Two essential ingredients in macroscopic Maxwell equations are the electric and magnetic dipole. Their spatial variations generate a localized charge and current distribution, respectively. However, it turns out to be a difficult task to calculate these two quantities in periodic crystals. The valid theory for electric polarization is given in PRB 47 1651(1993), and that for orbital magnetization is given in PRB 74 024408(2006). These theories bring deeper understanding to the electric and magnetic dipole, as well as related concepts, such as the charge pumping, thermoelectric current, optical conductivity and so on.
However, the above discussion is based on the first order correction in the Maxwell equations. At second order, the electric and magnetic quadrupoles are required. Here, I will focus on the magnetic quadrupole, which corresponds to a medium that breaks time reversal and inversion symmetry but retains the combined one. I will introduce my theory of spin and orbital magnetic quadrupole in periodic crystals and demonstrate corresponding experimental phenomena. I will show that the spin quadrupole can lead to an intrinsic Edelstein effect, i.e. a net magnetization, through a temperature gradient. This net magnetization can be measured through MOKE experiments. Moreover, the orbital quadrupole can lead to a nonlinear anomalous Nernst current through a temperature gradient, which is the leading order contribution in systems with combined TI symmetry. I will further demonstrate this nonlinear current in a loop-current state in certain cuprates.
Y. Gao, D. Vanderbilt, and D. Xiao, arXiv:1706.03685.
Y. Gao and D. Xiao, arXiv:1803.06726.
Dr. Yang Gao received his B.S. degree in physics from Peking University in 2009, and a Ph.D. at the University of Texas at Austin in 2016. He is currently a postdoc in the Physics Department of Carnegie Mellon University. Dr. Gao’s research is focused on the semiclassical dynamics of Bloch electron dynamics. In particular, he has developed a second order theory that allows the systematic study of nonlinear transport and optical phenomena in crystals. His present interest includes Landau level physics, anomalous thermoelectric transport, spin transport, and magnetoelectric coupling.