# Band inversion at critical magnetic fields in a silicene quantum dot

## TL;DR

This paper investigates how magnetic and electric fields influence band inversion in silicene quantum dots, revealing that the magnetic field strength critically affects topological phase transitions and edge state behaviors.

## Contribution

It demonstrates the dependence of band inversion on magnetic field strength and boundary-induced chirality in silicene quantum dots, highlighting different behaviors of zero Landau level edge states.

## Key findings

- Band inversion depends on magnetic field strength.
- Edge states show different behaviors based on boundary chirality.
- Critical magnetic fields induce topological phase transitions.

## Abstract

We have found out that the band inversion in a silicene quantum dot (QD), in perpendicular magnetic $B$ and electric $\Delta_z$ fields, drastically depends on the strength of the magnetic field. We study the energy spectrum of the silicene QD where the electric field provides a tunable band gap $\Delta$. Boundary conditions introduce chirality, so that negative and positive angular momentum $m$ zero Landau level (ZLL) edge states show a quite different behavior regarding the band-inversion mechanism underlying the topological insulator transition. We show that, whereas some ZLLs suffer band inversion at $\Delta=0$ for any $B>0$, other ZLLs only suffer band inversion above critical values of the magnetic field at nonzero values of the gap.