A giant thermal Hall effect in the vicinity of the superconducting phase transition.

We extend the thermodynamic approach for the description of the thermal Hall effect in the vicinity of a superconducting phase transition, in the fluctuation dominated regime. We show that the Hall heat conductivity is proportional to the product of temperature derivatives of the chemical potential and of the magnetization of the system. We argue that the latter derivative shows the strong singularity in the vicinity of the phase transition, while the former does not contain the characteristic for fermionic systems smallness (T /EF ), what additionally increases the effect. We derive the analytical formula predicting the temperature dependence of the thermal Hall conductivity in the vicinity of the critical temperature for different magnetic fields. Moreover, we study the phenomenon in the regime of quantum fluctuations, in the vicinity of the second critical field and at very low temperatures. We demonstrate how it fades away in a full agreement with the third law of thermodynamics. The developed approach qualitatively explains the recently observed giant thermal Hall effect in cuprates [1].