Phonon Dichroisms Revealing Unusual Electronic Quantum Geometry

Abstract

The quantum geometry tensor, intrinsic geometric characteristics of electronic states, plays a crucial role in the various nontrivial electromagnetic phenomena in quantum materials. Here, we reveal that quantum geometry significantly modifies phonon dichroisms through electron-phonon interactions in solids that break time-reversal and spatial inversion symmetries. Specifically, the circular phonon dichroism is primarily dominated by the heat magnetic moments, while the linear phonon dichroism depends on the heat Drude weight, a thermal analog of band Drude weight. Furthermore, we establish the f-sum rule for the heat magnetic moment that facilitates its experimental detections. We demonstrate our key findings in an archetypal model system: ferromagnetic two-dimensional electron gases with Rashba spin-orbit coupling. Our work uncovers the quantum-geometric origin of common phonon dichroisms and predicts the detectable signature of the heat magnetic moment of electrons in solids.

Figures (4)

• Figure 1: Schematic of the magnetic circular dichroism via electron-phonon coupling due to the the heat magnetic moments ($\boldsymbol{m}^{E}$) of the self-rotating electronic wave packet. The light and solid atoms indicate the lattice vibration. The green up (blue down) arrow refers to the absorptions of the right (left) circularly polarized phonons. The sizes of arrows indicate different strength of absorptions.
• Figure 2: (a) The energy band of Rashba 2DEG in the presence (colored solid lines) or absence (dashed line) of out-of-plane Zeeman fields. (b) The corresponding radial distribution of the three quantum geometric quantities: Berry curvature, orbital magnetic moment and HMM of the $E_{-}$ band.
• Figure 3: (a)-(d) Damping coefficients of $\gamma^{R/L}$ phonon modes versus the phonon wave-vector $\boldsymbol{q}$ of Rashba 2DEG. (a) $\boldsymbol{q}-$dependence of $\gamma^{R/L}$ at several typical energies and $k_{Fmin}=\sqrt{\left(\mu-\Delta\right)/t}$. Insert shows the region for evident difference and $\gamma^{R}$ and $\gamma^{L}$. (b) Two-peak signature in ratio of $\left(\gamma^{L}-\gamma^{R}\right)/\left(\gamma^{R}+\gamma^{L}\right)$ at phonon energies of $\text{$\hbar$}\omega=0.5,\:1.0\:\mathrm{meV}$. (c) Decomposition of strength of circular phonon dichroism in terms of the interband and intraband processes. (d) Origin of two-peak structure in the damping coefficients of $\gamma^{R/L}$. We fixed $\boldsymbol{q}$ at a direction $\arctan(q_{y}/q_{x})=\pi/4$ and $q>0$. $\mu=0.1\:\mathrm{eV}$ is relative to the band bottom.
• Figure 4: Temperature- and Fermi energy- dependence of the integration of the circular phonon dichroism of Rashba 2DEG with $q/k_{Fmin}=0.04$.