Valley–spin Seebeck effect in heavy group-IV monolayers

Abstract

Akin to electron spin, the valley has become another highly valued degree of freedom in modern electronics, specifically after tremendous studies on monolayers of group-IV materials, i.e. graphene, silicene, germanene and stanene. Except for graphene, the other heavy group-IV monolayers have observable intrinsic spin–orbit interactions due to their buckled structures. Distinct from the usual electric or optical control of valley and spin, we here employ a temperature difference to drive electron motion in ferromagnetic heavy group-IV monolayers via designing a caloritronic device locally modulated by an interlayer electric (Ez) field. A unique valley–spin Seebeck (VSS) effect is discovered, with the current contributed only by one (the other) valley and one (the other) spin moving along one (the opposite) direction. This effect is suggested to be detected below the critical temperature about 18 K for silicene, 200 K for germanene and 400 K for stanene, arising from the characteristic valley–spin nondegenerate band structures tuned by the Ez field, but cannot be driven in graphene without spin–orbit interaction. Above the critical temperature, the VSS effect is broken by overlarge temperature broadening. Besides the temperature, it is also found that the Ez field can drive a transition between the VSS effect and the normal spin Seebeck effect. Further calculations indicate that the VSS effect is robust against many realistic perturbations. Our research represents a conceptually but substantially major step towards the study of the Seebeck effect. These findings provide a platform for encoding information simultaneously by the valley and spin quantum numbers of electrons in future thermal-logic circuits and energy-saving devices.