We derive a generalized set of Ward identities that captures the effects of topological charge on Hall transport. The Ward identities follow from the (2+1)-dimensional momentum algebra, which includes a central extension proportional to the topological charge density. In the presence of topological objects like Skyrmions, we observe that the central term leads to a direct relation between the thermal Hall conductivity and the topological charge density. We extend this relation to incorporate the effects of a magnetic field and an electric current. The topological charge density produces a distinct signature in the electric Hall conductivity, which is identified in existing experimental data and yields further novel predictions. For insulating materials with translation invariance, the Hall viscosity can be directly determined from the Skyrmion density and the thermal Hall conductivity to be measured as a function of momentum.
|Journal||Physical Review Letters|
|State||Published - Sep 9 2016|
Bibliographical noteFunding Information:
We thank Sumit Das, Lance De Long, Michael Eides, Ori Ganor, Petr Hoava, Carlos Hoyos, Seungjoon Hyun, Seok Kim, Elias Kiritsis, Kimyeong Lee, Keh-Fei Liu, Hitoshi Murayama, Yaron Oz, Sumiran Pujari, Shinsei Ryu, Sang-Jin Sin, David Tong, Oskar Vafek, and Piljin Yi for helpful discussions. We are especially thankful to Jung Hoon Han for numerous illuminating discussions on Skyrmions and invaluable comments on the draft. Finally, we would like to thank our referees for numerous helpful comments. B. S. K. is grateful to the members of the Berkeley Center for Theoretical Physics, Berkeley, and KIAS, Seoul, for their warm hospitality during his visits. This work is partially supported by NSF Grant No. PHY-1214341.
© 2016 American Physical Society.
ASJC Scopus subject areas
- Physics and Astronomy (all)