  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 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.
