Anomalous thermoelectric and thermal Hall effects in irradiated altermagnets

TL;DR

The paper shows that a $d$-wave altermagnet can be driven into a Chern-insulating phase by off-resonant elliptically polarized light, enabling intrinsic anomalous thermoelectric and thermal Hall responses. It develops a framework combining semiclassical transport with Berry curvature and Floquet theory to compute the intrinsic conductivities $\sigma_{xy}^{in}$, $\alpha_{xy}^{in}$, and $\kappa_{xy}^{in}$, and demonstrates universal low-$T$ relations tied to band topology. In a concrete model, irradiation opens gaps at the $\Gamma$ and $M$ points and induces a topological transition at a critical amplitude $A_0^{c}$, giving a total Chern number $|C|=1$. At $T\to0$, $\alpha_{xy}^{in}$ vanishes inside bulk gaps yet shows features near band edges, while $\kappa_{xy}^{in}$ is quantized in the gapped regions, offering experimental handles to probe bandwidth and topology through transport.

Abstract

In this study, we show that a $d$-wave altermagnet can be transformed into a Chern insulator by irradiating it with elliptically polarized light from a high-frequency photon beam. We further explore the intrinsic anomalous thermoelectric and thermal Hall effects in light-irradiated altermagnets. At extremely low temperatures, the thermoelectric Hall coefficient, which exhibits a linear temperature dependence for the thermoelectric Hall conductivity, vanishes within the gapped region between the conduction and valence bands. However, it displays peaks and dips at the boundaries of the gap, suggesting that thermoelectric Hall conductivity can be used to probe the bandwidth. Similarly, the low-temperature thermal Hall coefficient, which also shows a linear temperature dependence for the thermal Hall conductivity, becomes quantized in the gapped region between the conduction and valence bands. This quantization indicates that thermal Hall conductivity can serve as a probe for the topological properties of the system.

Figures (4)

• Figure 1: Schematic illustration of intrinsic thermoelectric and thermal Hall effects in a d-wave altermagnet, with and without light irradiation. Here, $J_{e,y}^{in}$, $J_{te,y}^{in}$, and $J_{t,y}^{in}$ denote the intrinsic electric, thermoelectric, and thermal Hall current densities, respectively. $T$ is the system temperature, and $\textbf{E}$ represents the applied external electric field. (a) Without light irradiation. All intrinsic Hall responses vanish, i.e., $J_{e,y}^{in}\!=\!J_{te,y}^{in}\!=\!J_{t,y}^{in}\!=\!0$, and the Dirac cones around the $\Gamma$ and $M$ points in the Brillouin zone remain gapless. (b) With light irradiation. Finite intrinsic Hall electric, thermoelectric, and thermal currents emerge, $J_{e,y}^{in}\!\neq\!0$, $J_{te,y}^{in}\!\neq\!0$, and $J_{t,y}^{in}\!\neq\!0$, accompanied by the opening of gaps at the Dirac cones around the $\Gamma$ and $M$ points in the Brillouin zone.
• Figure 2: Band structures [Eq. \ref{['eq:Ek']}] of altermagnets in the absence ($A_{0}\!=\!0$) and presence ($A_{0}\!\neq\!0$) of optical irradiation. (a) $A_{0}\!=\!0$, (b) $A_{0}\!=\!1.0$ nm$^{-1}$, (c) $A_{0}\!=\!A_{0}^{c}\simeq1.4$ nm$^{-1}$, and (d) $A_{0}\!=\!1.8$ nm$^{-1}$. The conduction and valence bands are shown in red and blue, respectively, while the green shaded regions denote the bandwidths, which remain much smaller than the driving optical frequency. Other parameters are $t_{0}\!=\!0$ eV$\cdot$nm$^2$, $v\!=\!1$ eV$\cdot$nm, $J_{d}\!=\!1$ eV$\cdot$nm$^2$, $\alpha\!=\!1$, $\hbar\omega\!=\!4$ eV, $\varphi\!=\!\pi/2$, and $a\!=\!1$ nm.
• Figure 3: (a) Chern number $C$ [Eq. \ref{['eq:C_0']}] as a function of the light amplitude $A_{0}$ in the gapped phase at $\mu=0$. (b) Bandwidth $\Delta$ versus the light amplitude $A_{0}$. All other parameters are the same as those used in Fig. \ref{['Fig:E_Gamma_X_M_Y_TB_together']}.
• Figure 4: Top row: [(a1) and (b1)] Band structures [Eq. \ref{['eq:Ek']}] for (a1) $A_{0}\!=\!1$ nm$^{-1}$ and (b1) $A_{0}\!=\!1.8$ nm$^{-1}$. The red and blue curves denote the conduction and valence bands, respectively. The green shaded regions highlight the energy gaps between the conduction and valence bands, while the purple shaded regions indicate the bandwidths near the $\Gamma$ point. Middle row: [(a2) and (b2)] Reduced thermoelectric Hall coefficient $\alpha_{xy}^{\rm in}/(e^{3}L_{0}T/h)$ [Eq. \ref{['eq:alpha_xy_in_LT_C']}] as a function of the chemical potential $\mu$ at $T=20$ K for (a2) $A_{0}\!=\!1$ nm$^{-1}$ and (b2) $A_{0}\!=\!1.8$ nm$^{-1}$. Bottom row: [(a3) and (b3)] Reduced thermal Hall coefficient $\kappa_{xy}^{\rm in}/(e^{2}L_{0}T/h)$ [Eq. \ref{['eq:kappa_xy_in_LT_C']}] versus the chemical potential $\mu$ for (a3) $A_{0}\!=\!1$ nm$^{-1}$ and (b3) $A_{0}\!=\!1.8$ nm$^{-1}$. All other parameters are the same as those used in Fig. \ref{['Fig:E_Gamma_X_M_Y_TB_together']}.