# Tunable Dirac points and zero-energy modes in periodic curved graphene superlattices

## TL;DR

This paper explores how curvature and electrostatic potentials in graphene superlattices can be used to tune Dirac points, energy gaps, and the emergence of new Dirac points, offering new ways to control electronic properties.

## Contribution

It introduces the concept of using curvature in graphene superlattices to tune Dirac points and energy gaps, revealing new Dirac points and tunable electronic features.

## Key findings

- Dirac points can be shifted by asymmetric potentials and curvature.
- Curvature enables the appearance of extra tunable energy gaps.
- New Dirac points can emerge under smaller potentials with curvature.

## Abstract

We combined periodic ripples and electrostatic potentials to form curved graphene superlattices and studied the effects of space-dependent Fermi velocity induced from curvature on their electronic properties. With equal periods and symmetric potentials, the Dirac points do not move, but their locations shift under asymmetric potentials. This shift can be tuned by curvature and potentials. Tunable extra gaps in band structures can appear with unequal periods. The existence of new Dirac points is proposed, such that these new Dirac points can appear under smaller potentials with curvature, and their locations can be changed even under a fixed potential by adjusting the curvature. Our results suggest that curvature provides a new possible dimension to tune the electronic properties in graphene superlattices and a platform to more easier study physics near new Dirac points.