[Paper Review] Peierls transition and edge reconstruction in phosphorene nanoribbons

Ajanta Maity, Akansha Singh+1 more|arXiv (Cornell University)|Apr 9, 2014

2D Materials and Applications2 references18 citations

TL;DR

This study uses density functional theory (DFT) to investigate atomic and electronic structures of phosphorene nanoribbons (PNRs), revealing that pure linear PNRs undergo edge reconstruction while wider zigzag PNRs experience a Peierls transition, both opening band gaps. Mixed PNRs with both edge types exhibit both phenomena simultaneously, transforming all PNRs into semiconductors—critical for electronic applications.

ABSTRACT

Atomic and electronic structures of phosphorene nanoribbons are studied within density functional theory. These novel materials present different physical phenomena expected in two very different physical systems: one dimensional metallic chains and semiconductor surfaces. While `rugged' nanoribbons are semiconducting in their layer-terminnated structures, pure `linear' and `zigzag' nanoribbons are metallic due to metallic edge states. Linear nanoribbons undergo edge reconstruction and zigzag nanoribbons beyond a certain width undergo Peierls transition leading to opening of a band gap in the electronic structure and lowering of total energy. Mixed nanoribbons with linear and zigzag edges on the two sides turn out to be a curious case that display both edge reconstruction and Peierls transition simultaneously. Most phosphoeren nanoribbons turn out to be semiconductors having important implications for their application.

Motivation & Objective

• To understand the atomic and electronic structure of phosphorene nanoribbons (PNRs) using first-principles DFT calculations.
• To investigate whether PNRs with different edge types (linear, zigzag, mixed) exhibit metallic or semiconducting behavior.
• To determine the role of edge reconstruction and Peierls transitions in modifying electronic band structures and lowering total energy.
• To clarify conflicting prior reports on metallic behavior in zigzag PNRs by accounting for Peierls distortion.
• To assess the relative stability of various PNR structures through cohesive energy analysis.

Proposed method

• Performed DFT calculations using the PBE exchange-correlation functional and PAW pseudopotentials.
• Used a 500 eV plane-wave cutoff and (8×1×8) k-point mesh for monolayers; (8×1×1) and (1×1×8) meshes for nanoribbons along x and z directions.
• Applied vacuum spacing of 15 Å in non-periodic directions to avoid interlayer interactions.
• Performed full atomic relaxation with forces below 0.01 eV/Å using conjugate gradient optimization.
• Used the VASP code for all calculations and validated select results with the HSE06 hybrid functional.
• Analyzed band structures, orbital contributions, and charge density distributions to identify edge states and reconstruction effects.

Experimental results

Research questions

• RQ1 Do phosphorene nanoribbons with pure linear or zigzag edges undergo structural and electronic transitions that open a band gap?
• RQ2 Can mixed phosphorene nanoribbons with both linear and zigzag edges simultaneously exhibit edge reconstruction and Peierls transition?
• RQ3 How do the cohesive energies of different PNR types compare, and which structure is most stable?
• RQ4 Why do previous studies report metallic behavior in zigzag PNRs, and how does Peierls distortion resolve this?
• RQ5 What is the role of broken inversion symmetry in mixed PNRs in influencing edge state localization and band gap formation?

Key findings

• Pure linear phosphorene nanoribbons (l-PNRs) undergo edge reconstruction, lowering total energy and forming a band gap.
• Wider zigzag phosphorene nanoribbons (z-PNRs) undergo Peierls transition, opening a band gap and reducing total energy by 1.44 eV.
• Mixed PNRs with both linear and zigzag edges simultaneously exhibit edge reconstruction at the linear edge and Peierls transition at the zigzag edge, resulting in a 0.125 eV band gap.
• All PNRs except narrow z-PNRs (1–3 atoms wide) become semiconducting due to structural instabilities, with the edge-reconstructed l-PNR being the most stable with a cohesive energy of 5.333 eV/atom.
• The cohesive energy of the mixed PNR after reconstruction and Peierls transition is 5.327 eV/atom, intermediate between l-PNR and z-PNR values.
• Orbital analysis confirms that the top valence band in mixed PNRs arises from p_x and p_y orbitals on zigzag edge atoms, while conduction bands originate from p_x and p_y orbitals on linear edge atoms.