Unconventional Thermal Magnon Hall Effect in a Ferromagnetic Topological Insulator

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Unconventional Thermal Magnon Hall Effect in a Ferromagnetic Topological Insulator


Christian Moulsdale, Pierre A. Pantaleón, Ramon Carrillo-Bastos, Yang Xian


We present theoretically the thermal Hall effect of magnons in a ferromagnetic lattice with a Kekul\'e-O coupling (KOC) modulation and a Dzyaloshinskii-Moriya interaction (DMI). Through a strain-based mechanism for inducing the KOC modulation, we identify four topological phases in terms of the KOC parameter and DMI strength. We calculate the thermal magnon Hall conductivity ${\kappa^{xy}}$ at low temperature in each of these phases. We predict an unconventional conductivity due to a non-zero Berry curvature emerging from band proximity effects in the topologically trivial phase. We find sign changes of ${\kappa^{xy}}$ as a function of the model parameters, associated with the local Berry curvature and occupation probability of the bulk bands. Throughout, ${\kappa^{xy}}$ can be easily tuned with external parameters such as the magnetic field and temperature.

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Question from one of the expert in our Board. How do you define the thermal Hall effect in this system?
The usual linear response approach to, say,  electrical transport calculates current-current corellator and the corresponding Drude diagram, where the vertices are $e {\bf v}$. But with thermal transport - transport of energy its much trickier, because it's not clear how to define energy current especially in interacting systems. Do you face a similar challenge in this system? It's not entirely obvious where Eqs. (15) & (16) come from.
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Thanks for the question. The heat currents are due to a temperature gradient. Because it is a statistical force, a nice trick is to introduce a fictitious gravitational field. On the other hand, you are right that Eqs. 15 and 16 are not obvious. A beautiful explanation that deserves to be read can be found in arXiv:1103.1221v3

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