Designing high-finesse resonant cavities for electronic waves faces challenges due to short electron coherence lengths in solids. Previous approaches, e.g. the seminal nanometer-

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]

No abstract

Magic-angle twisted trilayer graphene (MATTG) has emerged as a moiré material that exhibits strong electronic correlations and unconventional superconductivity 1,2 . However, local spectroscopic studies of this system are still lacking. Here we perform high-resolution scanning tunnelling microscopy and spectroscopy of MATTG that reveal extensive regions of atomic reconstruction favouring mirror-symmetric stacking. In these regions, we observe symmetry-breaking electronic transitions and doping-dependent band-structure deformations similar to those in magic-angle bilayers, as expected theoretically given the commonality of flat bands 3,4 . Most notably in a density window spanning two to three holes per moiré unit cell, the spectroscopic signatures of superconductivity are manifest as pronounced dips in the tunnelling conductance at the Fermi level accompanied by coherence peaks that become gradually suppressed at elevated temperatures and magnetic fields. The observed evolution of the conductance with doping is consistent with a gate-tunable transition from a gapped superconductor to a nodal superconductor, which is theoretically compatible with a sharp transition from a Bardeen-Cooper-Schrieffer superconductor to a Bose-Einstein-condensation superconductor with a nodal order parameter. Within this doping window, we also detect peak-dip-hump structures that suggest that superconductivity is driven by strong coupling to bosonic modes of MATTG. Our results will enable further understanding of superconductivity and correlated states in graphene-based moiré structures beyond twisted bilayers 5 .