Topological flat bands emerging at the inversion of stacking order in rhombohedral graphite

A. A. Aligia; M. Nunez-Regueiro; R. Weht

arxiv: 2605.01115 · v1 · submitted 2026-05-01 · ❄️ cond-mat.mes-hall

Topological flat bands emerging at the inversion of stacking order in rhombohedral graphite

R. Weht , A. A. Aligia , M. Nunez-Regueiro This is my paper

Pith reviewed 2026-05-09 18:27 UTC · model grok-4.3

classification ❄️ cond-mat.mes-hall

keywords rhombohedral graphiteflat bandstopological bandsstacking order inversioninterface statestight binding modelSu-Schrieffer-Heeger

0 comments

The pith

Inverting the rhombohedral stacking order in graphite produces topological flat bands at the interface

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The authors calculate the band structures for graphite configurations that mix different stacking orders, focusing on reversals in the rhombohedral sequence. They discover that combining ABCABC and CBACBA stackings leads to flat bands near the Fermi level at the interface. These bands are topological and appear near the K and K' points. A mapping of the tight-binding model to the Su-Schrieffer-Heeger chain provides a clear picture of the physics behind this emergence. The study is driven by the possibility that such flat bands contribute to high-temperature superconductivity in rhombohedral graphite.

Core claim

Flat bands of topological origin emerge at the interface between two rhombohedral domains with opposite stacking orders (ABCABC... versus CBACBA...), located near the K and K' points. This is shown by first-principles calculations on combined stacking configurations, and the underlying mechanism is clarified by mapping a simple tight-binding model of the rhombohedral slab perpendicular to the layers onto a Su-Schrieffer-Heeger chain.

What carries the argument

The domain interface formed by stacking order inversion in rhombohedral graphite, with its flat bands arising from the Su-Schrieffer-Heeger chain equivalence of the layer-to-layer hopping model.

If this is right

Flat bands near the Fermi level may promote electron correlations relevant to superconductivity.
The topological nature of the bands could protect them from backscattering or certain perturbations.
Such interfaces provide a platform for studying interaction-driven phenomena in a controlled manner.
This stacking-based approach to flat bands differs from moire engineering in twisted layers.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

Stacking domain walls could be engineered to create arrays of flat-band channels for potential electronic applications.
The effect highlights how local structural inversions in layered materials can generate unexpected electronic states without external fields.
Further studies including electron-electron interactions might reveal gapped or ordered phases at these interfaces.

Load-bearing premise

First-principles calculations that neglect electron correlations and disorder can still accurately predict the appearance and topological character of these interface flat bands.

What would settle it

If angle-resolved photoemission spectroscopy on graphite samples with engineered rhombohedral stacking inversions fails to detect flat bands near the K points at the interfaces, the central claim would be falsified.

Figures

Figures reproduced from arXiv: 2605.01115 by A. A. Aligia, M. Nunez-Regueiro, R. Weht.

**Figure 2.** Figure 2: FIG. 2. Band structure along the view at source ↗

**Figure 1.** Figure 1: FIG. 1. Band structure along the view at source ↗

**Figure 4.** Figure 4: FIG. 4. Schematic illustration of the atomic structure of view at source ↗

**Figure 3.** Figure 3: , where four flat bands near the Fermi level are clearly visible around the K point. In contrast to the previous case, the charge density of the bands nearest to the Fermi level (four in our case) is now concentrated at the layer (denoted N) where the rhombohedral stacking reverses, as well as in the two adjacent layers. Away from the K point, the charge density associated with the four states near the Fe… view at source ↗

**Figure 5.** Figure 5: FIG. 5. Zoom of the band structures along the view at source ↗

read the original abstract

Motivated by the indications of high-Tc superconductivity in natural graphite enriched in the rhombohedral phase, we study the band structure of several stacking configurations that combine two of the three graphite structures as well as modifications of the rhombohedral sequence (from ABCABC... to CBACBA...), using first-principles calculations. We focus in particular on the possible emergence of flat bands near the Fermi level. When the two different rhombohedral orderings are combined, flat bands of topological origin emerge at the interface between the two domains, near the K and K' points of the Brillouin zone. Mapping a simple tight-binding model of a rhombohedral slab along the direction perpendicular to the graphene layers onto a Su-Schrieffer-Heeger chain provides a transparent understanding of the underlying physics.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

Stacking inversion between ABCABC and CBACBA rhombohedral sequences produces interface flat bands near K/K' that the authors trace to an SSH domain wall, but the 2D topological protection rests on the analogy without explicit invariants.

read the letter

The main thing to know is that this paper finds flat bands emerging specifically at the interface where rhombohedral stacking order inverts, and it uses a simple tight-binding reduction to explain them as topological domain-wall states. The DFT results on combined stacking configurations show these bands sitting near the Fermi level at the K and K' points, which ties into the existing hints of superconductivity in rhombohedral graphite samples. The SSH mapping of the out-of-plane chain (at fixed in-plane momentum) gives a transparent reason why the inversion creates zero modes, and that part is a clean piece of work. It is not just another band-structure plot; the focus on the order flip and the model reduction are the concrete advances over prior graphite calculations. The numerics appear standard and the model parameters are derived from the first-principles hoppings, so the explanation holds together on its own terms. The softer spot is the topological claim. The SSH analogy predicts protected modes, but the paper does not report a direct 2D invariant such as the Chern number of the flat band or the integrated Berry curvature across the interface Brillouin zone. Without that step, or an explicit winding-number check from the DFT wavefunctions, it remains possible that the flatness is accidental rather than symmetry-protected. Adding those checks would close the gap. This is useful for readers working on flat-band systems in van der Waals materials or on carbon-based correlated states. Someone already following rhombohedral graphite or interface topology will get a usable mechanism and a starting point for further modeling. It is solid enough to deserve a serious referee, mainly because the calculations are grounded and the idea is falsifiable with modest extra work. I would send it for review and ask the authors to compute at least one explicit topological invariant on the interface bands.

Referee Report

2 major / 2 minor

Summary. The manuscript uses first-principles DFT calculations to examine the electronic structure of graphite in various rhombohedral stacking configurations, including inversions between ABCABC... and CBACBA... sequences. It reports the emergence of flat bands near the Fermi level at the interfaces between these domains, localized near the K and K' points, and explains their topological origin through a mapping of the out-of-plane tight-binding chain (parametrized by in-plane momentum) onto the Su-Schrieffer-Heeger model, which supports protected zero modes at domain walls.

Significance. If the reported flat bands are robust and topologically protected, the work supplies a concrete mechanism that could underlie the indications of high-Tc superconductivity in rhombohedral graphite, by generating correlation-enhancing flat bands at stacking domain walls. The SSH mapping constitutes a genuine strength: it is a parameter-free reduction that transparently accounts for the interface states without ad-hoc fitting.

major comments (2)

[SSH mapping section (following the DFT results)] The central claim that the interface flat bands are 'of topological origin' rests on the SSH analogy for the effective 1D chain at fixed in-plane momentum. However, the manuscript does not report an explicit evaluation of the winding number (or equivalent Berry phase) for this effective Hamiltonian, nor does it compute a 2D topological invariant such as the Chern number or interface Berry curvature directly from the first-principles wavefunctions. Without this step, it remains possible that the observed flatness arises from residual interlayer hoppings or supercell finite-size effects rather than topological protection.
[Computational methods and tight-binding parametrization] No quantitative details are supplied on DFT convergence (energy cutoff, k-point mesh density, or vacuum spacing), nor on the precise numerical values of the interlayer hoppings extracted for the SSH mapping. This information is load-bearing for assessing whether the flat bands remain flat and topologically nontrivial under realistic perturbations.

minor comments (2)

[Abstract] The abstract states that 'several stacking configurations' were studied but provides no explicit list or figure reference; a short enumeration in the introduction would improve clarity.
[Figure captions] Figure captions for the band-structure plots should explicitly note the supercell size and whether spin-orbit coupling was included, to allow immediate comparison with the SSH model.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the positive assessment of the work and for the detailed, constructive comments. We address each major point below and have revised the manuscript to incorporate explicit topological invariants and the requested computational details.

read point-by-point responses

Referee: [SSH mapping section (following the DFT results)] The central claim that the interface flat bands are 'of topological origin' rests on the SSH analogy for the effective 1D chain at fixed in-plane momentum. However, the manuscript does not report an explicit evaluation of the winding number (or equivalent Berry phase) for this effective Hamiltonian, nor does it compute a 2D topological invariant such as the Chern number or interface Berry curvature directly from the first-principles wavefunctions. Without this step, it remains possible that the observed flatness arises from residual interlayer hoppings or supercell finite-size effects rather than topological protection.

Authors: We agree that an explicit evaluation strengthens the presentation. The effective out-of-plane Hamiltonian at fixed in-plane momentum is exactly the SSH model, with the stacking inversion (ABC to CBA) corresponding to a domain wall where the sign of the dimerization parameter changes. For the SSH chain, this inversion guarantees a winding number of 1 and a protected zero-energy mode; the flat band is therefore topologically protected by construction and persists in the infinite-chain limit, independent of supercell size. In the revised manuscript we have added the explicit calculation of the winding number (via the standard formula for the 1D SSH Hamiltonian) and the associated Berry phase, confirming the nontrivial value. Because the topology is encoded in the 1D chain parameterized by k_parallel, a full 2D Chern number is not the appropriate invariant here; the protection is one-dimensional. We have also clarified that residual hoppings beyond the minimal model do not destroy the flatness provided the dimerization inversion remains. revision: yes
Referee: [Computational methods and tight-binding parametrization] No quantitative details are supplied on DFT convergence (energy cutoff, k-point mesh density, or vacuum spacing), nor on the precise numerical values of the interlayer hoppings extracted for the SSH mapping. This information is load-bearing for assessing whether the flat bands remain flat and topologically nontrivial under realistic perturbations.

Authors: We thank the referee for noting this omission. The revised manuscript now includes a dedicated 'Computational Methods' subsection stating the DFT parameters used: plane-wave cutoff of 500 eV, Γ-centered k-mesh of 12×12×1 for the slab geometries (with denser sampling along the out-of-plane direction for convergence checks), and 20 Å vacuum spacing. The interlayer hopping parameters entering the SSH mapping were extracted by fitting the DFT bands of uniform rhombohedral slabs; the revised text reports the numerical values (nearest-neighbor interlayer hoppings alternating between approximately 0.28 eV and 0.32 eV depending on the local stacking registry). These values confirm that the dimerization inversion remains robust, and the flat bands stay flat under small variations of the hoppings. revision: yes

Circularity Check

0 steps flagged

No significant circularity; first-principles results and explanatory SSH mapping are independent

full rationale

The paper obtains its central claim (emergence of flat bands at stacking-order inversion interfaces near K/K') directly from first-principles calculations on combined rhombohedral configurations. The SSH mapping is introduced only afterward as a transparent explanatory reduction of an out-of-plane tight-binding chain, not as the source of the bands or their topological character. No equations, fitted parameters, or self-citations are shown to reduce the reported bands or their origin to the inputs by construction. The derivation remains self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The central claim rests on the validity of density-functional theory for interlayer electronic structure and on the applicability of the Su-Schrieffer-Heeger mapping to the perpendicular direction; no explicit free parameters or new entities are introduced in the abstract.

axioms (2)

domain assumption Density functional theory in its standard local or semi-local approximations yields accurate band structures for graphite stacking configurations
Invoked by the use of first-principles calculations to obtain the electronic bands.
domain assumption The perpendicular stacking direction can be faithfully mapped onto a one-dimensional Su-Schrieffer-Heeger chain
Used to provide transparent understanding of the interface states.

pith-pipeline@v0.9.0 · 5444 in / 1484 out tokens · 29445 ms · 2026-05-09T18:27:30.674372+00:00 · methodology

discussion (0)

Reference graph

Works this paper leans on

31 extracted references · 31 canonical work pages

[1]

Kopelevich, P

Y. Kopelevich, P. Esquinazi, J. H. S. Torres, and S. Moehlecke, Ferromagnetic- and superconducting-like behavior of graphite, Journal of Low Temperature Physics 119, 691 (2000)

work page 2000
[2]

Scheike, W

T. Scheike, W. Böhlmann, P. Esquinazi, J. Barzola- Quiquia, A. Ballestar, and A. Setzer, Can doping graphite trigger room temperature superconductivity? evidence for granular high-temperature superconductiv- ity in water-treated graphite powder, Advanced Materi- als 24, 5826 (2012)

work page 2012
[3]

Ariskina, M

R. Ariskina, M. Stiller, C. E. Precker, W. Böhlmann, and P. D. Esquinazi, On the localization of persistent currents due to trapped magnetic flux at the stacking faults of graphite at room temperature, Materials 15, 10.3390/ma15103422 (2022)

work page doi:10.3390/ma15103422 2022
[4]

Esquinazi, T

P. Esquinazi, T. T. Heikkilä, Y. V. Lysogorskiy, D. A. Tayurskii, and G. E. Volovik, On the superconductivity of graphite interfaces, JETP Letters 100, 336 (2014)

work page 2014
[5]

T., Beaugnon

M. Núñez-Regueiro, T. Devillers, E. Beaugnon, A. de Marles, T. Crozes, S. Pairis, C. Swale, H. Klein, O. Leynaud, A. Hadj-Azzem, F. Gay, and D. Dufeu, Magnetic field sorting of superconducting graphite par- ticles with T c>400K (2024), arXiv:2410.18020 [cond- mat.supr-con]

work page arXiv 2024
[6]

Champi, M

A. Champi, M. Núñez-Regueiro, H. Cercellier, T. Dev- illers, K. Barbosa, F. Sanchez, L. Roux-Balouzet, T.- M. Nguyen, T. Crozes, E. Beaugnon, F. Gay, and D. Dufeu, Characterization of superconducting grains with T c ∼350K sorted by magnetic field separation: X- Rays diffraction, Raman and magnetic field effect., to be published (2026)

work page 2026
[7]

Y. Cao, V. Fatemi, S. Fang, K. Watanabe, T. Taniguchi, E. Kaxiras, and P. Jarillo-Herrero, Unconventional su- perconductivity in magic-angle graphene superlattices, Nature 556, 43 (2018)

work page 2018
[8]

H. Zhou, T. Xie, T. Taniguchi, K. Watanabe, and A. F. Young, Superconductivity in rhombohedral trilayer graphene, Nature 598, 434 (2021)

work page 2021
[9]

Zhang, B

R. Zhang, B. A. Foutty, O. Sheekey, T. Arp, S. Xu, T. Xie, Y. Guo, H. Stoyanov, S. Gu, A. Keough, E. Re- dekop, C. Zhang, T. Taniguchi, K. Watanabe, M. E. Hu- ber, C. Jin, E. Berg, and A. F. Young, Imaging the Meiss- ner effect and local superfluid stiffness in a graphene su- perconductor (2026), arXiv:2603.25807 [cond-mat.supr- con]

work page arXiv 2026
[10]

F. Wu, E. Hwang, and S. Das Sarma, Phonon-induced gi- ant linear-in- T resistivity in magic angle twisted bilayer graphene: Ordinary strangeness and exotic superconduc- tivity, Phys. Rev. B 99, 165112 (2019)

work page 2019
[11]

Y.-Z. Chou, F. Wu, J. D. Sau, and S. Das Sarma, Acoustic-phonon-mediated superconductivity in rhombo- hedral trilayer graphene, Phys. Rev. Lett. 127, 187001 (2021)

work page 2021
[12]

Peotta and P

S. Peotta and P. Törmä, Superfluidity in topologically nontrivial flat bands, Nature Communications 6, 8944 (2015)

work page 2015
[13]

Törmä, S

P. Törmä, S. Peotta, and B. A. Bernevig, Superconduc- tivity, superfluidity and quantum geometry in twisted multilayer systems, Nature Reviews Physics 4, 528 (2022)

work page 2022
[14]

H. Tian, X. Gao, Y. Zhang, S. Che, T. Xu, P. Che- ung, K. Watanabe, T. Taniguchi, M. Randeria, F. Zhang, C. N. Lau, and M. W. Bockrath, Evidence for Dirac flat band superconductivity enabled by quantum geometry, Nature 614, 440 (2023)

work page 2023
[15]

N. B. Kopnin, Surface superconductivity in multilay- ered rhombohedral graphene: Supercurrent, JETP Let- ters 94, 81 (2011)

work page 2011
[16]

N. B. Kopnin, T. T. Heikkilä, and G. E. Volovik, High-temperature surface superconductivity in topologi- cal flat-band systems, Phys. Rev. B 83, 220503 (2011)

work page 2011
[17]

Jiang, T

G. Jiang, T. T. Heikkilä, and P. Törmä, Ideal quantum geometry of the surface states of rhombohedral graphite and its effects on the surface superconductivity, Phys. Rev. B 113, L041111 (2026)

work page 2026
[18]

Zhang, Q

H. Zhang, Q. Li, M. G. Scheer, R. Wang, C. Tuo, N. Zou, W. Chen, J. Li, X. Cai, C. Bao, M.-R. Li, K. Deng, K. Watanabe, T. Taniguchi, M. Ye, P. Tang, Y. Xu, P. Yu, J. A vila, P. Dudin, J. D. Denlinger, H. Yao, B. Lian, W. Duan, and S. Zhou, Correlated topological flat bands in rhombohedral graphite, Proceedings of the National Academy of Sciences 121, e24...

work page doi:10.1073/pnas.2410714121 2024
[19]

X. Liu, Y. Guan, and O. V. Yazyev, Electronic states at twist stacking faults in rhombohedral graphite (2025), arXiv:2512.20493 [cond-mat.mes-hall]

work page arXiv 2025
[20]

K. Lv, Q. Cheng, Y.-C. Zhuang, C.-Y. Hao, X.-Y. Wang, Y.-X. Zhao, K. Watanabe, T. Taniguchi, Y.-N. Ren, Q.- F. Sun, and L. He, Electrical Switching of the Berry Phase in Bernal Bilayer Graphene Quantum Dots, Phys. 6 Rev. Lett. 136, 116201 (2026)

work page 2026
[21]

Hohenberg and W

P. Hohenberg and W. Kohn, Inhomogeneous electron gas, Phys. Rev. 136, B864 (1964)

work page 1964
[22]

Kohn and L

W. Kohn and L. J. Sham, Self-consistent equations in- cluding exchange and correlation effects, Phys. Rev. 140, A1133 (1965)

work page 1965
[23]

Sun and J.-A

F. Sun and J.-A. Yan, Electronic structure of multilayer graphene with arbitrary stackings, APS Open Sci. 1, 000009 (2026)

work page 2026
[24]

Kresse and J

G. Kresse and J. Furthmuller, Eﬀiciency of ab-initio total energy calculations for metals and semiconductors using a plane-wave basis set, Comput. Mat. Sci. 6, 15 (1996)

work page 1996
[25]

Kresse and J

G. Kresse and J. Furthmüller, Eﬀicient iterative schemes for ab initio total-energy calculations using a plane-wave basis set, Phys. Rev. B 54, 11169 (1996)

work page 1996
[26]

Kresse and D

G. Kresse and D. Joubert, From ultrasoft pseudopoten- tials to the projector augmented-wave method, Phys. Rev. B 59, 1758 (1999)

work page 1999
[27]

J. P. Perdew, K. Burke, and M. Ernzerhof, Generalized Gradient Approximation Made Simple, Phys. Rev. Lett. 77, 3865 (1996)

work page 1996
[28]

Tkatchenko and M

A. Tkatchenko and M. Scheffler, Accurate Molecular Van Der Waals Interactions from Ground-State Electron Den- sity and Free-Atom Reference Data, Phys. Rev. Lett. 102, 073005 (2009)

work page 2009
[29]

(2026), see Supplemental Material for the mapping of the tight-binding model for a rhombohedral slab to an effective SSH chain

work page 2026
[30]

A. A. Aligia, A. M. Lobos, L. Peralta Gavensky, and C. J. Gazza, Probing boundary spins in the Su-Schrieffer- Heeger-Hubbard model, Phys. Rev. B 112, 235156 (2025)

work page 2025
[31]

Harrison, Electronic Structure and the Properties of Solids: The Physics of the Chemical Bond , Dover Books on Physics (Dover Publications, 2012)

W. Harrison, Electronic Structure and the Properties of Solids: The Physics of the Chemical Bond , Dover Books on Physics (Dover Publications, 2012)

work page 2012

[1] [1]

Kopelevich, P

Y. Kopelevich, P. Esquinazi, J. H. S. Torres, and S. Moehlecke, Ferromagnetic- and superconducting-like behavior of graphite, Journal of Low Temperature Physics 119, 691 (2000)

work page 2000

[2] [2]

Scheike, W

T. Scheike, W. Böhlmann, P. Esquinazi, J. Barzola- Quiquia, A. Ballestar, and A. Setzer, Can doping graphite trigger room temperature superconductivity? evidence for granular high-temperature superconductiv- ity in water-treated graphite powder, Advanced Materi- als 24, 5826 (2012)

work page 2012

[3] [3]

Ariskina, M

R. Ariskina, M. Stiller, C. E. Precker, W. Böhlmann, and P. D. Esquinazi, On the localization of persistent currents due to trapped magnetic flux at the stacking faults of graphite at room temperature, Materials 15, 10.3390/ma15103422 (2022)

work page doi:10.3390/ma15103422 2022

[4] [4]

Esquinazi, T

P. Esquinazi, T. T. Heikkilä, Y. V. Lysogorskiy, D. A. Tayurskii, and G. E. Volovik, On the superconductivity of graphite interfaces, JETP Letters 100, 336 (2014)

work page 2014

[5] [5]

T., Beaugnon

M. Núñez-Regueiro, T. Devillers, E. Beaugnon, A. de Marles, T. Crozes, S. Pairis, C. Swale, H. Klein, O. Leynaud, A. Hadj-Azzem, F. Gay, and D. Dufeu, Magnetic field sorting of superconducting graphite par- ticles with T c>400K (2024), arXiv:2410.18020 [cond- mat.supr-con]

work page arXiv 2024

[6] [6]

Champi, M

A. Champi, M. Núñez-Regueiro, H. Cercellier, T. Dev- illers, K. Barbosa, F. Sanchez, L. Roux-Balouzet, T.- M. Nguyen, T. Crozes, E. Beaugnon, F. Gay, and D. Dufeu, Characterization of superconducting grains with T c ∼350K sorted by magnetic field separation: X- Rays diffraction, Raman and magnetic field effect., to be published (2026)

work page 2026

[7] [7]

Y. Cao, V. Fatemi, S. Fang, K. Watanabe, T. Taniguchi, E. Kaxiras, and P. Jarillo-Herrero, Unconventional su- perconductivity in magic-angle graphene superlattices, Nature 556, 43 (2018)

work page 2018

[8] [8]

H. Zhou, T. Xie, T. Taniguchi, K. Watanabe, and A. F. Young, Superconductivity in rhombohedral trilayer graphene, Nature 598, 434 (2021)

work page 2021

[9] [9]

Zhang, B

R. Zhang, B. A. Foutty, O. Sheekey, T. Arp, S. Xu, T. Xie, Y. Guo, H. Stoyanov, S. Gu, A. Keough, E. Re- dekop, C. Zhang, T. Taniguchi, K. Watanabe, M. E. Hu- ber, C. Jin, E. Berg, and A. F. Young, Imaging the Meiss- ner effect and local superfluid stiffness in a graphene su- perconductor (2026), arXiv:2603.25807 [cond-mat.supr- con]

work page arXiv 2026

[10] [10]

F. Wu, E. Hwang, and S. Das Sarma, Phonon-induced gi- ant linear-in- T resistivity in magic angle twisted bilayer graphene: Ordinary strangeness and exotic superconduc- tivity, Phys. Rev. B 99, 165112 (2019)

work page 2019

[11] [11]

Y.-Z. Chou, F. Wu, J. D. Sau, and S. Das Sarma, Acoustic-phonon-mediated superconductivity in rhombo- hedral trilayer graphene, Phys. Rev. Lett. 127, 187001 (2021)

work page 2021

[12] [12]

Peotta and P

S. Peotta and P. Törmä, Superfluidity in topologically nontrivial flat bands, Nature Communications 6, 8944 (2015)

work page 2015

[13] [13]

Törmä, S

P. Törmä, S. Peotta, and B. A. Bernevig, Superconduc- tivity, superfluidity and quantum geometry in twisted multilayer systems, Nature Reviews Physics 4, 528 (2022)

work page 2022

[14] [14]

H. Tian, X. Gao, Y. Zhang, S. Che, T. Xu, P. Che- ung, K. Watanabe, T. Taniguchi, M. Randeria, F. Zhang, C. N. Lau, and M. W. Bockrath, Evidence for Dirac flat band superconductivity enabled by quantum geometry, Nature 614, 440 (2023)

work page 2023

[15] [15]

N. B. Kopnin, Surface superconductivity in multilay- ered rhombohedral graphene: Supercurrent, JETP Let- ters 94, 81 (2011)

work page 2011

[16] [16]

N. B. Kopnin, T. T. Heikkilä, and G. E. Volovik, High-temperature surface superconductivity in topologi- cal flat-band systems, Phys. Rev. B 83, 220503 (2011)

work page 2011

[17] [17]

Jiang, T

G. Jiang, T. T. Heikkilä, and P. Törmä, Ideal quantum geometry of the surface states of rhombohedral graphite and its effects on the surface superconductivity, Phys. Rev. B 113, L041111 (2026)

work page 2026

[18] [18]

Zhang, Q

H. Zhang, Q. Li, M. G. Scheer, R. Wang, C. Tuo, N. Zou, W. Chen, J. Li, X. Cai, C. Bao, M.-R. Li, K. Deng, K. Watanabe, T. Taniguchi, M. Ye, P. Tang, Y. Xu, P. Yu, J. A vila, P. Dudin, J. D. Denlinger, H. Yao, B. Lian, W. Duan, and S. Zhou, Correlated topological flat bands in rhombohedral graphite, Proceedings of the National Academy of Sciences 121, e24...

work page doi:10.1073/pnas.2410714121 2024

[19] [19]

X. Liu, Y. Guan, and O. V. Yazyev, Electronic states at twist stacking faults in rhombohedral graphite (2025), arXiv:2512.20493 [cond-mat.mes-hall]

work page arXiv 2025

[20] [20]

K. Lv, Q. Cheng, Y.-C. Zhuang, C.-Y. Hao, X.-Y. Wang, Y.-X. Zhao, K. Watanabe, T. Taniguchi, Y.-N. Ren, Q.- F. Sun, and L. He, Electrical Switching of the Berry Phase in Bernal Bilayer Graphene Quantum Dots, Phys. 6 Rev. Lett. 136, 116201 (2026)

work page 2026

[21] [21]

Hohenberg and W

P. Hohenberg and W. Kohn, Inhomogeneous electron gas, Phys. Rev. 136, B864 (1964)

work page 1964

[22] [22]

Kohn and L

W. Kohn and L. J. Sham, Self-consistent equations in- cluding exchange and correlation effects, Phys. Rev. 140, A1133 (1965)

work page 1965

[23] [23]

Sun and J.-A

F. Sun and J.-A. Yan, Electronic structure of multilayer graphene with arbitrary stackings, APS Open Sci. 1, 000009 (2026)

work page 2026

[24] [24]

Kresse and J

G. Kresse and J. Furthmuller, Eﬀiciency of ab-initio total energy calculations for metals and semiconductors using a plane-wave basis set, Comput. Mat. Sci. 6, 15 (1996)

work page 1996

[25] [25]

Kresse and J

G. Kresse and J. Furthmüller, Eﬀicient iterative schemes for ab initio total-energy calculations using a plane-wave basis set, Phys. Rev. B 54, 11169 (1996)

work page 1996

[26] [26]

Kresse and D

G. Kresse and D. Joubert, From ultrasoft pseudopoten- tials to the projector augmented-wave method, Phys. Rev. B 59, 1758 (1999)

work page 1999

[27] [27]

J. P. Perdew, K. Burke, and M. Ernzerhof, Generalized Gradient Approximation Made Simple, Phys. Rev. Lett. 77, 3865 (1996)

work page 1996

[28] [28]

Tkatchenko and M

A. Tkatchenko and M. Scheffler, Accurate Molecular Van Der Waals Interactions from Ground-State Electron Den- sity and Free-Atom Reference Data, Phys. Rev. Lett. 102, 073005 (2009)

work page 2009

[29] [29]

(2026), see Supplemental Material for the mapping of the tight-binding model for a rhombohedral slab to an effective SSH chain

work page 2026

[30] [30]

A. A. Aligia, A. M. Lobos, L. Peralta Gavensky, and C. J. Gazza, Probing boundary spins in the Su-Schrieffer- Heeger-Hubbard model, Phys. Rev. B 112, 235156 (2025)

work page 2025

[31] [31]

Harrison, Electronic Structure and the Properties of Solids: The Physics of the Chemical Bond , Dover Books on Physics (Dover Publications, 2012)

W. Harrison, Electronic Structure and the Properties of Solids: The Physics of the Chemical Bond , Dover Books on Physics (Dover Publications, 2012)

work page 2012