First-principles calculations on the intrinsic resistivity of borophene: anisotropy and temperature dependence

The intrinsic resistivity arising from electron-phonon scattering is an important property of metals, especially at room temperature. Borophene, a kind of successfully synthesized two-dimensional (2D) boron sheet, exhibits metallic electronic transport behavior. In this paper, we report first-principles calculations on the intrinsic resistivity of two borophene allotropes, called (12) and (3). At first, we find that the intrinsic resistivity of the two structures shows non-trivial anisotropy which amounts to at least 28%. In addition, our calculations indicate that the intrinsic resistivity of (12) and (3) are both proportional to temperature in the high-temperature region (>160 K). However, in the low-temperature region (<70 K), the T-4-law of the intrinsic resistivity predicted by the Bloch-Gruneisen theory for 2D metals holds true for (12) but breaks down for (3). Based on a detailed analysis, we find that the two borophenes have complicated Fermi surfaces with multiple branches. Optical phonon modes in (12) and the Umklapp process in (3) play non-trivial roles in the low-temperature region. All of these factors influencing the intrinsic resistivity of borophene are beyond the simplifications adopted in the Bloch-Gruneisen theory. Therefore, we conclude that the Bloch-Gruneisen theory is inapplicable to explain the temperature dependence of the intrinsic resistivity of (12) and (3), two experimentally available 2D metals.