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The emergence of flat electronic bands and of the recently discovered strongly correlated and superconducting phases in twisted bilayer graphene crucially depends on the interlayer twist angle upon approaching the magic angle $\theta_M…

We review the theoretical modelling of moir\'e materials, focusing on various aspects of magic-angle twisted bilayer graphene (MA-TBG) viewed through the lens of Hartree-Fock mean-field theory. We first provide an elementary introduction to…

Strongly Correlated Electrons · Physics 2026-03-20 Yves H. Kwan , Ziwei Wang , Glenn Wagner , Nick Bultinck , Steven H. Simon , Siddharth A. Parameswaran

Recent experimental discoveries of superconductivity and other exotic electronic states in twisted bilayer graphene (TBG) call for a reconsideration of our traditional theories of these states, usually based on the assumption of the…

Superconductivity · Physics 2019-09-06 Tero T. Heikkila , Timo Hyart

Graphene moir\'e systems are ideal environments for investigating complex phase diagrams and gaining fundamental insights into the mechanisms underlying exotic states of matter, as they permit controlled manipulation of electronic…

Moir\'e superlattice in twisted bilayer graphene has been proven to be a versatile platform for exploring exotic quantum phases. Extensive investigations have been invoked focusing on the zero-magnetic-field phase diagram at the magic twist…

Encapsulating graphene in hexagonal Boron Nitride has several advantages: the highest mobilities reported to date are achieved in this way, and precise nanostructuring of graphene becomes feasible through the protective hBN layers.…

Mesoscale and Nanoscale Physics · Physics 2021-01-04 Yongping Du , Ning Xu , Xianqing Lin , Antti-Pekka Jauho

Moir\'{e} systems such as magic-angle twisted bilayer graphene have attracted significant attention due to their ability to host correlated phenomena including superconductivity and strongly correlated insulating states. By defining the…

Strongly Correlated Electrons · Physics 2025-09-08 Liangtao Peng , Giovanni Vignale , Shaffique Adam

Twisted graphene multilayers have demonstrated to yield a versatile playground to engineer controllable electronic states. Here, by combining first-principles calculations and low-energy models, we demonstrate that twisted graphene…

Mesoscale and Nanoscale Physics · Physics 2020-09-04 Alejandro Lopez-Bezanilla , J. L. Lado

Twisted bilayer graphene (tBLG) including interlayer interaction and rotational disorder shows anomalous electron transport as a function of twist-angles (tAs). In this work, we address the electronic properties and electron transport of…

Mesoscale and Nanoscale Physics · Physics 2023-06-13 Farzaneh Shayeganfar , Ali Ramazani , Nicholas X Fang

Transport experiments in twisted bilayer graphene revealed multiple superconducting domes separated by correlated insulating states. These properties are generally associated with strongly correlated states in a flat mini-band of the…

Strongly interacting electrons in solid-state systems often display tendency towards multiple broken symmetries in the ground state. The complex interplay between different order parameters can give rise to a rich phase diagram. Here, we…

We present electronic structure calculations of twisted double bilayer graphene (TDBG): A tetralayer graphene structure composed of two AB-stacked graphene bilayers with a relative rotation angle between them. Using first-principles…

Mesoscale and Nanoscale Physics · Physics 2019-11-05 F. J. Culchac , Rodrigo B. Capaz , Leonor Chico , E. Suarez Morell

Recent experiments show how a bilayer graphene twisted around a certain magic angle becomes superconducting as it is doped into a region with approximate flat bands. We investigate the mean-field $s$-wave superconducting state in such a…

Superconductivity · Physics 2018-12-19 T. J. Peltonen , R. Ojajärvi , T. T. Heikkilä

In recent experiments, superconductivity and correlated insulating states were observed in twisted bilayer graphene (TBG) with small magic angles, which highlights the importance of the flat bands near Fermi energy. However, the moir\'e…

Materials Science · Physics 2020-02-11 Jing-Yang You , Bo Gu , Gang Su

We study a minimal Hubbard model for electronically driven superconductivity in a correlated flat mini-band resulting from the superlattice modulation of a twisted graphene multilayer. The valley degree of freedom drastically modifies the…

Strongly Correlated Electrons · Physics 2018-08-30 Cenke Xu , Leon Balents

Magic-angle twisted bilayer graphene (MA-TBG) exhibits intriguing quantum phase transitions triggered by enhanced electron-electron interactions when its flat-bands are partially filled. However, the phases themselves and their connection…

Mesoscale and Nanoscale Physics · Physics 2021-04-14 Shuang Wu , Zhenyuan Zhang , K. Watanabe , T. Taniguchi , Eva Y. Andrei

For twisted bilayer graphene close to magic angle, we show that the effects of lattice relaxation and the Hartree interaction both become simultaneously important. Including both effects in a continuum theory reveals a Lifshitz transition…

Strongly Correlated Electrons · Physics 2024-04-30 Mohammed M. Al Ezzi , Liangtao Peng , Zhengyu Liu , Jonah Huang Zi Chao , Gayani N. Pallewela , Darryl Foo , Shaffique Adam

In twisted bilayer graphene (TBG) devices, local strains frequently coexist and intertwine with the twist-angle-dependent moir\'e superlattice, significantly influencing the electronic properties of TBG, yet their combined effects remain…

Patterning graphene with a spatially-periodic potential provides a powerful means to modify its electronic properties. Dramatic effects have been demonstrated in twisted bilayers where coupling to the resulting moir\'e-superlattice yields…

Mesoscale and Nanoscale Physics · Physics 2021-06-09 Yutao Li , Scott Dietrich , Carlos Forsythe , Takashi Taniguchi , Kenji Watanabe , Pilkyung Moon , Cory R. Dean

In flat bands, superconductivity can lead to surprising transport effects. The superfluid "mobility", in the form of the superfluid weight $D_s$, does not draw from the curvature of the band but has a purely band-geometric origin. In a…

Superconductivity · Physics 2021-01-20 Valerio Peri , Zhida Song , B. Andrei Bernevig , Sebastian D. Huber