Spin-orbit coupling is an essential ingredient in topological materials, conventional and quantum-gas-based alike. Engineered spin-orbit coupling in ultracold-atom systems-unique in their experimental control and measurement opportunities-provides a major opportunity to investigate and understand topological phenomena. Here we experimentally demonstrate and theoretically analyze a technique for controlling spin-orbit coupling in a two-component Bose-Einstein condensate using amplitude-modulated Raman coupling.
The purpose of this paper is to investigate experimentally the shift of the eutectoid point in the Fe–C binary system when applying a high magnetic field. The eutectoid carbon content is observed to shift from 0.77 wt% to 0.83 wt% under a 12 T magnetic field. A practical and complete calculation method is proposed—on the basis of the statistical thermodynamic model—to calculate the Gibbs free energy of the related phases and predict the shift of the eutectoid point due to a magnetic field in both composition and temperature coordinates. The composition values are seen to be in fair agreement with the experimental data. The calculation of both shifts shows that the rise in eutectoid temperature because of the 12 T field is 28.97 °C. The impact of the magnetic field on both eutectoid carbon content and eutectoid temperature is not linear. The rate of the shift of both carbon content and temperature decreases as the magnetic field rises.
Fractional quantization can emerge in non-correlated systems due to the parity anomaly, while its condensed matter realization is a challenging problem. We propose that in axion insulators (AIs), parity anomaly manifests a unique fractional boundary excitation: the half-quantized helical hinge currents. These helical hinge currents microscopically originate from the lateral Goos-Hänchen (GH) shift of massless side-surface Dirac electrons that are totally reflected from the hinges. Meanwhile, due to the presence of the massive top and bottom surfaces of the AI, the helical current induced by the GH shift is half-quantized. The semiclassical wave packet analysis uncovers that the hinge current has a topological origin and its half quantization is robust to parameter variations. Lastly, we propose an experimentally feasible six-terminal device to identify the half-quantized hinge channels by measuring the nonreciprocal conductances. Our results advance the realization of the half quantization and topological magnetoelectric responses in AIs.
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