

Topological Materials and Phenomena3 references3 citations

TL;DR

This paper proposes two-dimensional Dirac node line (DNL) semimetals in a bipartite square lattice using pz/px,y or pz/s orbital tight-binding models, where band inversion induces robust DNLs insensitive to spin-orbit coupling. First-principles calculations confirm Be2C and BeH2 monolayers as realizations with Fermi circles at Γ and K points, topologically protected by non-zero invariants and edge states, enabling a new route to 2D DNL materials.

ABSTRACT

As a new type of quantum matter, Dirac node line (DNL) semimetals are currently attracting widespread interest in condensed matter physics and material science. The DNL featured by a closed line consisting of linear band crossings in the lattice momentum space are mostly predicted in three-dimensional materials. Here, we propose tight-binding (TB) models of pz/px,y or pz/s orbitals in a two-dimensional (2D) bipartite square lattice for the 2D version of DNL semimetals. The DNL states in these models are caused by the inversion of the bands with different symmetries and thus robust again spin-orbit coupling (SOC). By means of first-principles calculations, we demonstrate two candidate 2D materials of these models: Be2C and BeH2 monolayers, which have Fermi circles centered at Γ (0,0) and K (1/2, 1/2) points, respectively. The topological nontriviality is verified by the non-zero topological invariant and the edge states. This work opens an avenue for design of 2D DNL semimetals.

Motivation & Objective

• To propose a two-dimensional realization of Dirac node line (DNL) semimetals in a bipartite square lattice, extending the concept from 3D materials.
• To demonstrate that DNLs in 2D systems can be robust against spin-orbit coupling due to band inversion with different symmetries.
• To identify realizable 2D materials—Be2C and BeH2 monolayers—that host DNLs at high-symmetry momentum points.
• To verify the topological nontriviality of these DNL states using topological invariants and edge state analysis.

Proposed method

• Construct tight-binding models using pz/px,y or pz/s orbitals on a two-dimensional bipartite square lattice to simulate electronic band structures.
• Use symmetry analysis to show that DNLs arise from band inversion between states with different orbital symmetries, ensuring robustness against spin-orbit coupling.
• Perform first-principles density functional theory (DFT) calculations on Be2C and BeH2 monolayers to validate the model predictions.
• Compute the Z2 topological invariant to confirm the nontrivial topology of the DNL phase.
• Analyze edge states in finite-sized systems to confirm the topological protection of the DNLs.
• Map the Fermi surface and identify the location of node lines at Γ (0,0) and K (1/2,1/2) points in momentum space.

Experimental results

Research questions

• RQ1 Can Dirac node lines be realized in two-dimensional bipartite square lattices, despite the reduced dimensionality compared to 3D systems?
• RQ2 What symmetry mechanisms protect the DNLs from being gapped by spin-orbit coupling in 2D systems?
• RQ3 Which real 2D materials can host DNLs, and what are their key electronic structures?
• RQ4 How can the topological nature of the DNL phase be confirmed using topological invariants and edge states?
• RQ5 What is the momentum-space location and shape of the DNLs in candidate materials like Be2C and BeH2?

Key findings

• The DNLs in the proposed 2D models are robust against spin-orbit coupling due to band inversion between orbitals with different symmetries.
• Be2C monolayer exhibits a Fermi circle centered at the Γ point (0,0) in momentum space, indicating a DNL at this high-symmetry point.
• BeH2 monolayer hosts a Fermi circle centered at the K point (1/2, 1/2), confirming a DNL at this location.
• The DNL phase in both materials is topologically nontrivial, as evidenced by a non-zero Z2 topological invariant.
• Edge states are observed in finite-sized systems, confirming the topological protection of the DNLs.
• First-principles calculations validate that both Be2C and BeH2 monolayers are realizable candidates for 2D Dirac node line semimetals.