Drumhead Surface States of Rhombohedral Graphite with Near Ideal Quantum Geometry Condition
Abstract
The ideal quantum geometry (IQG) condition for the trace of quantum metric (TrG(k)) being equal to the magnitude of Berry curvature (|Ω(k)|) as in |Ω|/TrG=1 has been associated with realizing fractional Chern insulators for the flat bands in a few layers of rhombohedral graphene (RG). More recently the IQG condition has also been proposed for superconductivity in the flat bands of thick RG layers. Using density functional theory and Wannier functions, we study the symmetry-protected topology of bulk RG, drumhead surface states (DSS) of semi-infinite RG surface and slabs, and the IQG condition for thin and thick RG slabs. We find that bulk RG is a weak topological insulator with spin-orbit coupling (SOC), besides being effectively a chiral semimetal with chiral nodal lines without SOC. We also find that the DSS flat bands of thick RG slabs have a sizable convex curvature with dispersion depth agreeing with the recent angle-resolved photoemission spectroscopy experiment. The calculated IQG also shows a convex shape with the K point at the center having a minimum with approximately |Ω|/TrG≈1. But the inner rim of the DSS region approaches the IQG condition of |Ω|/TrG=1. These results on thick RG slabs from first-principles calculations provide useful information for the pristine DSS at the single-particle level for future studies to consider when enhanced electron correlation and many-body interaction will be included.
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BibTeX
@misc{wang2026drumhead,
title = {{Drumhead Surface States of Rhombohedral Graphite with Near Ideal Quantum Geometry Condition}},
author = {Lin-Lin Wang},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2607.28491},
eprint = {2607.28491},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2607.28491},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Drumhead Surface States of Rhombohedral Graphite with Near Ideal Quantum Geometry Condition
AU - Lin-Lin Wang
PY - 2026
DA - 2026/10/20
PB - arXiv
DO - 10.48550/arxiv.2607.28491
UR - https://arxiv.org/abs/2607.28491
AB - The ideal quantum geometry (IQG) condition for the trace of quantum metric (TrG(k)) being equal to the magnitude of Berry curvature (|Ω(k)|) as in |Ω|/TrG=1 has been associated with realizing fractional Chern insulators for the flat bands in a few layers of rhombohedral graphene (RG). More recently the IQG condition has also been proposed for superconductivity in the flat bands of thick RG layers. Using density functional theory and Wannier functions, we study the symmetry-protected topology of bulk RG, drumhead surface states (DSS) of semi-infinite RG surface and slabs, and the IQG condition for thin and thick RG slabs. We find that bulk RG is a weak topological insulator with spin-orbit coupling (SOC), besides being effectively a chiral semimetal with chiral nodal lines without SOC. We also find that the DSS flat bands of thick RG slabs have a sizable convex curvature with dispersion depth agreeing with the recent angle-resolved photoemission spectroscopy experiment. The calculated IQG also shows a convex shape with the K point at the center having a minimum with approximately |Ω|/TrG≈1. But the inner rim of the DSS region approaches the IQG condition of |Ω|/TrG=1. These results on thick RG slabs from first-principles calculations provide useful information for the pristine DSS at the single-particle level for future studies to consider when enhanced electron correlation and many-body interaction will be included.
ER -