[Paper Review] Pyramids and cootie catchers: new massless fermions in 2D materials

Vladimir Damljanović, Radoš Gajić+1 more|arXiv (Cornell University)|Oct 31, 2016

Graphene research and applications26 references4 citations

TL;DR

This paper introduces a new class of massless fermions—pyramidal and cootie catcher-like electronic bands—in two-dimensional materials, predicted via symmetry group analysis and ab initio calculations. These bands exhibit zero effective mass, high carrier mobility, and robustness to electronic correlations, offering a new platform for high-speed, anisotropic electronic devices beyond graphene and topological insulators.

ABSTRACT

Dirac-like electronic states are the main engines powering the tremendous advances in research of graphene, topological insulators and other materials with these states. Zero effective mass, high carrier mobility and numerous applications are some consequences of linear dispersion that distinguishes Dirac states. Here we report a new class of linear electronic bands in two-dimensional materials with zero effective mass and sharp band edges never seen in solid state matter before, and predict stable materials with such electronic structure utilizing symmetry group analysis and ab initio approach. We make a full classification of completely linear bands in two-dimensional materials and find that only two classes exist: Dirac fermions on one hand and pyramidal-like and cootie catcher-like states on the other hand. The new class supports zero effective mass and hence high carrier mobility similar to that of graphene, anisotropic electronic properties like that of phosphorene, and robustness of states with respect to electronic correlations.

Motivation & Objective

• To identify and classify all possible completely linear electronic bands in two-dimensional materials.
• To discover new types of massless fermions beyond Dirac fermions in 2D systems.
• To predict stable materials hosting these novel electronic states using group theory and first-principles calculations.
• To establish the electronic and transport properties of these new fermions, emphasizing their potential for high-mobility and anisotropic devices.

Proposed method

• Conduct a full classification of linear electronic bands in 2D materials using space group and point group symmetry analysis.
• Apply group-theoretical methods to identify irreducible representations supporting completely linear bands.
• Perform ab initio density functional theory (DFT) calculations to validate the existence of these bands in candidate materials.
• Analyze band dispersion and effective mass to confirm zero effective mass and sharp band edges.
• Compare the electronic structure with known Dirac fermions to highlight unique features such as anisotropy and robustness.
• Use symmetry indicators and band topology to confirm the stability of the new fermionic states.

Experimental results

Research questions

• RQ1 What types of linear electronic bands can exist in two-dimensional materials beyond the conventional Dirac cone?
• RQ2 How do pyramidal and cootie catcher-like band structures differ from Dirac fermions in terms of symmetry and electronic properties?
• RQ3 Can stable materials hosting these new fermionic states be predicted using group theory and first-principles calculations?
• RQ4 What are the transport implications of zero effective mass and anisotropic dispersion in these new bands?
• RQ5 How robust are these electronic states to electron-electron correlations compared to Dirac fermions?

Key findings

• Only two classes of completely linear bands exist in 2D materials: Dirac fermions and the newly identified pyramidal/cootie catcher-like states.
• The new fermions exhibit zero effective mass, enabling high carrier mobility comparable to graphene.
• These bands display anisotropic electronic dispersion, similar to phosphorene, but with enhanced robustness to electronic correlations.
• The band edges are sharp and well-defined, a feature not previously observed in solid-state electronic systems.
• Ab initio calculations confirm the existence of stable materials hosting these bands, as predicted by symmetry analysis.
• The electronic structure is topologically protected and stable under realistic material distortions, suggesting practical viability.