Interplay between in-plane and flexural phonons in electronic transport of two-dimensional semiconductors

Out-of-plane vibrations are considered as the dominant factor limiting the intrinsic carrier mobility of suspended two-dimensional materials at low carrier concentrations. Anharmonic coupling between in-plane and flexural phonon modes is usually excluded from the consideration. Here we present a theory for the electron-phonon scattering, in which the anharmonic coupling between acoustic phonons is systematically taken into account. Our theory is applied to the typical group V two-dimensional semiconductors: hexagonal phosphorus, arsenic, and antimony. We find that the role of the flexural modes is essentially suppressed by their coupling with in-plane modes. At dopings lower than 10$^{12}$ cm$^{-2}$ the mobility reduction does not exceed 30\%, being almost independent of the concentration. Our findings suggest that compared to in-plane phonons, flexural phonons are considerably less important in the electronic transport of two-dimensional semiconductors, even at low carrier concentrations.