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Topological insulators, along with Chern insulators and quantum Hall insulator phases, are considered as paradigms for symmetry protected topological phases of matter. This article reports the experimental realization of the timereversal invariant helical edge-modes in bilayer graphene/ monolayer WSe 2 -based heterostructuresa phase generally considered as a precursor to the field of generic topological insulators. Our observation of this elusive phase depended crucially on our ability to create mesoscopic devices comprising both a moirésuperlattice potential and strong spin−orbit coupling; this resulted in materials whose electronic band structure could be tuned from trivial to topological by an external displacement field. We find that the topological phase is characterized by a bulk bandgap and by helical edge-modes with electrical conductance quantized exactly to 2e 2 /h in zero external magnetic field. We put the helical edge-modes on firm ground through supporting experiments, including the verification of predictions of the Landauer−Buẗtiker model for quantum transport in multiterminal mesoscopic devices. Our nonlocal transport properties measurements show that the helical edge-modes are dissipationless and equilibrate at the contact probes. We achieved the tunability of the different topological phases with electric and magnetic fields, which allowed us to achieve topological phase transitions between trivial and multiple, distinct topological phases. We also present results of a theoretical study of a realistic model which, in addition to replicating our experimental results, explains the origin of the topological insulating bulk and helical edge-modes. Our experimental and theoretical results establish a viable route to realizing the time-reversal invariant 2  topological phase of matter.

Proximity-induced spin–orbit coupling in graphene has led to the observation of intriguing phenomena like time-reversal invariant $${{\mathbb{Z}}}_{2}$$ Z 2 topological phase and spin-orbital filtering effects. An understanding of the effect of spin–orbit coupling on the band structure of graphene is essential if these exciting observations are to be transformed into real-world applications. In this research article, we report the experimental determination of the band structure of single-layer graphene (SLG) in the presence of strong proximity-induced spin–orbit coupling. We achieve this in high-mobility hexagonal boron nitride (hBN)-encapsulated SLG/WSe2 heterostructures through measurements of quantum oscillations. We observe clear spin-splitting of the graphene bands along with a substantial increase in the Fermi velocity. Using a theoretical model with realistic parameters to fit our experimental data, we uncover evidence of a band gap opening and band inversion in the SLG. Further, we establish that the deviation of the low-energy band structure from pristine SLG is determined primarily by the valley-Zeeman SOC and Rashba SOC, with the Kane–Mele SOC being inconsequential. Despite robust theoretical predictions and observations of band-splitting, a quantitative measure of the spin-splitting of the valence and the conduction bands and the consequent low-energy dispersion relation in SLG was missing—our combined experimental and theoretical study fills this lacuna.

We report the experimental observation of Ising superconductivity in three-dimensional NbSe 2 stacked with single-layer MoS 2 . The angular dependence of the upper critical magnetic field and the temperature dependence of the upper parallel critical field confirm the appearance of two-dimensional Ising superconductivity in threedimensional NbSe 2 with a single-layer MoS 2 overlay. We show that the superconducting phase has strong Ising spin-orbit correlations which make the holes spin nondegenerate. Our observation of Ising superconductivity in heterostructures of few-layer NbSe 2 of thickness ∼15 nm with single-layer MoS 2 raises the interesting prospect of observing topological chiral superconductors with nontrivial Chern numbers in a momentum-space spin-split fermionic system.

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