# Real-time evolution and quantized charge pumping in magnetic Weyl semimetals

## TL;DR

This paper investigates charge pumping in magnetic Weyl semimetals using real-time evolution, demonstrating quantized charge transfer robustness against disorder and doping effects, revealing topological properties without a bulk gap.

## Contribution

It introduces a real-time evolution method to study topological charge pumping in Weyl semimetals, showing quantization and robustness in disordered and doped conditions.

## Key findings

- Quantized charge pumping occurs in magnetic Weyl semimetals.
- Quantization remains robust against small disorder.
- Doped systems retain detectable quantized charge pumping.

## Abstract

Real-time evolution and charge pumping in magnetic Weyl semimetals are studied by solving the time-dependent Schr\"{o}dinger equations. In the adiabatic limit of the real-time evolution, we show that the total pumped charge is quantized in the magnetic Weyl semimetals as in the quantum Hall system although the Weyl semimetal has no bulk gap. We examine how the disorder affects the charge pumping. As a result, we show that the quantized pumped charge is robust against the small disorder and find that the pumped charge increases in the intermediate disorder region. We also examine the doping effects on the charge pumping and show that the remnant of the quantized pumped charge at zero doping can be detected. Our results show that the real-time evolution is a useful technique for detecting the topological properties of the systems with no bulk gap and/or disorders.