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Dirac points in two-dimensional electronic structures are a source for topological electronic states due to the $pm pi$ Berry phase that they sustain. Here we show that two rutile multilayers (namely (WO$_2$)$_2$/(ZrO$_2$)$_n$ and (PtO$_2$)$_2$/(ZrO$_2$)$_n$, where an active bilayer is sandwiched by a thick enough (n=6 is sufficient) band insulating substrate, show semi-metallic Dirac dispersions with a total of four Dirac cones along the $Gamma-M$ direction. These become gapped upon the introduction of spin-orbit coupling, giving rise to an insulating ground state comprising four edge states. We discuss the origin of the lack of topological protection in terms of the valley spin-Chern numbers and the multiplicity of Dirac points. We show with a model Hamiltonian that mirror-symmetry breaking would be capable of creating a quantum phase transition to a strong topological insulator, with a single Kramers pair per edge.
We report an unconventional quantum spin Hall phase in the monolayer T$_text{d}$-WTe$_2$, which exhibits hitherto unknown features in other topological materials. The low-symmetry of the structure induces a canted spin texture in the $yz$ plane, whic
Stanene was proposed to be a quantum spin hall insulator containing topological edges states and a time reversal invariant topological superconductor hosting helical Majorana edge mode. Recently, experimental evidences of existence of topological edg
We report on the observation of the acoustic spin Hall effect that facilitates lattice motion induced spin current via spin orbit interaction (SOI). Under excitation of surface acoustic wave (SAW), we find a spin current flows orthogonal to the propa
We propose to engineer time-reversal-invariant topological insulators in two-dimensional (2D) crystals of transition metal dichalcogenides (TMDCs). We note that, at low doping, semiconducting TMDCs under shear strain will develop spin-polarized Landa
We study the mechanisms of the spin Hall effect (SHE) and anomalous Hall effect (AHE) in 3$d$ ferromagnetic metals (Fe, Co, permalloy (Ni$_{81}$Fe$_{19}$; Py), and Ni) by varying their resistivities and temperature. At low temperatures where the phon