Dichroism from Chiral Thermoelectric Probes: Generalized Sum Rules for Orbital and Heat Magnetizations

TL;DR

This work develops a unified framework that links ground-state orbital and heat magnetizations to experimentally accessible excitation spectra via thermoelectric dichroism. By leveraging zero-temperature Kubo relations and Kramers–Kronig consistency, it derives spectral representations for $M$ and $M^Q$ and shows how frequency-integrated, chiral excitation rates probe the full magnetization content, with purely electrical drives accessing the Chern number and mixed/thermal drives revealing the magnetization densities. A hierarchical partitioning of magnetization contributions is introduced, including real-space markers for open boundaries and a generalized scheme to access higher-order heat magnetizations. The results enable practical experimental routes (e.g., cold-atom lattices, circuit QED) to disentangle ground-state topological and geometric properties from dynamical spectroscopic data, broadening the toolbox for characterizing quantum materials and engineered quantum systems.

Abstract

We introduce a unified framework that relates orbital and heat magnetizations to experimentally accessible excitation spectra, through thermoelectric probes and generalized sum rules. By analyzing zero-temperature transport coefficients and applying Kramers-Kronig relations, we derive spectral representations of magnetization densities from thermoelectric correlation functions. Excitation rates under chiral thermoelectric drives then naturally emerge as direct probes of these Kubo-type correlators, placing orbital and heat magnetizations on equal footing with the topological Chern number. As a direct consequence of our formalism, we introduce a hierarchical construction that organizes orbital and heat magnetizations into distinct physical contributions accessible through sum rules, and also derive real-space markers of these magnetizations. From an experimental standpoint, we propose concrete implementations of thermoelectric dichroic measurements in quantum-engineered platforms based on modulated strain fields. These results establish thermoelectric dichroic measurements as a versatile route to access and disentangle fundamental ground-state properties.

Figures (2)

• Figure 1: Panels $(a)$, $(b)$, and $(c)$ show the Hall conductivity, orbital magnetization, and heat magnetization of the Haldane model as a function of the chemical potential $\mu$, for $\Delta_{AB}=0$, $t_2/t_1=0.5$, and $\varphi=0.7\pi$. The gray shaded region indicates the bulk gap. Panels $(d)$, $(e)$, and $(f)$ display the frequency-resolved excitation rates $\Gamma_{\alpha\beta}^{\pm,xy}(\omega)$ in Eq. \ref{['Gamma_pm_PBC']} and the corresponding differential rates $\Delta\Gamma_{\alpha\beta}^{xy}(\omega)$ (see Eq. \ref{['Delta_Gamma_PBC']}) for the three chiral drives $ee$, $eQ$, and $QQ$. For the mixed electric-heat drive ($eQ$) we have chosen $V_{0e}/V_{0Q} = t_1/e$. The delta functions in the rate expressions have been approximated by Lorentzians with a broadening of $\eta/t_1=0.02$ to improve visibility. The chemical potential is $\mu/t_1=-1$ (filled circle in panels $(a)$-$(c)$). The integrated differential rate is indicated in the boxed inset.
• Figure 2: Panels $(a)$, $(b)$ and $(c)$ show the frequency-resolved excitation rates $\Gamma_{\alpha\beta}^{\pm,xy}(\omega)$ [Eq. \ref{['Gamma_pm_OBC']}] and the corresponding differential rates $\Delta\Gamma_{\alpha\beta}^{xy}(\omega)$ [Eq. \ref{['DR_OBC']}] for the three chiral drives ($ee$, $eQ$, and $QQ$) in a Haldane-model flake with open boundaries. The system contains $15 \times 60$ sites, and all model parameters match those used in Fig. \ref{['rates_PBC']}$(a)$-$(c)$. The insets in panels $(a)$-$(b)$ zoom in on the bulk response. Thick solid lines indicate the corresponding thermodynamic-limit rates obtained with periodic boundary conditions. For the mixed electric-heat drive ($eQ$), we set $V_{0e}/V_{0Q} = t_1/e$. Delta functions in the rate expressions are approximated by Lorentzians with broadening $\eta/t_1=0.03$ to improve visibility.