Mini Band Gap Generation in Magnetic Beta-Borophene: Effects of Optical Phonon Interaction

Abstract

In this work we report for the first time, to the best of our concern, the tunable electronic properties of Beta-Borophene (BB) on the polar substrate (ZrO_2). We provide an analytical prescription for the calculation of ground state energy in presence electron-phonon (e-ph) interaction, within the framework of the Lee-Low-Pines theory. In the theoretical investigation of the polaron formation in BB, we describe its effective masses, polaronic band-gap, mobility, and Fermi velocities, which are different in each coordinate due to the out-of-plane buckling structure. We also analyze how the average effective mass and Fermi velocities of the charge carriers in the buckling structure are affected by the external magnetic field. It is shown that the polaronic energy becomes more effective in presence of a magnetic field, which we confirm through an analytical prescription. The characteristics of the evolution of average effective mass and average effective Fermi velocity in the presence of a magnetic field are critically discussed. We find that the average effective Fermi velocity is less sensitive, while the other one is greatly influenced by the magnetic field.