# Possible Topological Phase Transition in Fe-Vacancy-Ordered $\beta$-Fe$_{4+\delta}$Se$_{5}$ Nanowires

## TL;DR

This study investigates a topological phase transition in Fe-vacancy-ordered $eta$-Fe$_{4+ ext{delta}}$Se$_{5}$ nanowires, revealing a first-order metal-insulator transition, colossal magnetoresistance, and potential topological implications related to charge-orbital ordering.

## Contribution

It provides the first evidence of a topological transition linked to magnetotransport and charge-orbital ordering in FeSe-based nanowires with Fe-vacancy order.

## Key findings

- First-order metal-insulator transition at ~28 K
- Colossal positive magnetoresistance near transition temperature
- Transition from 2D-like to 1D-like conduction

## Abstract

We studied the electrical transport on $\beta$-Fe$_{4+\delta}$Se$_{5}$ single-crystal nanowires, exhibiting $\sqrt{5}\times\sqrt{5}$ Fe-vacancy order and mixed valence of Fe. We observed a first-order metal-insulator transition of the transition temperature at $\sim$28~K at zero magnetic field. The dielectric relaxation reveals that the transition is related to an energy gap expansion of $\sim$12~meV, involving the charge-orbital ordering. At nearly 28~K, colossal positive magnetoresistance emerges, resulting from the magnetic-field dependent shift of the transition temperature. Through the transition, the magnetotransport behavior transits from two-dimension-like to one-dimension-like conduction. The transition temperature demonstrates anisotropy with the $c$-axis as the preferred orientation in magnetic fields, suggesting the spin-orbital coupling. Our findings demonstrate the novel magnetoresistive transition intimating a topological transition in the Fe-vacancy-ordered $\beta$-Fe$_{4+\delta}$Se$_{5}$ nanowires. The results provide valuable information to better understand the orbital nature and the emergence of superconductivity in FeSe-based materials.