# Emergent chirality and enantiomeric selectivity in layered NbOX$_2$ crystals

**Authors:** Martin Gutierrez-Amigo, Claudia Felser, Ion Errea, Maia G. Vergniory  
**arXiv:** [2505.09749](https://arxiv.org/abs/2505.09749)  
**Date:** 2025-05-14  
**Summary page:** https://www.summarizepaper.com/en/paper/2505.09749v1/

## Key points

- Study focuses on chirality emergence in layered NbOX$_2$ crystals
- Intermediate achiral $C 2/m$ phase acts as a crucial link between high- and low-symmetry phases
- Insulating $C 2$ phase exhibits remarkable electronic properties, including flat Niobium $d$-orbital bands near Fermi level associated with obstructed atomic limit (OAL)
- Topologically non-trivial surface states under specific cleavage conditions in the $C 2$ phase
- Stabilization mechanisms for intermediate $C 2/m$ phase include ionic quantum or thermal fluctuations, lattice anharmonicity, pressure, and external electric fields
- External electric field can bias system towards preferred chirality by breaking symmetries and lifting energy degeneracy between enantiomers
- Small energy barrier between enantiomers in the $C 2$ phase enables precise control over handedness
- Proposed mechanism for selective handedness stabilization using electric fields and temperature-dependent anharmonic effects

## Summary

In their study titled "Emergent chirality and enantiomeric selectivity in layered NbOX$_2$ crystals," Martin Gutierrez-Amigo, Claudia Felser, Ion Errea, and Maia G. Vergniory delve into the fascinating realm of chirality emergence in crystalline solids. The authors focus on a new family of layered compounds known as $\mathrm{NbOX_2}$ and explore the intricate relationship between their achiral $I m m m$ phase and chiral $C 2$ phase. Through meticulous first-principles calculations, they unveil an intermediate achiral $C 2/m$ phase that acts as a crucial link between the high- and low-symmetry phases within a three-dimensional order parameter space. The insulating $C 2$ phase exhibited by these compounds showcases remarkable electronic properties, including flat Niobium $d$-orbital bands near the Fermi level that are associated with an obstructed atomic limit (OAL). This unique configuration hosts topologically non-trivial surface states under specific cleavage conditions. By delving into the Born-Oppenheimer energy surfaces (BOES), the researchers uncover intriguing insights. They find that the shallow energy minima of the $C 2$ phase hint at possible stabilization mechanisms for the intermediate $C 2/m$ phase. This stabilization could be achieved through various avenues such as ionic quantum or thermal fluctuations, lattice anharmonicity resulting from these fluctuations, or external factors like pressure. Moreover, the authors demonstrate how an external electric field can play a pivotal role in biasing the system towards a preferred chirality by breaking necessary symmetries and lifting energy degeneracy between enantiomers. This effect, coupled with the small energy barrier between enantiomers in the $C 2$ phase, enables precise control over handedness and leads to a proposed mechanism for selective handedness stabilization using electric fields and temperature-dependent anharmonic effects. Overall, this comprehensive study establishes a robust framework for understanding chirality emergence in layered materials and lays out a promising pathway for designing systems with tunable enantiomeric populations. The findings not only contribute significantly to materials design but also shed light on fundamental principles governing chirality in crystalline solids.