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On the Vertices of Delta-modular Polyhedra
Bludov Mikhail, Gribanov Dmitry, Klimenko Maxim, Kupavskii Andrey, L\'angi Zsolt, Rogozin Alexander, Voronov Vsevolod
https://arxiv.org/abs/2506.12774

On the Vertices of Delta-modular Polyhedra
Let $P$ be a polytope defined by the system $A x \leq b$, where $A \in R^{m \times n}$, $b \in R^m$, and $\text{rank}(A) = n$. We give a short geometric proof of the following tight upper bound on the number of vertices of $P$: $$ n! \cdot \fracΔ{Δ_{\text{average}}} \cdot \text{vol}(B_2) \sim \frac{1}{\sqrt{πn}} \cdot \left(\frac{2 π}{e}\right)^{n/2} \cdot n^{n/2} \cdot \fracΔ{Δ_{\text{average}}}, $$ where $Δ$ is the maximum absolute value of $n \times n$ subdeterminants of $A$, and $�…

To the genocide-loving German from mastodon.social who reported @… for being antisemitic:
Fuck you, you genocide-loving piece of shit, opposing genocide isn’t antisemitism. What you’re doing – conflating being anti-genocide with being antisemitic – is the greatest antisemitism as you’re de facto stating that all Jews are pro-genocide.

Diverse high-Chern-number quantum anomalous Hall insulators in twisted rhombohedral graphene
Naitian Liu, Zhangyuan Chen, Jing Ding, Wenqiang Zhou, Hanxiao Xiang, Xinjie Fang, Linfeng Wu, Xiaowan Zhan, Le Zhang, Qianmei Chen, Kenji Watanabe, Takashi Taniguchi, Na Xin, Shuigang Xu
https://arxiv.org/abs/2507.11347

Diverse high-Chern-number quantum anomalous Hall insulators in twisted rhombohedral graphene
Quantum anomalous Hall (QAH) insulators with high Chern number (C) enables multiple dissipationless edge channels for low-power-consumption electronics. We report the realization of multiple high-C QAH insulators including C=3,5,6, and 7 in twisted monolayer-rhombohedral pentalayer graphene. In twist angles of approximately 1.40°, we observe QAH effect with C=5 at a filling of one electron per moiré unit cell, persisting up to 2 Kelvin. Furthermore, incommensurate QAH insulators with C=5,6, a…

Comment on "Electric conductivity of graphene: Kubo model versus a nonlocal quantum field theory model (arXiv:2403.02279v3)"
M. Bordag, N. Khusnutdinov, G. L. Klimchitskaya, V. M. Mostepanenko
https://arxiv.org/abs/2506.10792

Comment on "Electric conductivity of graphene: Kubo model versus a nonlocal quantum field theory model (arXiv:2403.02279v3)"
Recently, Rodriguez-Lopez, Wang, and Antezza [arXiv:2403.02279v3; Phys. Rev. B v.111, 115428 (2025)] compared the theoretical descriptions of electric conductivity of graphene given by the Kubo model and quantum field theory in terms of the polarizationtensor. According to these authors, in the spatially nonlocal case, the quantum field theoretical description contains ``hard inconsistencies". To bring the predictions of quantum field theory in agreement with those following from the Kubo model…

Magnetic force microscopy versus scanning quantum-vortex microscopy: Probing pinning landscape in granular niobium films
A. Yu. Aladyshkin, R. A. Hovhannisyan, S. Yu. Grebenchuk, S. A. Larionov, A. G. Shishkin, O. V. Skryabina, A. V. Samokhvalov, A. S. Mel'nikov, D. Roditchev, V. S. Stolyarov
https://arxiv.org/abs/2507.05172…

Magnetic force microscopy versus scanning quantum-vortex microscopy: Probing pinning landscape in granular niobium films
We provide an overview of the methodology and fundamental principles associated with newly developed experimental technique -- scanning quantum-vortex microscopy [Hovhannisyan et al., Commun. Mater., vol. 6, 42 (2025)]. This approach appears promising for experimental studies of vortex pinning phenomena in superconducting films and nanodevices. In particular, we studied the magnetic properties of magnetron-sputtered niobium (Nb) films by low-temperature magnetic force microscopy. As the tempera…

Quantum anomalous Hall effects and Hall crystals at fractional filling of helical trilayer graphene
Sen Niu, Jason Alicea, D. N. Sheng, Yang Peng
https://arxiv.org/abs/2505.24146 …

Quantum anomalous Hall effects and Hall crystals at fractional filling of helical trilayer graphene
Helical trilayer graphene realizes a versatile moiré system in which anomalous Hall effects have been recently observed at integer and fractional fillings. Focusing on helical trilayers near the magic angle and under a substrate potential, we demonstrate that an isolated higher Chern band with Chern number $|C_{band}|=2$ emerges, enabling the exploration of many-body states beyond the conventional Landau level paradigm. We use exact diagonalization to predict a rich phase diagram of …

Wafer-scale Programmed Assembly of One-atom-thick Crystals
Seong-Jun Yang, Ju-Hyun Jung, Eunsook Lee, Edmund Han, Min-Yeong Choi, Daesung Jung, Shinyoung Choi, Jun-Ho Park, Dongseok Oh, Siwoo Noh, Ki-Jeong Kim, Pinshane Y. Huang, Chan-Cuk Hwang, Cheol-Joo Kim
https://arxiv.org/abs/2507.22677

Wafer-scale Programmed Assembly of One-atom-thick Crystals
Crystalline films offer various physical properties based on the modulation of their thicknesses and atomic structures. The layer-by-layer assembly of atomically thin crystals provides powerful means to arbitrarily design films at the atomic-level, which are unattainable with existing growth technologies. However, atomically-clean assembly of the materials with high scalability and reproducibility remains challenging. We report programmed crystal assembly (PCA) of graphene and monolayer hexagon…

Quantum Monte Carlo study of artificial triangular graphene quantum dots
E. Bulut Kul, G\"okhan \"Oztarhan, M. N. \c{C}{\i}nar, A. D. G\"u\c{c}l\"u
https://arxiv.org/abs/2506.08621

Quantum Monte Carlo study of artificial triangular graphene quantum dots
We investigate the magnetic phases of triangular graphene quantum dots (TGQDs) with zigzag edges using variational and quantum Monte Carlo methods. These systems serve as quantum simulators for bipartite lattices with broken sublattice symmetry, providing a platform to study the extended Hubbard model's emergent magnetic phenomena, including Lieb's magnetism at half-filling, edge depolarization upon single-electron addition, and Nagaoka ferromagnetism. Our non-perturbative quantum…

Chern junctions in Moir\'e-Patterned Graphene/PbI2
Sun Yan, M. Monteverde, V. Derkach, K. Watanabe, T. Taniguchi, F. Chiodi, H. Bouchiat, A. D. Chepelianskii
https://arxiv.org/abs/2508.04935

Chern junctions in Moiré-Patterned Graphene/PbI2
Expanding the moiré material library continues to unlock novel quantum phases and emergent electronic behaviors. In this work, we introduce PbI2 into the moiré family and investigate the magnetotransport properties of moiré superlattice in a hexagonal boron nitride/graphene/PbI2 heterostructures. In high-field quantum Hall regime, we observe a robust dissipationless transport at charge neutrality point, indicative of incompressible states stabilized at the filling factor vh = 0. Additionally…

From Wye-Delta to Cross-Square Recursion Configurations in Graphene-Based Quantum Hall Arrays
Ngoc Thanh Mai Tran, Marta Musso, Dominick S. Scaletta, Wei-Chen Lin, Valery Ortiz Jimenez, Dean G. Jarrett, Massimo Ortolano, Curt A. Richter, Chi-Te Liang, David B. Newell, Albert F. Rigosi
https://arxiv.org/abs/2508.03347

From Wye-Delta to Cross-Square Recursion Configurations in Graphene-Based Quantum Hall Arrays
In electrical metrology, the quantum Hall effect is accessed at the Landau level filling factor ν = 2 plateau to define and disseminate the unit of electrical resistance (ohm). The robustness of the plateau is only exhibited at this Landau level filling factor and thus places a constraint on the quantized resistances that are accessible when constructing quantized Hall array resistance standards (QHARS) using epitaxial graphene on SiC. To overcome devices constrained by using Hall elements in …