Polarons and molecules in a mixed-dimensional Fermi gas

Abstract

We address the problem of a single impurity atom moving in a two-dimensional (2D) layer immersed in a 3D Fermi gas. Using a variational approach, we show that in this mixed-dimensional (MD) system, there is a transition between polaron and molecule ground states, similar to the case of pure 3D. Moreover, we find that the attractive polaron energy in MD is higher than that in 3D, while molecular energy in MD is lower than that in 3D, which leads to a shift of the critical interaction strength of transition. Further analysis shows that the energy difference between 3D and MD systems is attributed to the increment of the effective mass of the impurity, which is induced by the spatial constraint on the impurity.