^{2}) and vanishing longitudinal resistance under zero magnetic field (where h is the Planck constant, e is the elementary charge, and the Chern number C is an … Quantum Hall effect requires • Two-dimensional electron gas • strong magnetic field • low temperature Note: Room Temp QHE in graphene ... carry Hall current (with non-zero Chern number) Quantization of Hall conductance, Laughlin’s gauge argument (1981) 1 2 () 2 ii e i i e e However, up to now, QAHE was only observed experimentally in topological insulators with Chern numbers C= 1 and 2 at very low temperatures. "This unique property makes QAH insulators a good candidate for use in quantum computers and other small, fast electronic devices." The relation between two different interpretations of the Hall conductance as topological invariants is clarified. (If you have for example a 2-dimensional insulator with time-reversal symmetry it can exhibit a Quantum Spin Hall phase). Abstract: Due to the potential applications in the low-power-consumption spintronic devices, the quantum anomalous Hall effect (QAHE) has attracted tremendous attention in past decades. Chern insulator has successfully explained the 2D quantum Hall effect under a magnetic ﬁeld [40–42] and the quan-tum anomalous Hall effect [43–48]. Quantum anomalous Hall effect can occur due to RSOC and staggered potentials. A team of researchers from Penn State has experimentally demonstrated a quantum phenomenon called the high Chern number quantum anomalous Hall (QAH) effect. Soon after, F.D.M. In 1988, Haldane theoretically proposed that QHE can be realized without applying external magnetic field, i.e. Chern number, and the transverse conductivity is equal to the sum of the Chern numbers of the occupied Landau levels. Such a toy model turned out to be the crucial ingredient for the original proposal These effects are observed in systems called quantum anomalous Hall insulators (also called Chern insulators). Agreement. Under a gap condition on the corresponding planar model, this quantum number is shown to be equal to the quantized Hall conductivity as given by the Kubo–Chern formula. And we hope you, and your loved ones, are staying safe and healthy. [1], The effect was observed experimentally for the first time in 2013 by a team led by Xue Qikun at Tsinghua University. These effects are observed in systems called quantum anomalous Hall insulators (also called Chern insulators). A team of researchers from Penn State has experimentally demonstrated a quantum phenomenon called the high Chern number quantum anomalous Hall (QAH) effect. As a useful tool to characterize topological phases without … ... have been well established. 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