# Coexistence of ultraheavy and ultrarelativistic Dirac quasiparticles in sandwiched trilayer graphene

## TL;DR

This paper demonstrates that twisted sandwiched trilayer graphene can stably host coexisting ultraheavy flat bands and ultrarelativistic Dirac quasiparticles near the Fermi energy, controllable by external fields, offering a new platform for exploring strongly correlated and topological phases.

## Contribution

It introduces a stable twisted sandwiched graphene structure with coexisting flat and Dirac bands, controllable via external fields, advancing the understanding of strongly correlated quantum materials.

## Key findings

- Stable flat bands coexist with Dirac cones at 1.5° twist.
- Atomistic calculations predict relaxation to high-symmetry stacking.
- External fields can tune the energy offset between bands.

## Abstract

Electrons in quantum materials exhibiting coexistence of dispersionless (flat) bands piercing dispersive (steep) bands can give rise to strongly correlated phenomena, and are associated with unconventional superconductivity. It is known that in twisted trilayer graphene steep Dirac cones can coexist with band flattening, but the phenomenon is not stable under layer misalignments. Here we show that such a twisted sandwiched graphene (TSWG) -- a three-layer van der Waals heterostructure with a twisted middle layer -- can have very stable flat bands coexisting with Dirac cones near the Fermi energy when twisted to 1.5 degrees. These flat bands require a specific high-symmetry stacking order, and our atomistic calculations predict that TSWG always relaxes to it. Additionally, with external fields, we can control the relative energy offset between the Dirac cone vertex and the flat bands. Our work establishes twisted sandwiched graphene as a new platform for research into strongly interacting phases, and topological transport beyond Dirac and Weyl semimetals.