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Topology plays an increasingly important role in modern condensed matter physics. Insulators can now be classified by their topology similarly to how geometric shapes are classified. The more familiar topology of geometric shapes is determined by integrating a local property (geometric curvature) over the entire surface of the shape, thus yielding a global invariant that does not change even if the shape is modified (so long as one doesn’t poke a new hole through it). Topology for materials is similarly determined by integrating Berry curvature over the surface of a material’s Brillouin zone. The resulting global invariant is the Berry phase of the material (related to the “winding” number), which determines its topological classification. This classification is invariant to changes in the material’s Hamiltonian, so long as it doesn’t collapse to zero anywhere in the Brillouin zone (which is analogous to poking a hole in a geometric shape). If two materials with different topological classifications are fused at a boundary then the Hamiltonian must cross zero there, resulting in a conducting edge state.^{1} This was first predicted by Kane and Mele in a 2D model of graphene that included spin-orbit coupling.^{2} Spin-orbit coupling is not strong enough to experimentally induce such behavior in graphene, but Bernevig, *et al.* recognized that HgTe quantum wells fulfill the conditions required by the Kane-Mele model for topological behavior. This was subsequently confirmed experimentally by Koenig, *et al.*, thus triggering an avalanche of research into topological insulators.

The Crommie group is actively studying 2D topological insulators, also referred to as quantum spin Hall insulators (QSHIs). This name comes from the fact that spin-orbit coupling in a QSHI causes an electron traveling with spin-up to be deflected to one side, similar to how a B-field deflects moving charged particles. Quantization then leads to an edge-state circulating in one direction for the spin-up electrons, similar to how an applied B-field results in chiral edge-states in the quantum Hall effect.^{1-4} Spin-orbit coupling flips sign with spin polarization, and so electrons with spin-down deflect in the opposite direction and create an edge-state with opposite circulation and spin polarization. The helical edge-states of a QSHI thus exhibit spin-velocity locking **(Fig. 1d)**

In 2014 Qian, *et. al* ^{5} predicted that single-layer transition metal dichalcogenide (TMD) materials of the form 1T’-MX_{2} are QSHIs when M = Mo, W, and X = S, Se, Te **(Fig. 1a)**. The origin of the effect is a crossing of bands (band inversion) induced by the 1T’ phase which causes this material to satisfy the Kane-Mele criteria for creating a 2D topological insulator **(Fig. 1b)**. This was predicted to lead to the formation of topologically-protected edge-states that exhibit spin velocity locking **(Figs 1c, d)**. This prediction was exciting because TMDs are stand-alone single-layer materials that can be fabricated via exfoliation, CVD, or molecular beam epitaxy (MBE) techniques, and they are ideal for device applications. Also, the expected energy gaps of TMDs are much larger than for HgTe quantum wells, and even exceed room temperature.