Peltier effect of phonons driven by electromagnetic waves

Steady current in metals induces a thermal gradient, a phenomenon known as the Peltier effect. The Peltier effect is one of the fundamental phenomena in the thermoelectric properties of materials and is also used in applications such as refrigerators. In this work, we show that an analogous phenomenon occurs by phonons in a noncentrosymmetric insulator, e.g., ferroelectrics, subject to linearly polarized light. Under light illumination, an energy current of phonons occurs through a nonlinear optical effect similar to the bulk photovoltaic effect. We formulate the nonlinear Peltier coefficient of the energy current carried by phonon photocurrent using nonlinear response theory. From the general formula, we show that the phonon photocurrent occurs only in a noncentrosymmetric system with two or more optical phonon bands. We demonstrate the generation of the energy current using a one-dimensional ion chain with three ions in a unit cell, which predicts the generation of an experimentally observable energy current using available THz-infrared light sources.