We studied the electronic structure and optic absorption of phosphorene (monolayer of black phosphorus) under strain. Strain was found to be a powerful tool for the band structure engineering. The in-plane strain in armchair or zigzag direction changes the effective masse components along both directions, while the vertical strain only has significant effect on the effective mass in the armchair direction. The band gap is narrowed by compressive in-plane strain and tensile vertical strain. Under certain strain configurations, the gap is closed and the energy band evolutes to the semi-Dirac type: the dispersion is linear in the armchair direction and is gapless quadratic in the zigzag direction. The band-edge optic absorption is completely polarized along the armchair direction, and the polarization rate is reduced when the photon energy increases. Strain not only changes the absorption edge, but also the absorption polarization.
We investigate the thermoelectric effect on a topological insulator surface with particular interest in impurity-induced resonant states. To clarify the role of the resonant states, we calculate the dc and ac conductivities and the thermoelectric coefficients along the longitudinal direction within the full Born approximation. It is found that at low temperatures, the impurity resonant state with strong energy de-pendence can lead to a zero-energy peak in the dc conductivity, whose height is sensitively dependent on the strength of scattering potential, and even can reverse the sign of the thermopower, implying the switching from n- to p-type carriers. Also, we exhibit the thermoelectric signatures for the filling process of a magnetic band gap by the resonant state. We further study the impurity effect on the dynamic optical conductivity, and find that the resonant state also generates an optical conductivity peak at the absorption edge for the interband transition. These results provide new perspectives for understanding the doping effect on topological insulator materials.
We investigate the Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction between two magnetic impurities placed on a phosphorene surface based on the tight-binding model. It is found that the RKKY interaction exhibits strong anisotropy along different lattice directions and is sensitive to the deformed direction. The RKKY interaction is largest for impurities distributed in the armchair direction while the strain effect is strongest for the deformation exerted along the zigzag direction. Applied linear strain can increase the RKKY magnitude nonlinearly, and observably prolong the decay rate from the exponent to the R 1 2 law with the impurity distance. Most interestingly, near the straininduced closing point of the bandgap, we find that the RKKY interaction is no longer simply ferromagnetic or antiferromagnetic, but presents oscillatory behavior, exhibiting the transition from ferromagnetism to antiferromagnetism. This originates from the combination effect of negative energy in the conduction band due to modification of the Fermi surface and the narrowing bandgap, and importantly both of them are reached simultaneously just by tuning the strain. Therefore, the strain effect proves to be an alternative approach to engineering impurity interactions in phosphorene materials.
We study the positive longitudinal magnetoconductivity (LMC) and planar Hall effect in Weyl semimetals, following a recent-developed theory by integrating the Landau quantization with Boltzmann equation. It is found that, in the weak magnetic field regime, the LMC and planar Hall conductivity (PHC) obey cos 6 θ and cos 5 θ sin θ dependence on the angle θ between the magnetic and electric fields. For higher magnetic fields, the LMC and PHC cross over to cos 2 θ and cos θ sin θ dependence, respectively. Interestingly, the PHC could exhibit quantum oscillations with varying θ, due to the periodic-in-1/B oscillations of the chiral chemical potential. When the magnetic and electric fields are noncollinear, the LMC and PHC will deviate from the classical B-quadratic dependence, even in the weak magnetic field regime.
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