Unified Formalism for calculating Polarization, Magnetization, and more in a Periodic Insulator

In this paper, we propose a unified formalism, using Green's functions, to integrate out the electrons in an insulator under uniform electromagnetic fields. We derive a perturbative formula for the Green's function in the presence of uniform magnetic or electric fields. Applying the formula, we derive the formula for the polarization, the orbital magnetization, and the orbital magneto-polarizability, without assuming time reversal symmetry. Specifically, we realize that the terms linear in the electric field can only be expressed in terms of the Green's functions in one extra dimension. This observation directly leads to the result that the coefficient of the $\theta$ term in any dimensions is given by a Wess-Zumino-Witten-type term, integrated in the extended space, interpolating between the original physical Brillouin zone and a trivial system, with the group element replaced by the Green's function. This generalizes an earlier result for the case of time reversal invariance [see Z. Wang, X.-L. Qi, and S.-C. Zhang, Phys. Rev. Lett. {\bf 105}, 256803 (2010)].Comment: 16 pages, 1 figure. The version accepted by PR

Search for serendipitous TNO occultation in X-rays

To study the population properties of small, remote objects beyond Neptune's orbit in the outer solar system, of kilometer size or smaller, serendipitous occultation search is so far the only way. For hectometer-sized Trans-Neptunian Objects (TNOs), optical shadows actually disappear because of diffraction. Observations at shorter wave lengths are needed. Here we report the effort of TNO occultation search in X-rays using RXTE/PCA data of Sco X-1 taken from June 2007 to October 2011. No definite TNO occultation events were found in the 334 ks data. We investigate the detection efficiency dependence on the TNO size to better define the sensible size range of our approach and suggest upper limits to the TNO size distribution in the size range from 30 m to 300 m. A list of X-ray sources suitable for future larger facilities to observe is proposed.Comment: Accepted to publish in MNRA

Numerical Studies of Quantum Oscillations in the Superconducting vortex mixed state

We studied the quantum oscillations in superconducting vortex mixed states with d-wave pairing. We showed that the Onsager relation does not always apply. Furthermore, at mean field level the quantum oscillations from electron pockets are suppressed by the pairing. We conclude that an interpretation of the experimental results asccoming from the four hole pockets created by a $(\pi,\pi)$ folding cannot be ruled out.Comment: 5 pages, 6 figure