Twisted Graphene Bilayers and Quasicrystals: A Cut and Projection Approach

Aragón, J. L.; Naumis, Gerardo G.; Gómez-Rodríguez, A.

doi:10.3390/cryst9100519

Cited by 7 publications

(6 citation statements)

References 34 publications

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“…The rotated homo-bilayer moiré is the most commonly described in the theoretical literature, and the process to create a commensurable moiré bilayer by a relative rotation is described now. When commensuration between the two monolayers exists, the lattice vectors of a rotated moiré supercell can be obtained following a process delineated in [282,[292][293][294][295] and multiple other publications. Let…”

Section: Different Ways To Create Moirésmentioning

confidence: 99%

See 1 more Smart Citation

Mechanical, electronic, optical, piezoelectric and ferroic properties of strained graphene and other strained monolayers and multilayers: an update

Naumis,

Herrera,

Poudel

et al. 2023

Rep. Prog. Phys.

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This is an update of a previous review on the subject \cite{Naumis_2017}. Experimental and theoretical advances for straining graphene and other metallic, insulating, ferroelectric, ferroelastic, ferromagnetic and multiferroic 2D materials have been considered. Specific topics of discussion include: (i) methods to induce valley and sublattice polarisation ($\mathbf{P}$) in graphene, (ii) time-dependent strain and its impact on graphene's electronic properties, (iii) the role of local and global strain on superconductivity and other highly correlated and/or topological phases of graphene, inducing polarisation $\mathbf{P}$ on hexagonal boron nitride monolayers {\it via} strain, (iv) measuring strain, and modifying through strain the optoelectronic properties of transition metal dichalcogenides, (v) ferroic 2D materials with intrinsic elastic ($\sigma$), electric ($\mathbf{P}$) and magnetic ($\mathbf{M}$) polarisation under strain, as well as incipient 2D multiferroics and (vi) moir'e bilayers exhibiting flat electronic bands and exotic quantum phase diagrams, and other bilayer or few-layer systems exhibiting ferroic orders tunable by rotations and shear strain. The review features the extremely recent experimental realizations of a tunable two-dimensional Quantum Spin Hall effect in germanene, of monoelemental 2D ferroelectric bismuth, and 2D multiferroic NiI$_2$. The document was structured for a discussion of effects taking place in monolayers first, followed by discussions concerning bilayers and few-layers, and it represents a fresh and up-to-date overview of exciting and newest developments on the fast-paced field of 2D materials.

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Section: Different Ways To Create Moirésmentioning

confidence: 99%

“…A powerful method to describe the structure of twisted 2D materials relies on the cut and projection method used to generate quasicrystals [294,[318][319][320]. There, the projected structure is interpreted as the set of points of best fit between the two rotated structures [294].…”

Section: Magic Angle Twisted Bilayer Graphenementioning

confidence: 99%

Mechanical, electronic, optical, piezoelectric and ferroic properties of strained graphene and other strained monolayers and multilayers: an update

Naumis,

Herrera,

Poudel

et al. 2023

Rep. Prog. Phys.

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“…Quasicrystal (QC), an ordered but not periodic structure, is famous for exotic tiling patterns with fractality [1][2][3][4][5][6][7][8][9][10]. They are represented by self-similar structures as a compensation of the absence of translational symmetry [8,[10][11][12][13][14][15][16].…”

Section: Introductionmentioning

confidence: 99%

“…In this regard, we focus on quasicrystals with new local tiling patterns, which can be understood by cut-andproject scheme to construct quasicrystalline structures from the high-dimensional lattice [4,5,8,25]. According to the translations in high-dimensional lattice, the distinct local tiling patterns emerge from the atomic rearrangement, which is also known as a phason flip [12,[26][27][28][29][30][31].…”

Section: Introductionmentioning

confidence: 99%

Quantum bridge states and sub-dimensional transports in quasicrystals

Jeon¹,

Lee²

2022

Preprint

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Exotic tiling patterns of quasicrystals have gotten a lot of attention for unique quantum phenomena such as critical state and multifractality. In this regard, finding new quasi-periodic tiling patterns and the relevant quantum states is one of the main interests in quasicrystals. Here, we focus on new types of quasicrystals described by coexisting phason flips and discuss their quantum transports with distinct local tiling patterns. It turns out that such new tilings are uniquely descended from the translation of high-dimensional lattices and their projection, in particular, a four-dimensional hypercubic lattice. Such unconventional tiling gives rise to sub-dimensionally confined states forming a bridge, so-called quantum bridge states. It turns out that electrons in such states could be strongly localized by applying a magnetic field at a particular time but are transported to the sites which share the same local patterns along the bridge with time evolution. The speed of transport is controlled via magnetic field strength, and one can even expect electron transportation between multiple bridges where their numbers are determined by the translation vectors of a four-dimensional hypercubic lattice. Our work paves a way to discover anomalous quantum states and their transports uniquely present in quasicrystals with new tiling structures.

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“…It's interesting to investigate the consequence of such enlarged rotation symmetries in the LA-THBs. Though their single-particle properties have been studied [52][53][54][55][56][57][58][59][60], physical properties driven by electron-electron (e-e) interaction have not been studied. Here we propose to use these materials to generate symmetry-protected highangular-momentum (HAM) topological superconductivities (TSCs), absent in crystalline materials.…”

mentioning

confidence: 99%

High-Angular-Momentum Topological Superconductivity in the Largest-Angle Twisted Homo-bilayer Systems

Liu¹,

Zhang²,

Chen³

et al. 2022

Preprint

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We study the largest-angle twisted homo-bilayer (LA-THB) systems, hosting Moiréless quasicrystal (QC) structure. We propose to use these materials to generate high-angular-momentum (HAM) topological superconductivities (TSCs) protected by their QC symmetries absent on conventional crystalline materials. This proposal is based on our universal Ginzburg-Landau theory based analysis which yields the general conclusion that, when each Dn-symmetric (n is even) monolayer hosts SC with pairing angular momentum l ≤ n 2 , the interlayer Josephson coupling will induce SC with pairing angular momentum L = l or L = n − l in the LA-THB, determined by microscopic details. The latter one is just the HAM TSC if l > 0. Based on our revised perturbational-band theory, we develop general microscopic framework to study the QC LA-THBs involving electronelectron interactions, adopting which we study three examples, i.e. the 30 • -twisted bilayer graphene, the 30 • -twisted bilayer BC3, and the 45 • -twisted bilayer cuprates. The g + ig-h + ih-and d + id-TSCs with HAM L = 4, 5 and 2 can emerge in certain doping regimes in these systems, respectively.

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Twisted Graphene Bilayers and Quasicrystals: A Cut and Projection Approach

Cited by 7 publications

References 34 publications

Mechanical, electronic, optical, piezoelectric and ferroic properties of strained graphene and other strained monolayers and multilayers: an update

Mechanical, electronic, optical, piezoelectric and ferroic properties of strained graphene and other strained monolayers and multilayers: an update

Quantum bridge states and sub-dimensional transports in quasicrystals

High-Angular-Momentum Topological Superconductivity in the Largest-Angle Twisted Homo-bilayer Systems

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