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Quantum spin Hall edge states in twisted-bilayer 1T-WTe$_2$

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 Added by Felix L\\\"upke Dr.
 Publication date 2020
  fields Physics
and research's language is English




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The quantum spin Hall (QSH) effect, characterized by topologically protected spin-polarized edge states, was recently demonstrated in monolayers of the transition metal dichalcogenide (TMD) 1T-WTe$_2$. However, the robustness of this topological protection remains largely unexplored in van der Waals heterostructures containing one or more layers of a QSH insulator. In this work, we use scanning tunneling microscopy and spectroscopy (STM/STS), to study twisted bilayer (tBL) WTe$_2$ with three different orientations and compare it to a topologically trivial as-grown bilayer. We observe the characteristic spectroscopic signature of the QSH edge state in the twisted bilayers, including along a coinciding edge where two sets of QSH edge states sit on top of the other. By comparing our experimental observations to first principles calculations, we conclude that the twisted bilayers are weakly coupled, preserving the QSH states and preventing back scattering.



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The two-dimensional topological insulators (2DTI) host a full gap in the bulk band, induced by spin-orbit coupling (SOC) effect, together with the topologically protected gapless edge states. However, the SOC-induced gap is usually small, and it is challenging to suppress the bulk conductance and thus to realize the quantum spin Hall (QSH) effect. In this study, we find a novel mechanism to effectively suppress the bulk conductance. By using the quasiparticle interference (QPI) technique with scanning tunneling spectroscopy (STS), we demonstrate that the QSH candidate single-layer 1T-WTe$_2$ has a semi-metal bulk band structure with no full SOC-induced gap. Surprisingly, in this two-dimensional system, we find the electron interactions open a Coulomb gap which is always pinned at the Fermi energy (E$_F$). The opening of the Coulomb gap can efficiently diminish the bulk state at the E$_F$ and is in favor of the observation of the quantized conduction of topological edge states.
A monolayer of WTe$_2$ has been shown to display quantum spin Hall (QSH) edge modes persisting up to 100~K in transport experiments. Based on density-functional theory calculations and symmetry-based model building including the role of correlations and substrate support, we develop an effective electronic model for WTe$_2$ which fundamentally differs from other prototypical QSH settings: we find that the extraordinary robustness of quantum spin Hall edge modes in WTe$_2$ roots in a glide symmetry due to which the topological gap opens away from high-symmetry points in momentum space. While the indirect bulk gap is much smaller, the glide symmetry implies a large direct gap of up to 1~eV in the Brillouin zone region of the dispersing edge modes, and hence enables sharply boundary-localized QSH edge states depending on the specific boundary orientation.
The quantum spin Hall (QSH) state was recently demonstrated in monolayers of the transition metal dichalcogenide 1T-WTe$_2$ and is characterized by a band gap in the two-dimensional (2D) interior and helical one-dimensional (1D) edge states. Inducing superconductivity in the helical edge states would result in a 1D topological superconductor, a highly sought-after state of matter. In the present study, we use a novel dry-transfer flip technique to place atomically-thin layers of WTe$_2$ on a van der Waals superconductor, NbSe$_2$. Using scanning tunneling microscopy and spectroscopy (STM/STS), we demonstrate atomically clean surfaces and interfaces and the presence of a proximity-induced superconducting gap in the WTe$_2$ for thicknesses from a monolayer up to 7 crystalline layers. At the edge of the WTe$_2$ monolayer, we show that the superconducting gap coexists with the characteristic spectroscopic signature of the QSH edge state. Taken together, these observations provide conclusive evidence for proximity-induced superconductivity in the QSH edge state in WTe$_2$, a crucial step towards realizing 1D topological superconductivity and Majorana bound states in this van der Waals material platform.
We study the low energy edge states of bilayer graphene in a strong perpendicular magnetic field. Several possible simple boundaries geometries related to zigzag edges are considered. Tight-binding calculations reveal three types of edge state behaviors: weakly, strongly, and non-dispersive edge states. These three behaviors may all be understood within a continuum model, and related by non-linear transformations to the spectra of quantum Hall edge--states in a conventional two-dimensional electron system. In all cases, the edge states closest to zero energy include a hole-like edge state of one valley and a particle-like state of the other on the same edge, which may or may not cross depending on the boundary condition. Edge states with the same spin generically have anticrossings that complicate the spectra, but which may be understood within degenerate perturbation theory. The results demonstrate that the number of edge states crossing the Fermi level in clean, undoped bilayer graphene depends BOTH on boundary conditions and the energies of the bulk states.
Recently, it has been pointed out that the twisting of bilayer WSe$_2$ would generate topologically non-trivial flat bands near the Fermi energy. In this work, we show that twisted bilayer WSe$_2$ (tWSe$_2$) with uniaxial strain exhibits a large nonlinear Hall (NLH) response due to the non-trivial Berry curvatures of the flat bands. Moreover, the NLH effect is greatly enhanced near the topological phase transition point which can be tuned by a vertical displacement field. Importantly, the nonlinear Hall signal changes sign across the topological phase transition point and provides a way to identify the topological phase transition and probe the topological properties of the flat bands. The strong enhancement and high tunability of the NLH effect near the topological phase transition point renders tWSe$_2$ and related moire materials new platforms for rectification and second harmonic generations.
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