English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

We derive the Hamiltonian for trilayer moir\'e systems with the Coulombinteraction projected onto the bands near the charge neutrality point.Motivated by the latest experimental results, we focus on the twisted symmetrictrilayer graphene (TSTG) with a mirror-symmetry with respect to the middlelayer. We provide a full symmetry analysis of the non-interacting Hamiltonianwith a perpendicular displacement field coupling the band structure madeotherwise of the twisted bilayer graphene (TBG) and the high velocity Diracfermions, and we identify a hidden non-local symmetry of the problem. In thepresence of this displacement field, we construct an approximatesingle-particle model, akin to the tripod model for TBG, capturing the essenceof non-interacting TSTG. We also derive more quantitative perturbation schemesfor the low-energy physics of TSTG with displacement field, obtaining thecorresponding eigenstates. This allows us to obtain the Coulomb interactionHamiltonian projected in the active band TSTG wavefunctions and derive the fullmany-body Hamiltonian of the system. We also provide an efficientparameterization of the interacting Hamiltonian. Finally, we show that thediscrete symmetries at the single-particle level promote the $\mathrm{U} \left(2 \right) \times \mathrm{U} \left( 2 \right)$ spin-valley symmetry to enlargedsymmetry groups of the interacting problem under different limits. Theinteracting part of the Hamiltonian exhibits a large $\mathrm{U} \left( 4\right) \times \mathrm{U} \left( 4 \right) \times \mathrm{U} \left( 4 \right)\times \mathrm{U} \left( 4 \right)$ symmetry in the chiral limit. Moreover, byidentifying a new symmetry which we dub spatial many-body charge conjugation,we show that the physics of TSTG is symmetric around charge neutrality.

TSTG I: Single-Particle and Many-Body Hamiltonians and Hidden Non-local Symmetries of Trilayer Moir\'e Systems with and without Displacement Field