Charge and heat transport of doped 8−Pmmn borophene with and without relaxation time approximation

Charge and heat transport of monolayer borophene are investigated by means of Boltzmann's transport equation, which is solved self-consistently and analyzed with the relaxation time approximation (RTA). To simulate a realistic experimental condition, a borophene monolayer is first considered to be affected by two types of randomly distributed impurity. Charge transport near the Dirac neutrality point and highly-doped regime changes according to the orientation of measurement, which reflects the anisotropy of the Dirac cone. Characteristic of electron at large doping follows the typical free electron gas but then decays onto interacting like ensemble at low doping signalled by an increase of resistivity around zero doping and a violation of Wiedemann-Franz's law. When acoustic phonon is accounted for, charge transport is found to be sensitive to the magnitude of electron-phonon interaction yielding further enhancement of resistivity at low and large doping. A resistivity consists of ${T}^{4}$ power law at low temperature, which evolves onto linear $T$ at high temperature. A similar trend is also observed when borophene is deposited on top of polar substrate, which manifests itself in the resistivity and mobility. Depending on the dielectric constant of the substrate, remote phonon scattering is shown to substantially affect transport at room temperature in a way that ultrahigh mobility at the order of ${10}^{6}\phantom{\rule{4pt}{0ex}}{\mathrm{cm}}^{2}/\mathrm{Vs}$ falls down to the order of ${10}^{4}\phantom{\rule{4pt}{0ex}}{\mathrm{cm}}^{2}/\mathrm{Vs}$. In contrast to charge transport, heat quantities such as thermopower, figure of merit do not provide any signature of anisotropy of low-energy dispersion and deviate from the Mott's formula. The impact of impurity or perturbation by lattice vibration could, however, be recognized upon varying temperature and charge density carrier. An interesting signature of electron-phonon interaction is shown by phonon drag effect, which not only varies with temperature according to ${T}^{3}$ but also depends on the orientation. It is argued that this unique trait might be a useful tool for the search of phonon drag effect in borophene, which has been proven to be difficult in other two-dimensional systems. The analysis is further elaborated with a survey on the electron cooling mechanism involving acoustic and optical phonon. At low temperature, power loss indicates that energy exchange between hot carrier and its environment depends on the carrier density, tilted velocity and dielectric constant. The use of polar substrate is shown to provide additional channel for relaxation of energy and momentum of hot electrons facilitating a faster cooling at high temperature.