Orbital Accumulation Induced by Chiral Phonons

Abstract

We theoretically investigate orbital accumulation driven by chiral phonons via orbital-dependent electron-lattice coupling. We derive a formula for the orbital accumulation induced by classical lattice dynamics or nonequilibrium phonons, using the Berry curvature, linear response theory, and the nonequilibrium Green's function method. We show that chiral phonons primarily couple to orbital quadrupole moments and that static orbital dipole accumulation can be generated in the second-order of lattice displacement. Our study provides a useful method for generating orbital accumulation without using spin-orbit interactions and suggests a strategy to boost its magnitude by harnessing band structure hot spots associated with orbital degeneracy.

Figures (4)

• Figure 1: (a) A square lattice with $p$ orbitals is embedded in the $xy$-plane, and a chiral phonon mode is injected along $+x$-axis. (b) The schematic of the hopping integrals, $t_\sigma$ and $t_\pi$, is depicted. (c) The displacement along $z$-axis, $u^z$, activates the hopping between $p_x$ and $p_z$ orbitals.
• Figure 2: (a) The coherent chiral displacement mode can be generated by, for instance, a surface acoustic wave (SAW) device. (b) When a chiral material with temperature gradient is attached, the thermal chiral phonon modes penetrate into the square lattice.
• Figure 3: The temperature dependence of $\langle L^x_{\bm 0}\rangle$ is shown. The unit of the vertical axis is the Bohr magnetron per site. (a) $\epsilon_F$ is changed as $-2.5,\,-2.0,\,-1.5\,{\rm eV}$, respectively, for $t_{\sigma} = -1.9 \,{\rm eV}$, and $t_{\pi} = -2.0 \,{\rm eV}$. (b) $t_{\pi}$ is changed as $-1.9,\, -2.0,\,-2.1\,{\rm eV}$, respectively, with $t_{\sigma} = -1.9\,{\rm eV}$. The Fermi energy for $t_\pi = -2.0\,{\rm eV}$ is set to be $\epsilon_F=-1.5\,{\rm eV}$, and for other $t_\pi$, the Fermi energy is adjusted to have the same number of electrons.
• Figure 4: The orbital accumulation, $\langle L^x_0\rangle$, per site is described as a function of $\delta\epsilon^z$. The other parameters are taken to be $t_\sigma=-1.9\,{\rm eV}$, $t_\pi = -2.0\,{\rm eV}$, $\epsilon_F=-1.5\,{\rm eV}$, and $T=200\,{\rm K}$. The inset shows the schematic of the constant-energy surfaces for each value of $\delta\epsilon_z$. Black lines (red line) indicate the energy surface of $p_x$ and $p_y$ orbitals ($p_z$ orbital). When $\delta\epsilon_z\sim 0.2\,{\rm eV}$, the $p_z$ band is tangent to the other $p_x$, $p_y$ bands.