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We consider magnetotransport on a helical edge of a quantum spin Hall insulator, in the presence of bulk midgap states side coupled to the edge. In the presence of a magnetic field, the midgap levels are spin split, and hybridization of these levels with the itinerant edge states leads to backscattering, and the ensuing increase in the resistance. We show that there is a singular cusplike contribution to the positive magnetoresistance stemming from resonant midgap states weakly coupled to the edge. The singular behavior persists for both coherent and incoherent edge transport regimes. We use the developed theory to fit the experimental data for the magnetoresistance for monolayer WTe2 at liquid helium temperatures. The results of the fitting suggest that the cusplike behavior of the resistance in weak magnetic fields observed in experiments on monolayer WTe2 with long edge channels might indeed be explained by hybridization of the helical edge states with spin-split bulk midgap states. In particular, the dependence of the magnetoresistance on the direction of the external magnetic field is well described by the incoherent edge transport theory, at the same time being quite distinct from the one expected for a magnetic-field-induced edge gap. 

Uniaxial strain has been widely used as a powerful tool for investigating and controlling the properties of quantum materials. However, existing strain techniques have so far mostly been limited to use with bulk crystals. Although recent progress has been made in extending the application of strain to two-dimensional van der Waals (vdW) heterostructures, these techniques have been limited to optical characterization and extremely simple electrical device geometries. Here, we report a piezoelectric-based in situ uniaxial strain technique enabling simultaneous electrical transport and optical spectroscopy characterization of dual-gated vdW heterostructure devices. Critically, our technique remains compatible with vdW heterostructure devices of arbitrary complexity fabricated on conventional silicon/silicon dioxide wafer substrates. We demonstrate a large and continuously tunable strain of up to −0.15% at millikelvin temperatures, with larger strain values also likely achievable. We quantify the strain transmission from the silicon wafer to the vdW heterostructure, and further demonstrate the ability of strain to modify the electronic properties of twisted bilayer graphene. Our technique provides a highly versatile new method for exploring the effect of uniaxial strain on both the electrical and optical properties of vdW heterostructures and can be easily extended to include additional characterization techniques. 

Abstract 2D topological insulators promise novel approaches towards electronic, spintronic, and quantum device applications. This is owing to unique features of their electronic band structure, in which bulk-boundary correspondences enforces the existence of 1D spin–momentum locked metallic edge states—both helical and chiral—surrounding an electrically insulating bulk. Forty years since the first discoveries of topological phases in condensed matter, the abstract concept of band topology has sprung into realization with several materials now available in which sizable bulk energy gaps—up to a few hundred meV—promise to enable topology for applications even at room-temperature. Further, the possibility of combining 2D TIs in heterostructures with functional materials such as multiferroics, ferromagnets, and superconductors, vastly extends the range of applicability beyond their intrinsic properties. While 2D TIs remain a unique testbed for questions of fundamental condensed matter physics, proposals seek to control the topologically protected bulk or boundary states electrically, or even induce topological phase transitions to engender switching functionality. Induction of superconducting pairing in 2D TIs strives to realize non-Abelian quasiparticles, promising avenues towards fault-tolerant topological quantum computing. This roadmap aims to present a status update of the field, reviewing recent advances and remaining challenges in theoretical understanding, materials synthesis, physical characterization and, ultimately, device perspectives. 

Abstract A Chern insulator is a two-dimensional material that hosts chiral edge states produced by the combination of topology with time reversal symmetry breaking. Such edge states are perfect one-dimensional conductors, which may exist not only on sample edges, but on any boundary between two materials with distinct topological invariants (or Chern numbers). Engineering of such interfaces is highly desirable due to emerging opportunities of using topological edge states for energy-efficient information transmission. Here, we report a chiral edge-current divider based on Chern insulator junctions formed within the layered topological magnet MnBi 2 Te 4 . We find that in a device containing a boundary between regions of different thickness, topological domains with different Chern numbers can coexist. At the domain boundary, a Chern insulator junction forms, where we identify a chiral edge mode along the junction interface. We use this to construct topological circuits in which the chiral edge current can be split, rerouted, or switched off by controlling the Chern numbers of the individual domains. Our results demonstrate MnBi 2 Te 4 as an emerging platform for topological circuits design.