Correlated insulators and charge density wave states in chirally twisted triple bilayer graphene

TL;DR

This paper investigates the electronic phases of chirally twisted triple bilayer graphene, revealing flat bands with nontrivial topology and various correlated states, including charge density waves, influenced by stacking order and displacement fields.

Contribution

It provides a comprehensive theoretical analysis of the phase diagram of CTTBG, identifying the origins of experimentally observed correlated insulators and charge density waves.

Findings

Flat bands with nontrivial topology in both stacking orders.

Displacement field controls the transition between flavor polarized, intervalley coherent, and layer-polarized states.

Charge density wave states emerge from strong Coulomb interactions in flat bands.

Abstract

Motivated by recent experimental observations of displacement-field-tuned correlated insulators at integer and half-integer fillings in chirally twisted triple bilayer graphene (CTTBG), we study the single-particle and interacting physics of CTTBG. We find that there are two inequivalent stacking orders, {\it i.e.}, ABABBC and ABABAB, and both exhibit flat bands with nontrivial topology. We then use the Hartree-Fock approximation to calculate the rich phase diagram of CTTBG at all integer and half-integer fillings in both stacking orders and under the vertical displacement field. Under a small displacement field, the groundstates are flavor polarized states for ABABBC stacking order and intervalley coherent states for ABABAB stacking order at all integer and half-integer fillings. A larger displacement field will turn them into layer-polarized states. At half-integer fillings, the groundstates also exhibit charge density wave (CDW) order. For ABABAB stacking, the groundstates are always $2\times1$ stripe state among a range of displacement fields. For ABABBC stacking, the groundstates are also $2\times1$ stripe states under a small displacement field and a larger displacement will possibly favor further translation-symmetry-breaking, depending on filling and the direction of the displacement field. We demonstrate that the CDW states observed in the experiment can originate from the strong Coulomb interaction of the flat band electrons.