English
Related papers

Related papers: Hofstadter Butterfly in Graphene

200 papers

We present and discuss in detail practical techniques in formulating effective models to describe the dynamics of low-energy electrons in generic bilayer graphene. Starting from a tight-binding model using the $p_z$ orbital of carbon atoms…

Mesoscale and Nanoscale Physics · Physics 2022-05-26 H. Minh Lam , V. Nam Do

The interplay of twist and strain in bilayer graphene enables the formation of moir\'e patterns and narrow bands that host correlated and topological phases. While magic-angle twisted bilayer graphene has been widely studied, strain…

Mesoscale and Nanoscale Physics · Physics 2026-03-10 Federico Escudero , Dong Wang , Pierre A. Pantaleón , Shengjun Yuan , Francisco Guinea , Zhen Zhan

Twisted graphene bilayers show a complex electronic structure, further modified by interaction effects. The main features can be obtained from effective models, which make use a few phenomenological parameters. We analyze the influence of…

Strongly Correlated Electrons · Physics 2019-03-04 Niels R. Walet , Francisco Guinea

Twisted bilayer graphene (tBLG) has emerged as a promising platform to explore exotic electronic phases. However, the formation of moir\'e patterns in tBLG has thus far been confined to the introduction of twist angles between the layers.…

Materials Science · Physics 2023-10-10 Gabriel R. Schleder , Michele Pizzochero , Efthimios Kaxiras

We present simple models to describe the in-plane and the out-of-plane lattice relaxation in twisted bilayer and symmetrically twisted trilayer graphene. Analytical results and series expansions show that for twist angles {\theta} > 1…

Mesoscale and Nanoscale Physics · Physics 2023-11-28 Adrián Ceferino , Francisco Guinea

The occurrence of superconducting and insulating phases is well-established in twisted graphene bilayers, and they have also been reported in other arrangements of graphene layers. We investigate three such arrangements: untwisted AB…

Strongly Correlated Electrons · Physics 2021-08-11 Pierre A. Pantaleon , Tommaso Cea , Rory Brown , Niels R. Walet , Francisco Guinea

We report intriguing and hitherto overlooked low-field room temperature extremely large magnetoresistance (XMR) patterns in graphene/hexagonal boron nitride (h-BN) superlattices that emerge due to the existence of open orbits within each…

We study the atomic and electronic structures of the commensurate double moir\'{e} superlattices in fully relaxed twisted bilayer graphene (TBG) nearly aligned with the hexagonal boron nitride (BN). The single-particle effective Hamiltonian…

Mesoscale and Nanoscale Physics · Physics 2020-07-31 Xianqing Lin , Jun Ni

The aim of this article is to prove that for the graphene model like for a model considered by the physicist Hou on a kagome lattice, there exists a formula which is similar to the one obtained by Chambers for the Harper model. As an…

Analysis of PDEs · Mathematics 2014-08-13 Bernard Helffer , Philippe Kerdelhué , Jimena Royo-Letelier

Graphene has exceptional optical, mechanical and electrical properties, making it an emerging material for novel optoelectronics, photonics and for flexible transparent electrode applications. However, the relatively high sheet resistance…

Mesoscale and Nanoscale Physics · Physics 2013-02-06 Guang-Xin Ni , Yi Zheng , Sukang Bae , Chin Yaw Tan , Orhan Kahya , Jing Wu , Byung Hee Hong , Kui Yao , Barbaros Özyilmaz

The observability of the Hofstadter spectrum generated by a Wigner crystal using photoluminescence techniques is studied. Itinerant hole geometries are examined, in which a hole may combine directly with electrons in the lattice. It is…

Condensed Matter · Physics 2007-05-23 Lian Zheng , H. A. Fertig

In this paper, we use Floquet theory to theoretically study the effect of monochromatic circularly and linearly polarized light on the Hofstadter butterfly in the square lattice, which is induced by uniform perpendicular magnetic field. In…

Mesoscale and Nanoscale Physics · Physics 2022-06-28 Ming Zhao , Qi Chen , Xue-Dong Tian , Liang Du

Continuum atomic relaxation models for twisted bilayer graphene involve minimization of the sum of intralayer elastic energy and interlayer adhesion energy. The elastic energy favors a rigid twist i.e. no distortion in the twisted honeycomb…

Strongly Correlated Electrons · Physics 2025-10-10 Jian Kang , Oskar Vafek

Rational design of artificial lattices yields effects unavailable in simple solids, and vertical superlattices of multilayer semiconductors are already used in optical sensors and emitters. Manufacturing lateral superlattices remains a much…

The Hofstadter butterfly is a quantum fractal with a highly complex nested set of gaps, where each gap represents a quantum Hall state whose quantized conductivity is characterized by topological invariants known as the Chern numbers. Here…

Other Condensed Matter · Physics 2016-03-11 Gerardo Naumis , Indubala I. Satija

We present a model for interacting electrons in a continuum band structure that resembles a ``trashcan'', with a flat bottom of radius $k_b$ beyond which the dispersion increases rapidly with velocity $v$. The form factors of the Bloch…

Strongly Correlated Electrons · Physics 2025-03-14 B. Andrei Bernevig , Yves H. Kwan

Rotational misalignment or twisting of two mono-layers of graphene strongly influences its electronic properties. Structurally, twisting leads to large periodic supercell structures, which in turn can support intriguing strongly correlated…

Recent experimental advances have been marked by the observations of ballistic electron transport in moir\'e superlattices in highly aligned heterostructures of graphene and hexagonal boron nitride (hBN). Here, we predict that a…

Mesoscale and Nanoscale Physics · Physics 2023-05-10 Christian Moulsdale , Vladimir Fal'ko

We introduce a grating assisted tunneling scheme for tunable synthetic magnetic fields in photonic lattices, which can be implemented at optical frequencies in optically induced one- and two-dimensional dielectric photonic lattices. We…

A study of possible superconducting phases of graphene has been constructed in detail. A realistic tight binding model, fit to ab initio calculations, accounts for the Li-decoration of graphene with broken lattice symmetry, and includes $s$…

Superconductivity · Physics 2018-09-20 Rouhollah Gholami , Rostam Moradian , Sina Moradian , Warren E. Pickett