  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.

Materials Science;Mesoscale and Nanoscale Physics;Computational Physics