Impurity-induced triple point fermions in twisted bilayer graphene

Ramires, Aline; Lado, José L.

doi:10.1103/physrevb.99.245118

Cited by 52 publications

(61 citation statements)

References 67 publications

(95 reference statements)

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“…, and P v is the valley polarization operator [31,55,56] that weighs the states with ±1 depending on which graphene valley (K, K ) they originate from. This allows us to find the valley-Chern number through integration over energies and over the unit cell, i.e.,…”

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confidence: 99%

Electrically Tunable Flat Bands and Magnetism in Twisted Bilayer Graphene

et al. 2019

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Twisted graphene bilayers provide a versatile platform to engineer metamaterials with novel emergent properties by exploiting the resulting geometric moiré superlattice. Such superlattices are known to host bulk valley currents at tiny angles (α ≈ 0.3 • ) and flat bands at magic angles (α ≈ 1 • ). We show that tuning the twist angle to α * ≈ 0.8 • generates flat bands with triangular superlattice periodicity. When doped with ±6 electrons per moiré cell, these bands are half-filled and electronic interactions produce a symmetry-broken ground state (Stoner instability) with spin-polarized regions that order ferromagnetically. Application of an interlayer electric field breaks inversion symmetry and introduces valley-dependent dispersion that quenches the magnetic order. With these results, we propose a solid-state platform that realizes electrically tunable strong correlations. arXiv:1905.07651v3 [cond-mat.mes-hall]

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Electrically Tunable Flat Bands and Magnetism in Twisted Bilayer Graphene

et al. 2019

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“…As a reference, for twisted graphene multilayers t ≈ 3 eV and t ⊥ ≈ 0.15t. 1 Similar real-space models were used to study a variety of twisted graphene multilayers [10,36,50,51], providing a simple formalism to study the effect of dopants and impurities [52,53]. However, in contrast to continuum models [9,42,54], measuring of valley-related quantities with a real-space-based formalism is nontrivial.…”

Section: Electronic Structure Of Twisted Trilayer Graphenementioning

confidence: 99%

“…Valley physics in both DFT calculations and the tight-binding model are emergent symmetries, in the sense that valley are not easily defined in terms of real-space chemical orbitals. This limitation can be overcome by defining the so-called valley operator [21,52,55] in the tight-binding description. With the valley operator the expectation value of the valley can be computed in a real-space representation [22,56].…”

Section: Electronic Structure Of Twisted Trilayer Graphenementioning

confidence: 99%

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Electrical band flattening, valley flux, and superconductivity in twisted trilayer graphene

López-Bezanilla

Lado

2020

Phys. Rev. Research

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Twisted graphene multilayers have been 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 trilayers provide a tunable system where Van Hove singularities can be controlled electrically. In particular, it is shown that besides the band flattening, bulk valley currents appear, which can be quenched by local chemical dopants. We finally show that in the presence of electronic interactions, a nonuniform superfluid density emerges whose nonuniformity gives rise to spectroscopic signatures in dispersive higher-energy bands. Our results put forward twisted trilayers as a tunable van der Waals heterostructure displaying electrically controllable flat bands and bulk valley currents.

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“…From this perspect-ive, TSWG may open a feasible experimental path for realizing the coexistence of both strongly localized and ultramobile quasiparticles simultaneously, important for the "steep band/flat band" scenario of superconductivity. As the flat bands can pierce the Dirac cone extremely close to its vertex, TSWG can also be viewed as a potential platform for reaching the so-called triple point states, a fine tuning for which the low-energy physics is effectively described by the Dirac equation with pseudospin-1 (see also Refs 39,40. ).…”

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Ultraheavy and Ultrarelativistic Dirac Quasiparticles in Sandwiched Graphenes

et al. 2020

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Electrons in quantum materials exhibiting coexistence of dispersionless (flat) bands piercing dispersive (steep) bands can give rise to strongly correlated phenomena, and are associated with unconventional superconductivity. It is known that in twisted trilayer graphene steep Dirac cones can coexist with band flattening, but the phenomenon is not stable under layer misalignments. Here we show that such a twisted sandwiched graphene (TSWG) -a threelayer van der Waals heterostructure with a twisted middle layer -can have very stable flat bands coexisting with Dirac cones near the Fermi energy when twisted to 1.5 • . These flat bands require a specific high-symmetry stacking order, and our atomistic calculations predict that TSWG always relaxes to it. Additionally, with external fields, we can control the relative energy offset between the Dirac cone vertex and the flat bands. Our work establishes twisted sandwiched graphene as a new platform for research into strongly interacting phases, and topological transport beyond Dirac and Weyl semimetals.Graphene, an atomically thin crystal of carbon, provides an experimentally favorable platform for two dimensional (2D) Dirac physics as it exhibits ultrarelativistic Dirac cones in its band structure, described with massless quasiparticles when weak spin-orbit coupling is neglected. 1 1 arXiv:1907.00952v1 [cond-mat.str-el] 1 Jul 2019Bilayers of graphene in the energetically favorable Bernal (AB) stacking have quadratic dispersion and quasiparticles with well-defined effective mass. 1 Twisted bilayer graphene (TBG) -two rotationally mismatched graphene layers -can be fabricated at the so-called magic angle near 1.1 • , where it hosts ultraheavy fermions with remarkably flat, almost dispersionless electronic bands 2-5 of a topological origin. [5][6][7][8] The twist angle serves as a precise control of the interlayer coupling between the graphene monolayers, revealing the band flattening phenomena as an ultimate manifestation of hybridization of Dirac cones. Flat bands and the corresponding large density of electronic states can lead to novel strongly correlated phenomena. Indeed, since the recent discovery of correlated insulators and unconventional superconductivity in TBG, [9][10][11][12] van der Waals multilayer stacks have been further explored as a platform of exotic correlated physics. In particular, effectively 2D heterostructures consisting of flat sheets of graphene, transition metal dichalcogenides, and hexagonal boron nitride have been successful candidates for the moiré-induced correlated phenomena. [13][14][15][16][17][18][19][20][21][22][23] Recent experimental progress in studying correlations in multilayer heterostructures with more than two twisted graphene layers 13, 24-26 has led to a search for novel multilayer platforms with a particular focus on the trilayer geometry. 14,[27][28][29][30] In this work, we provide a detailed ab initio study of a unique extension of the TBG system: the twisted graphene sandwich (Fig. 1b), which is a promising construct of a...

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Impurity-induced triple point fermions in twisted bilayer graphene

Cited by 52 publications

References 67 publications

Electrically Tunable Flat Bands and Magnetism in Twisted Bilayer Graphene

Electrically Tunable Flat Bands and Magnetism in Twisted Bilayer Graphene

Electrical band flattening, valley flux, and superconductivity in twisted trilayer graphene

Ultraheavy and Ultrarelativistic Dirac Quasiparticles in Sandwiched Graphenes

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