# Gauge-invariant cutoff for Dirac electron systems with a vector potential

## TL;DR

This paper introduces a gauge-invariant energy cutoff method for Dirac electron systems, ensuring physically consistent electromagnetic response calculations in models like graphene and topological insulators.

## Contribution

A novel energy cutoff procedure that maintains gauge invariance in Dirac electron models, improving the physical accuracy of response function calculations.

## Key findings

- Response functions are gauge-invariant with the new cutoff.
- The method accurately describes electromagnetic responses in 2D Dirac systems.
- The approach resolves unphysical artifacts caused by traditional cutoffs.

## Abstract

The continuum Dirac model with an unbounded energy spectrum is widely used to describe low-energy states in various electron systems, such as graphene, topological insulators, and Weyl semimetals. However, if it is applied to analyze the electromagnetic response of electrons to a vector potential, we often find an unphysical result that breaks gauge invariance. This is an artifact caused by an energy or wavenumber cutoff, which is used to avoid divergence of the response. Here, we propose a modified energy cutoff procedure that preserves the gauge invariance. We use this procedure to calculate the response functions in a two-dimensional massless Dirac electron system. It is shown that the resulting functions properly describe the electromagnetic response in a gauge-invariant manner.