Observation of Time-Reversal Invariant Helical Edge-Modes in Bilayer Graphene/WSe${}_2$ Heterostructure

Abstract

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 time-reversal 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 moiré superlattice 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 grounds through supporting experiments, including the verification of predictions of the Landauer-B$\ddot{\mathrm{u}}$ttiker model for quantum transport in multi-terminal mesoscopic devices. Our non-local 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 ${\mathbb{Z}}_2$ topological phase of matter.

21 pages, 4 figures

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• Experimental observation of spin-split energy dispersion in high-mobility single-layer graphene/WSe2 heterostructures
• Observation of time-reversal symmetric Hall effect in graphene-WSe2 heterostructures at room temperature
• Supercurrent mediated by helical edge modes in bilayer graphene
• Emergent inhomogeneity and non-locality in a graphene field-effect transistor on a near-parallel moire superlattice of transition metal dichalcogenides
• Rashba spin splitting based on trilayer graphene systems
• Quantum Hall and Light Responses in a 2D Topological Semimetal
• Electric field tunable bands in doubly aligned bilayer graphene hBN moire superlattice
• Valley-Polarized Quantum Anomalous Hall Phase in Bilayer Graphene with Layer-Dependent Proximity Effects
• Proximity spin-orbit coupling in graphene on alloyed transition metal dichalcogenides