Peltier effect of phonons driven by electromagnetic waves

In semiconductors, a steady electric current causes a temperature gradient in a material, which is known as the Peltier effect. The Peltier effect is an example of the thermoelectric effect, which is a consequence of the energy current carried by charged carriers. As the thermoelectric effect is caused by the energy flow of electrons or holes, an analogous phenomenon can occur by a flow of other quasi-particles, such as magnons and phonons. In fact, a spin current analog of the Seebeck effect, another thermoelectric effect, is observed in magnetic insulators, in which case magnons and spinons carry the spin angular momentum. On the other hand, as accelerating magnons and phonons by the electromagnetic field is difficult, an analog of the Peltier effect, that is, externally controlling the temperature gradient by inducing the flux of quasiparticles, remains a challenge.

In this work, we show that a Peltier effect analog of phonons occurs in a material 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 photogalvanic energy current carried by phonons using nonlinear response theory. From the general formula, we show that the photogalvanic energy current occurs only in a non-centrosymmetric system with two or more optical phonon bands. We demonstrate the generation of the photogalvanic 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.