Valley-Polarized Metals and Quantum Anomalous Hall Effect in Silicene

TL;DR

This paper explores the rich topological phase diagram of silicene, demonstrating how electric and magnetic fields induce various phases like QAH, QSH, and valley-polarized metals, with potential for electric-field-controlled topological transitions.

Contribution

It introduces a comprehensive phase diagram of silicene under electric and exchange fields, revealing controllable topological phases and novel phenomena like valley polarization and skyrmion spin textures.

Findings

Identification of multiple topological phases in silicene.

Electric field induces a topological quantum phase transition.

Observation of momentum-space skyrmions in the QAH phase.

Abstract

Silicene is a monolayer of silicon atoms forming a two-dimensional honeycomb lattice, which shares almost every remarkable property with graphene. The low energy structure of silicene is described by Dirac electrons with relatively large spin-orbit interactions due to its buckled structure. The key observation is that the band structure is controllable by applying the electric field to a silicene sheet. We explore the phase diagram of silicene together with exchange field $M$ and by applying electric field $E_{z}$. There appear quantum anomalous Hall (QAH) insulator, valley polarized metal (VPM), marginal valley polarized metal (M-VPM), quantum spin Hall (QSH) insulator and band insulator (BI). They are characterized by the Chern numbers and/or by the edge modes of a nanoribbon. It is intriguing that electrons have been moved from a conduction band at the K point to a valence band at the K' point for $E_{z}>0$ in the VPM. We find in the QAH phase that flat gapless edge modes emerge and that spins form a momentum-space skyrmion to yield the Chern number. It is remarkable that a topological quantum phase transition can be induced simply by changing electric field in a single silicene sheet.