In this work, we theoretically propose an optical biosensor (consists of a BK7 glass, a metal film, and a graphene sheet) based on photonic spin Hall effect (SHE). We establish a quantitative relationship between the spin-dependent shift in photonic SHE and the refractive index of sensing medium. It is found that, by considering the surface plasmon resonance effect, the refractive index variations owing to the adsorption of biomolecules in sensing medium can effectively change the spin-dependent displacements. Remarkably, using the weak measurement method, this tiny spin-dependent shifts can be detected with a desirable accuracy so that the corresponding biomolecules concentration can be determined.
Haldane's model is extended to a square lattice related close to the so-called d+id state, in which the on-site energy is staggered and the next-nearest-neighbor hopping is anisotropic. From the phase diagram obtained, two types of phases are found, i.e., the normal insulator with Chern number C=0 and the Hall insulator with C=±1. We propose a way of simulating this model with cold atoms in an optical lattice. By measuring the atomic density profile, one can detect this phase diagram.
We numerically study the quantum Hall effect in biased bilayer graphene based on a tight-binding model in the presence of disorder. Integer quantum Hall plateaus with quantized conductivity σxy = νe 2 /h (where ν is any integer) are observed around the band center due to the split of the valley degeneracy by an opposite voltage bias added to the two layers. The central (n = 0) Dirac Landau level is also split, which leads to a pronounced ν = 0 plateau. This is consistent with the opening of a sizable gap between the valence and conduction bands. The exact spectrum in an open system further reveals that there are no conducting edge states near zero energy, indicating an insulator state with zero conductance. Consequently, the resistivity should diverge at Dirac point. Interestingly, the ν = 0 insulating state can be destroyed by disorder scattering with intermediate strength, where a metallic region is observed near zero energy. In the strong disorder regime, the Hall plateaus with nonzero ν are destroyed due to the float-up of extended levels toward the band center and higher plateaus disappear first.
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