We calculate frequency and temperature dependence of the anomalous ac Hall conductivity induced by impurity scattering in a chiral px +ipy superconductor, such as Sr2RuO4, with spontaneous time-reversal-symmetry breaking in the absence of an external magnetic field. We consider two models of disorder, Gaussian and non-Gaussian, characterized by the second and third moments of the random impurity potential, respectively. Within both models, we find that the anomalous Hall conductivity has a finite real value at zero frequency, exhibits singularities at the threshold of photon absorption across the superconducting gap, and decays as some power of the high frequency ω. The Hall conductivity increases linearly with the decrease of temperature below the superconducting transition and saturates at zero temperature. Using our results for the high-frequency Hall conductivity, we estimate the polar Kerr angle for light reflection from the material and compare it with the experimental measurements in Sr2RuO4 by Xia et al., Phys. Rev. Lett. 97, 167002 (2006).

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We demonstrate cooling of the center of mass motion of charged graphene nanoplatelets levitated in a quadrupole ion trap in high vacuum down to temperatures of 20 K. Parametric feedback based on optical measurements of particle motion was used to achieve the particle cooling at pressure p < 10 −6 Torr, and cooling along all three axes of motion was observed. Dependence of cooling on the electric fields was measured by varying DC voltages on a set of auxiliary electrodes used to spatially shift the trap minimum. Methods to calibrate mass and charge of the nanoplatelet by measuring its motion frequency dependence on discharge were also explored.