In an ultrathin topological insulator (TI) film, a hybridization gap opens in the TI surface states, and the system is expected to become either a trivial insulator or a quantum spin Hall insulator when the chemical potential is within the hybridization gap. Here we show, however, that these insulating states are destroyed by the presence of a large and long-range-correlated disorder potential, which converts the expected insulator into a metal. We perform transport measurements in ultrathin, dual-gated topological insulator films as a function of temperature, gate voltage, and magnetic field, and we observe a metallic-like, non-quantized conductivity, which exhibits a weak antilocalizationlike cusp at low magnetic field and gives way to a nonsaturating linear magnetoresistance at large field. We explain these results by considering the disordered network of electron-and hole-type puddles induced by charged impurities. We argue theoretically that such disorder can produce an insulator-to-metal transition as a function of increasing disorder strength, and we derive a condition on the band gap and the impurity concentration necessary to observe the insulating state. We also explain the linear magnetoresistance in terms of strong spatial fluctuations of the local conductivity, using both numerical simulations and a theoretical scaling argument.
The present study showed that a quantitative analogy of fully developed laminar flow in orthogonally rotating rectangular ducts and stationary curved rectangular ducts of arbitrary aspect ratio could be established. In order to clarify the similarity of the two flows, the dimensionless parameters K LR ¼ Re/(Ro) 1=2 and the Rossby number, Ro ¼ w m /Wd h , in a rotating straight duct were used as a set corresponding to the Dean number, K LC ¼ Re/k 1=2 , and curvature ratio, k ¼ R/d h , in a stationary curved duct. Under the condition that the value of the Rossby number and the curvature ratio was large enough, the flow field satisfied the 'asymptotic invariance property'; there were strong quantitative similarities between the two flows such as in the friction factors, flow patterns, and maximum axial velocity magnitudes for the same values of K LR and K LC . Based on these similarities, it is possible to predict the flow characteristics in rotating ducts by considering the flow in stationary curved ducts, and vice versa.
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