# Tuning Topologically Nontrivial States in the BHT-Ni Metal–Organic Framework

## TL;DR

This paper shows how to create special quantum states in a metal-organic framework by adjusting electron doping and structure.

## Contribution

The paper introduces a method to tune topologically nontrivial quantum states in the BHT-Ni framework through electron doping and structural symmetry.

## Key findings

- Two-electron doping induces a quantum spin Hall state with quantized spin Hall conductivity.
- Four-electron doping leads to a quantum anomalous Hall state with quantized anomalous Hall conductivity.
- Cis-like structures exhibit valley Hall effect and lose spin Hall conductivity due to broken inversion symmetry.

## Abstract

Using first-principles calculations,
we have demonstrated
the creation
of multiple quantum states in the experimentally accessible metal–organic
framework BHT-Ni. Specifically, quantum spin Hall and quantum anomalous
Hall states are induced by two- and four-electron doping, respectively.
Geometrical symmetry breaking is also investigated in cis- and trans-like
structures. For a low electron doping concentration of two electrons
per unit cell, the Fermi energy shifts to a nontrivial band gap between
the Dirac bands, predicting a quantized spin Hall conductivity. Subsequently
at a high electron doping concentration, an anomalous Hall conductivity
with a quantized value is observed. In addition, for a centrosymmetric
(trans-like) structure, it preserves the quantum spin Hall state and
quantized spin Hall conductivity. In contrast, in the noncentrosymmetric
(cis-like) structure, the breaking of space inversion symmetry leads
to the emergence of the valley Hall effect and the disappearance of
spin Hall conductivity.