Polarons and molecules in a mixed-dimensional Fermi gas

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.

Influence of Pressure on Polaron Energy in a Wurtzite GaN/AlxGa1-xN Quantum Well

The influence of hydrostatic pressure on the polaron energy level in wurtzite GaN/AlxGa1-xN quantum well is studied by a Lee-Low-Pines variational method, and the numerical results of the ground state energy, transition energy and contributions of different phonons to polaron energy (polaron effects) are given as functions of pressurepand compositionx. The results show that the ground state energy and transition energy in the wurtzite GaN/AlxGa1-xN quantum well decrease with the increase of the hydrostatic pressurep, and increase with the increase of the compositionx. The contributions of different phonons to polaron energy with pressurepand compositionxare obviously different. With the increase of hydrostatic pressure, the contribution of half-space phonon, confined phonon and the total contribution of phonons of all branches increases obviously, while the contribution of interface phonon slowly increases. During the increase of the composition, the contribution of interface phonon decreases and the contribution of half-space phonon increases slowly, while the contribution of confined phonon and the total contribution of phonons increases significantly. In general, the electron-optical phonon interaction play an important role in electronic states of GaN/AlxGa1-xN quantum wells and can not be neglected.

Free polaron energy levels in AlyGa1−yN/AlxGa1−xN triangle quantum well structures

In this work, a variational method is used to examine the problems relevant to the free polaron energy spectrum in a wurtzite Al[Formula: see text]Ga[Formula: see text]N/Al[Formula: see text]Ga[Formula: see text]N triangle quantum well structure. The numerical calculations for the ground state energy, transition energy and polaron energy shifts as the functions of well-width [Formula: see text] and composition [Formula: see text] are carried out by considering the anisotropies of the parameters, such as the optical phonon frequency, dielectric constant and electron effective mass, as well as their observed changes with coordinate [Formula: see text] in this system. The research results show that the polaron energy shift caused by the electron–optical phonon interaction is large, and leads to an obvious energy decrease in the Al[Formula: see text]Ga[Formula: see text]N/Al[Formula: see text]Ga[Formula: see text]N triangular quantum well structure. The contribution of the confined phonon is found to increase with the increasing of the well-width and composition [Formula: see text], while that of the half space phonon is observed to decrease with the increasing of the well-width and composition [Formula: see text]. The total contribution of the phonon increases with the increasing composition [Formula: see text], while a minimum is found to occur to the total contribution of the phonon during the decreasing process with the well-width. As the [Formula: see text] increases, the free polaron energies and transition energies decrease. Meanwhile, with the increasing of the composition [Formula: see text], the energy and transition energy are found to be increased. In the Al[Formula: see text]Ga[Formula: see text]N/Al[Formula: see text]Ga[Formula: see text]N triangular quantum well structure, the trends of the free polaron energy, transition energy and polaron energy shifts with the well-width and composition [Formula: see text] are found to be similar to those in the GaN/Al[Formula: see text]Ga[Formula: see text]N square quantum well structure. However, the corresponding values in the triangular quantum well structure are obviously greater than those in the square quantum well structure.