Proposed Model of the Giant Thermal Hall Effect in Two-Dimensional Superconductors: An Extension to the Superconducting Fluctuation Regime

We extend the thermodynamic approach for the description of the thermal Hall effect in two-dimensional superconductors above the critical temperature, where fluctuation Cooper pairs contribute to the conductivity, as well as in disordered normal metals where the particle-particle channel is important. We express the Hall heat conductivity in terms of the product of temperature derivatives of the chemical potential and of the magnetization of the system. Based on this general expression, we derive the analytical formalism that qualitatively reproduces the superlinear increase of the thermal Hall conductivity with the decrease of temperature observed in a large variety of experimentally studied systems [Grissonnanche et al., Nature (London) 571, 376 (2019)]. We also predict a nonmonotonic behavior of the thermal Hall conductivity in the regime of quantum fluctuations, in the vicinity of the second critical field and at very low temperatures.

Figure 1

The schematic showing the geometry of a thermal Hall effect measurement. The Hall bar is studied in the broken circuit geometry. The thermal flow in the $y$ direction is measured as a function of the temperature gradient applied in the $x$ direction and the magnetic field parallel to the $z$ axis.

Figure 2

Fluctuation induced thermal Hall conductivity ${\tilde{\kappa }}_{yx(2)}^{(\mathrm{fl})}$ (shown by the color scale and numbers in arbitrary units) as a function of dimensionless temperature and magnetic field. The blue area shows the normal phase above the superconducting transition, the yellow area corresponds to the superconducting state. Our consideration is valid in the blue area in the domain close to the critical temperature $T_{c0}$ [see Eq. (11)] and in the vicinity of the second critical field $H_{c2}(0)$ [see Eq. (17)].