Super skew scattering in two-dimensional Dirac material systems with a flat band

Abstract

The phenomenon of super scattering was previously found to arise in massless pseudospin-1 two-dimensional Dirac material systems with a flat band. Here we report the phenomenon of super skew scattering of massive pseudospin-1 quasiparticles, which does not arise in the corresponding massless system. In particular, the scatterer is electrically generated with a certain geometric shape, and the mass is induced by gap opening between the Dirac cones. Even for a circular scatterer, the occurrence of resonant states inside it can induce a sizable anomalous Hall current, which is associated with the gap opening. The striking finding is that a significant reduction in the scatterer size and/or the potential height does nothing to weaken the skew scattering and, for certain resonant states, even tends to strengthen the scattering. This phenomenon of super skew scattering in Dirac materials with a flat band is in stark contrast to the scattering of massive pseudospin-$\frac{1}{2}$ quasiparticles from the same configuration, where skew scattering is significantly weaker and a reduction in the scatterer strength can quickly diminish it. The phenomenon is established analytically for the case of a circular scatterer in the framework of continuum Hamiltonian, and is found to be robust for an elliptical scatterer, which is solved numerically by adopting the multiple-multipole method to massive pseudospin-1 scattering. Calculations of the electronic transport properties in the Lieb lattice system reveal the occurrence of a large anomalous Hall current as well, paving the way for experimental observation and test of super skew scattering. Because of the ``skew'' nature that is absent in massless pseudospin-1 systems, the phenomenon of super skew scattering in massive systems can be exploited for applications in novel electronic or photonic Hall devices.