The valence band maxima of most group VI transition metal dichalcogenide thin films remain at the Γ point all of the way from bulk to bilayer. In this paper, we develop a continuum theory of the ...moiré minibands that are formed in the valence bands of Γ-valley homobilayers by a small relative twist. Our effective theory is benchmarked against large-scale ab initio electronic structure calculations that account for lattice relaxation. As a consequence of an emergent Formula: see text symmetry, we find that low-energy Γ-valley moiré holes differ qualitatively from their K-valley counterparts addressed previously; in energetic order, the first three bands realize 1) a single-orbital model on a honeycomb lattice, 2) a two-orbital model on a honeycomb lattice, and 3) a single-orbital model on a kagome lattice.
Moiré bands in twisted double-layer graphene Bistritzer, Rafi; MacDonald, Allan H.
Proceedings of the National Academy of Sciences - PNAS,
07/2011, Volume:
108, Issue:
30
Journal Article
Peer reviewed
Open access
A moiré pattern is formed when two copies of a periodic pattern are overlaid with a relative twist. We address the electronic structure of a twisted two-layer graphene system, showing that in its ...continuum Dirac model the moiré pattern periodicity leads to moiré Bloch bands. The two layers become more strongly coupled and the Dirac velocity crosses zero several times as the twist angle is reduced. For a discrete set of magic angles the velocity vanishes, the lowest moiré band flattens, and the Dirac-point density-of-states and the counterflow conductivity are strongly enhanced.
The two-dimensional electron systems in graphene and in topological insulators are described by massless Dirac equations. Although the two systems have similar Hamiltonians, they are polar opposites ...in terms of spin-orbit coupling strength. We briefly review the status of efforts to achieve long spin-relaxation times in graphene with its weak spin-orbit coupling, and to achieve large current-induced spin polarizations in topological-insulator surface states that have strong spin-orbit coupling. We also comment on differences between the magnetic responses and dilute-moment coupling properties of the two systems, and on the pseudospin analogue of giant magnetoresistance in bilayer graphene.
It has recently been shown Y. Cao, J. M. Park, K. Watanabe, T. Taniguchi, and P. Jarillo-Herrero, Pauli-limit violation and re-entrant superconductivity in moiré graphene, Nature (London) 595, 526 ...(2021). that superconductivity in magic-angle twisted trilayer graphene survives to in-plane magnetic fields that are well in excess of the Pauli limit, and much stronger than the in-plane critical magnetic fields of magic-angle twisted bilayer graphene. The difference is surprising because twisted bilayers and trilayers both support the magic-angle flat bands thought to be the fountainhead of twisted graphene superconductivity. We show here that the difference in critical magnetic fields can be traced to a C2Mh symmetry in trilayers that survives in-plane magnetic fields, and also relative displacements between top and bottom layers that are not under experimental control at present. An gate electric field breaks the C2Mh symmetry and therefore limits the in-plane critical magnetic field.
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Graphene bilayers with a twist Andrei, Eva Y; MacDonald, Allan H
Nature materials,
12/2020, Volume:
19, Issue:
12
Journal Article
Peer reviewed
Open access
Near a magic twist angle, bilayer graphene transforms from a weakly correlated Fermi liquid to a strongly correlated two-dimensional electron system with properties that are extraordinarily sensitive ...to carrier density and to controllable environmental factors such as the proximity of nearby gates and twist-angle variation. Among other phenomena, magic-angle twisted bilayer graphene hosts superconductivity, interaction-induced insulating states, magnetism, electronic nematicity, linear-in-temperature low-temperature resistivity and quantized anomalous Hall states. We highlight some key research results in this field, point to important questions that remain open and comment on the place of magic-angle twisted bilayer graphene in the strongly correlated quantum matter world.
The discovery of magic angle twisted bilayer graphene has unveiled a rich variety of superconducting, magnetic, and topologically nontrivial phases. Here, we show that the zero-field states at odd ...integer filling factors in h -BN nonaligned devices are consistent with symmetry broken Chern insulators, as is evidenced by the observation of the anomalous Hall effect near moiré cell filling factor ν = + 1 . The corresponding Chern insulator has a Chern number C = ± 1 and a relatively high Curie temperature of Tc ≈ 4.5 K . In a perpendicular magnetic field above B > 0.5 T we observe a transition of the ν = + 1 Chern insulator from Chern number C = ± 1 to C = 3 , characterized by a quantized Hall plateau with Ryx = h/3e2. These observations demonstrate that interaction-induced symmetry breaking leads to zero-field ground states that include almost degenerate and closely competing Chern insulators, and that states with larger Chern numbers couple most strongly to the B field. In addition, the device reveals strong superconducting phases with critical temperatures of up to Tc ≈ 3.5 K . By providing the first demonstration of a system that allows gate-induced transitions between magnetic and superconducting phases, our observations mark a major milestone in the creation of a new generation of quantum electronics.
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The recent demonstrations of electrical manipulation and detection of antiferromagnetic spins have opened up a new chapter in the story of spintronics. Here, we review the emerging research field ...that is exploring the links between antiferromagnetic spintronics and topological structures in real and momentum space. Active topics include proposals to realize Majorana fermions in antiferromagnetic topological superconductors, to control topological protection and Dirac points by manipulating antiferromagnetic order parameters, and to exploit the anomalous and topological Hall effects of zero-net-moment antiferromagnets. We explain the basic concepts behind these proposals, and discuss potential applications of topological antiferromagnetic spintronics.
Magnetized topological insulator multilayers Lei, Chao; Chen, Shu; MacDonald, Allan H.
Proceedings of the National Academy of Sciences - PNAS,
11/2020, Volume:
117, Issue:
44
Journal Article
Peer reviewed
Open access
We discuss the magnetic and topological properties of bulk crystals and quasi–two-dimensional (quasi-2D) thin films formed by stacking intrinsic magnetized topological insulator (for example, Mn ...(SbₓBi1–x
)₂X₄ with X = Se,Te) septuple layers and topological insulator quintuple layers in arbitrary order. Our analysis makes use of a simplified model that retains only Dirac cone degrees of freedom on both surfaces of each septuple or quintuple layer. We demonstrate the model’s applicability and estimate its parameters by comparing with ab initio density-functional theory (DFT) calculations. We then employ the coupled Dirac cone model to provide an explanation for the dependence of thin-film properties, particularly the presence or absence of the quantum anomalous Hall effect, on film thickness, magnetic configuration, and stacking arrangement, and to comment on the design of Weyl superlattices.
We present a combined experimental and theoretical study of twisted double bilayer graphene with twist angles between 1° and 1.35°. Consistent with moiré band structure calculations, we observe ...insulators at integer moiré band fillings one and three, but not two. An applied transverse electric field separates the first moiré conduction band from neighboring bands, and favors the appearance of correlated insulators at 1/4, 1/2, and 3/4 band filling. Insulating states at 1/4 and 3/4 band filling emerge only in a parallel magnetic field (B||), whereas the resistivity at half band filling is weakly dependent on B||. Our findings suggest that correlated insulators are favored when a moiré flat band is spectrally isolated, and are consistent with a mean-field picture in which insulating states are established by breaking both spin and valley symmetries at 1/4 and 3/4 band filling and valley polarization alone at 1/2 band filling.
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The spin Hall effect (SHE)
achieves coupling between charge currents and collective spin dynamics in magnetically ordered systems and is a key element of modern spintronics
. However, previous ...research has focused mainly on non-magnetic materials, so the magnetic contribution to the SHE is not well understood. Here we show that antiferromagnets have richer spin Hall properties than do non-magnetic materials. We find that in the non-collinear antiferromagnet
Mn
Sn, the SHE has an anomalous sign change when its triangularly ordered moments switch orientation. We observe contributions to the SHE (which we call the magnetic SHE) and the inverse SHE (the magnetic inverse SHE) that are absent in non-magnetic materials and that can be dominant in some magnetic materials, including antiferromagnets. We attribute the dominance of this magnetic mechanism in Mn
Sn to the momentum-dependent spin splitting that is produced by non-collinear magnetic order. This discovery expands the horizons of antiferromagnet spintronics and spin-charge coupling mechanisms.
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