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Spin orbit coupling (SOC) is the key to realizing time-reversal invariant topological phases of matter [1, 2]. Famously, SOC was predicted by Kane and Mele[3] to stabilize a quantum spin Hall insulator; however, the weak intrinsic SOC in monolayer graphene [4][5][6][7] has precluded experimental observation. Here, we exploit a layer-selective proximity effect-achieved via van der Waals contact to a semiconducting transition metal dichalcogenide[8-21]-to engineer Kane-Mele SOC in ultra-clean bilayer graphene. Using high-resolution capacitance measurements to probe the bulk electronic compressibility, we find that SOC leads to the formation of a distinct incompressible, gapped phase at charge neutrality. The experimental data agrees quantitatively with a simple theoretical model in which the new phase results from SOC-driven band inversion. In contrast to Kane-Mele SOC in monolayer graphene, the inverted phase is not expected to be a time reversal invariant topological insulator, despite being separated from conventional band insulators by electric field tuned phase transitions where crystal symmetry mandates that the bulk gap must close [22]. Electrical transport measurements, conspicuously, reveal that the inverted phase has a conductivity ∼ e 2 /h, which is suppressed by exceptionally small in-plane magnetic fields. The high conductivity and anomalous magnetoresistance are consistent with theoretical models that predict helical edge states within the inversted phase, that are protected from backscattering by an emergent spin symmetry that remains robust even for large Rashba SOC. Our results pave the way for proximity engineering of strong topological insulators as well as correlated quantum phases in the strong spin-orbit regime in graphene heterostructures. arXiv:1901.01332v2 [cond-mat.mes-hall]

2014 Les concepts de la cristallographie sont étendus aux structures quasicristallines et appliqués aux quasicristaux icosaédriques. On montre que les symétries de rotation d'ordre N bidimensionnelles sont compatibles avec les réseaux de Bravais en dimension ~ (N ) (au moins), où ~ (N) est le nombre d'Euler, alors que pour la symétrie de l'icosaèdre tridimensionnelle, la dimension minimale est 6. La cristallographie de l'icosaèdre est traitée en detail. Une classification complète des structures périodiques en six dimensions avec symétrie icosaédrique est dérivée. 11 est surprenant de voir qu'il n'y a que quelques types d'« objets cristallographiques » en 6 dimensions avec la symétrie de l'icosaèdre, en fait trois structures type réseaux de Bravais, deux groupes ponctuels et onze groupes d'espace inequivalents. Le probleme de l'équivalence des groupes d'espace icosaédriques est étudié en détail. Comme dans le cas des cristaux ordinaires à trois dimensions, les symétries de groupes d'espace non « symmorphes » conduisent à l'extinction des pics de Bragg. Ces extinctions sont calculées systématiquement. Abstract. 2014 Crystallographic concepts are extended to quasicrystalline structures and applied to icosahedral quasicrystals. 2-dimensional N fold rotational symmetries are shown to be compatible with Bravais lattices in (at least) ~ (N) dimensions, where ~ (N) is the Euler number, while for 3-dimensional icosahedral symmetry the minimal dimension is 6. The case of icosahedral crystallography is worked out in detail. A complete classification of six-dimensional periodic structures with icosahedral symmetry is derived. There are surprisingly few types of 6-dimensional « crystallographic objects » with icosahedral symmetry, namely 3 Bravais lattice types, 2 point groups, and 11 inequivalent space groups. The problem of equivalence of icosahedral space groups is studied in detail. Similar to the case of ordinary 3-dimensional crystals, nonsymmorphic space group symmetries lead to extinction of Bragg peaks. These extinctions are calculated systematically.

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We argue that surface plasmons in moiré graphene feature an interesting regime in which Landau damping (dissipation via electron-hole pair excitation) is completely quenched. This surprising behavior is made possible by strong coupling in narrow-band systems, characterized by large values of the "fine structure" constant α = e 2 / κvF. Dissipation quenching occurs when dispersing plasmon modes rise above the particle-hole continuum, extending into the forbidden energy gap which is completely free of particle-hole excitations. The effect is predicted to be prominent in magic twist angle moiré graphene, where flat bands feature α 1. The absence of Landau damping enhances optical coherence, leading to speckle-like interference and other striking signatures in moiré graphene plasmonics that are directly accessible in ongoing near-field imaging experiments. arXiv:1905.13088v1 [cond-mat.mes-hall]