Self-trapping Transition Of Acoustic Polarons In Free-standing Slab

The rise of low-dimensional materials in the1980s is a new type ofconstructional materials. From its inception, it has been highlyconcerned by governments and scientists. Low-dimensional materialscompared to conventional materials with a high degree of fine, lightweight, good physical properties and other characteristics, which canmeet the high-tech field of electronic technology, aerospace,biotechnology, and other requirements for the material. Specialstructure of low-dimensional materials determines their specialperformance, then we research self-trapping transition of acousticpolarons in free-standing slab will have a very important significance.In this paper, our research is related to the self-trapping transitionof acoustic polarons in free-standing slab. The ground state energiesand the derivates of the acoustic polaron in free-standing slab areperformed by using the Huybrechts-like variational approach. In thispaper, we do twice unitary transformations for electron-acousticphonon coupling system. Then, by calculating the ground stateenergies of the acoustic polaron, we discuss phonon polaronself-trapping problem in free-standing slab. The research results show that free-standing slab acousticspolaron self-trapping criterion is larger than one-dimensionalacoustics polaron self-trapping standard, while is smaller thanthree-dimensional acoustics polaron self-trapping standard. So thedegree of difficulty of self-trapping transition of the acoustic polaronsin free-standing slab is between those in one-dimensional andthree-dimensional systems. This research in free-standing slab has acertain reference in the future.