Manipulating electronic dynamics of 8-Pmmn borophene with surface optical phonons

Abstract

Abstract In this work, the effects of surface optical (SO) phonons on the electronic spectrum of 8-Pmmn phase borophene have been investigated. To describe the analytical model we used a Fröhlich-type Hamiltonian on a borophene system within the continuum limit. Then, by following the analytical model with the Lee–Low–Pines variational approximation method, including two successive unitary transformations, the system Hamiltonian has been diagonalized. Our theoretical analysis indicates that SO absorption of the system strongly depends on the substrate-induced effects of the system. Moreover, it is observed that the polaronic energy gap decreases when increasing the internal distance z between the 8-Pmmn borophene and the particular substrate. Also, the energy gap increases with increasing phonon energy ( ℏ ω ). In addition, the resulting bandgap induced by the electron–SO phonon interaction can be tuned by the associated interaction strengths of the substrate. Furthermore, taking lattice vibrations into account, the surface phonon specific heat of the system has been evaluated as a function of temperature. The specific heat becomes constant at high temperatures, as in the Einstein model. We specifically evaluated the contribution from the lattice vibrations on specific internal distances, z. The increase in the internal distance z causes the peak to shift to lower thermal energy.